12a
0692
(K12a
0692
)
A knot diagram
1
Linearized knot diagam
3 8 6 7 11 4 2 12 1 5 10 9
Solving Sequence
5,10
11
4,6
7 12
1,3
9 8 2
c
10
c
5
c
6
c
11
c
3
c
9
c
8
c
2
c
1
, c
4
, c
7
, c
12
Ideals for irreducible components
2
of X
par
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
1
I
u
1
= h1645225595u
22
+ 1403326418u
21
+ ··· + 92459847924d + 6684425356,
− 57765211u
22
+ 603981722u
21
+ ··· + 61639898616c − 10033883264,
764605576u
22
+ 1158469312u
21
+ ··· + 46229923962b + 3650149526,
1181950799u
22
+ 2420172188u
21
+ ··· + 61639898616a − 56011531544,
u
23
+ 2u
22
+ ··· − 4u
2
+ 8i
I
u
2
= h−4u
3
a + 7u
2
a − 6u
3
− au + 7u
2
+ 7d + 2a − 12u + 10,
− 2u
3
a + 7u
2
a − 3u
3
− 4au + 7u
2
+ 7c + a − 6u + 5, u
3
a + 5u
3
+ 2au − 7u
2
+ 7b − 4a + 3u + 1,
− u
3
a + 2u
2
a − 2u
3
+ a
2
− 2au + 4u
2
− 2u + 1, u
4
− 2u
3
+ 2u
2
− u + 1i
I
u
3
= hu
7
+ u
6
− 2u
5
− u
4
+ 2u
3
+ 2u
2
+ d − 2u − 1, u
6
− u
4
+ 2u
2
+ c − 1,
− 22u
7
a − 11u
6
a − 20u
7
+ 9u
5
a − 10u
6
+ 21u
4
a + 25u
5
− 14u
3
a + 9u
4
− 43u
3
+ 37b + 7a + 37u + 40,
− 4u
7
a + 2u
7
+ ··· + 8a − 2, u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
I
u
4
= hu
7
c − 2u
7
− u
5
c − u
6
− u
4
c + 2u
5
+ 2u
3
c + 2u
4
+ 2u
2
c − 3u
3
− u
2
+ d − 3c + u + 3,
2u
7
c + u
6
c − u
7
− 2u
5
c − 3u
4
c + 2u
5
+ 2u
3
c + u
4
+ 2u
2
c − 3u
3
+ c
2
− u
2
− 3c + u + 2, −u
5
+ u
3
+ b − u,
u
3
+ a, u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
I
u
5
= hu
7
+ u
6
− 2u
5
− u
4
+ 2u
3
+ 2u
2
+ d − 2u − 1, u
6
− u
4
+ 2u
2
+ c − 1, −u
5
+ u
3
+ b − u, u
3
+ a,
u
8
+ u
7
− u
6
− 2u
5
+ u
4
+ 2u
3
− 2u − 1i
I
u
6
= hu
4
a − 3u
5
+ u
3
a + u
4
− u
2
a + 4u
3
+ au − 5u
2
+ d + 2a − u + 5,
2u
5
a − u
5
− 2u
3
a + u
4
+ 2u
2
a + 3u
3
+ 2au − 3u
2
+ 2c − 2a + u + 4,
u
4
a − u
5
+ u
4
+ u
3
+ au − 2u
2
+ b + u + 2,
− 3u
5
a − u
4
a − u
5
+ 3u
3
a − u
4
− 3u
2
a − u
3
+ 2a
2
− 3au + u
2
+ 4a − u − 2,
u
6
− u
5
− u
4
+ 3u
3
− u
2
− 2u + 2i
I
v
1
= ha, d + 1, c − a + 1, b + 1, v + 1i
I
v
2
= ha, d, c − 1, b + 1, v −1i
I
v
3
= hc, d − 1, b, a − 1, v −1i
I
v
4
= ha, da + c − v −1, dv −1, cv − v
2
+ a − v, b + 1i
* 9 irreducible components of dim
C
= 0, with total 86 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I. I
u
1
= h1.65 × 10
9
u
22
+ 1.40 × 10
9
u
21
+ · · · + 9.25 × 10
10
d + 6.68 ×
10
9
, −5.78 × 10
7
u
22
+ 6 .04 × 10
8
u
21
+ · · · + 6.16 × 10
10
c − 1.00 × 10
10
, 7.65 ×
10
8
u
22
+ 1.16 × 10
9
u
21
+ · · · + 4.62 × 10
10
b + 3.65 × 10
9
, 1.18 × 10
9
u
22
+
2.42 × 10
9
u
21
+ · · · + 6.16 × 10
10
a − 5.60 × 10
10
, u
23
+ 2u
22
+ · · · − 4u
2
+ 8i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
4
=
0.000937140u
22
− 0.00979855u
21
+ ··· − 0.137025u + 0.162782
−0.0177939u
22
− 0.0151777u
21
+ ··· + 0.995143u − 0.0722954
a
6
=
u
−u
3
+ u
a
7
=
−0.00986955u
22
− 0.00319991u
21
+ ··· + 1.12467u − 0.141695
−0.000912892u
22
− 0.00272992u
21
+ ··· + 0.908690u + 0.153401
a
12
=
−u
2
+ 1
−u
2
a
1
=
−0.0191751u
22
− 0.0392631u
21
+ ··· + 0.119456u + 0.908690
−0.0165392u
22
− 0.0250589u
21
+ ··· + 0.141695u − 0.0789564
a
3
=
0.00895666u
22
+ 0.000469997u
21
+ ··· − 0.215981u + 0.295096
−0.0120388u
22
− 0.00566656u
21
+ ··· + 0.980343u + 0.0138542
a
9
=
0.00903693u
22
+ 0.000279913u
21
+ ··· − 0.185021u + 0.995143
0.0116728u
22
+ 0.0144841u
21
+ ··· − 0.162782u + 0.00749712
a
8
=
−0.00173177u
22
− 0.0155024u
21
+ ··· − 0.175640u + 0.980343
0.0174433u
22
+ 0.0237607u
21
+ ··· − 0.295096u + 0.0716533
a
2
=
0.0171752u
22
+ 0.0429380u
21
+ ··· − 0.0481132u + 1.21453
0.0545823u
22
+ 0.0631700u
21
+ ··· + 0.915273u + 0.299257
(ii) Obstruction class = −1
(iii) Cusp Shapes =
15567855023
46229923962
u
22
+
8703838979
46229923962
u
21
+ ··· −
168604101146
23114961981
u +
87470148380
23114961981
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
23
+ 10u
22
+ ··· + 88u + 16
c
2
, c
7
u
23
− 2u
22
+ ··· + 8u − 4
c
3
, c
4
, c
6
c
8
, c
9
, c
12
u
23
+ 2u
22
+ ··· − u − 1
c
5
, c
10
u
23
− 2u
22
+ ··· + 4u
2
− 8
c
11
u
23
− 6u
22
+ ··· + 64u − 64
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
23
+ 6y
22
+ ··· + 1824y −256
c
2
, c
7
y
23
− 10y
22
+ ··· + 88y −16
c
3
, c
4
, c
6
c
8
, c
9
, c
12
y
23
− 24y
22
+ ··· − 9y −1
c
5
, c
10
y
23
− 6y
22
+ ··· + 64y −64
c
11
y
23
+ 10y
22
+ ··· − 6144y −4096
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.758227 + 0.807207I
a = 0.65983 + 1.27023I
b = 0.027613 + 0.769755I
c = −0.393809 − 0.363183I
d = −0.468974 − 0.379047I
−5.90461 + 1.36538I −0.279938 − 0.826772I
u = −0.758227 − 0.807207I
a = 0.65983 − 1.27023I
b = 0.027613 − 0.769755I
c = −0.393809 + 0.363183I
d = −0.468974 + 0.379047I
−5.90461 − 1.36538I −0.279938 + 0.826772I
u = 0.830705 + 0.204801I
a = 0.205779 − 0.701670I
b = −0.423290 − 0.486601I
c = −0.049881 − 0.483602I
d = 0.434396 + 0.280584I
0.25505 + 3.01929I 7.24264 − 9.08374I
u = 0.830705 − 0.204801I
a = 0.205779 + 0.701670I
b = −0.423290 + 0.486601I
c = −0.049881 + 0.483602I
d = 0.434396 − 0.280584I
0.25505 − 3.01929I 7.24264 + 9.08374I
u = 0.112218 + 1.144740I
a = −0.975240 + 0.062634I
b = −1.392930 + 0.053326I
c = −0.03579 + 1.68894I
d = 0.42369 + 2.68034I
8.23677 − 2.50119I 13.28602 + 3.12140I
u = 0.112218 − 1.144740I
a = −0.975240 − 0.062634I
b = −1.392930 − 0.053326I
c = −0.03579 − 1.68894I
d = 0.42369 − 2.68034I
8.23677 + 2.50119I 13.28602 − 3.12140I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.561270 + 1.026650I
a = −0.909276 + 0.320219I
b = −1.332320 + 0.271054I
c = −0.15598 + 1.57216I
d = 1.88354 + 1.80349I
5.56899 − 4.43236I 12.33564 + 2.61344I
u = 0.561270 − 1.026650I
a = −0.909276 − 0.320219I
b = −1.332320 − 0.271054I
c = −0.15598 − 1.57216I
d = 1.88354 − 1.80349I
5.56899 + 4.43236I 12.33564 − 2.61344I
u = −0.972761 + 0.735330I
a = 0.435991 + 1.279060I
b = −0.128148 + 0.852673I
c = −0.356815 − 0.494380I
d = −0.010338 − 0.309906I
−5.23569 − 7.16228I 1.72036 + 6.58026I
u = −0.972761 − 0.735330I
a = 0.435991 − 1.279060I
b = −0.128148 − 0.852673I
c = −0.356815 + 0.494380I
d = −0.010338 + 0.309906I
−5.23569 + 7.16228I 1.72036 − 6.58026I
u = −0.701924 + 1.071670I
a = −0.939216 − 0.403120I
b = −1.355040 − 0.342624I
c = 0.12877 + 1.51945I
d = −2.42854 + 1.67823I
2.90411 + 9.45510I 9.09507 − 6.28090I
u = −0.701924 − 1.071670I
a = −0.939216 + 0.403120I
b = −1.355040 + 0.342624I
c = 0.12877 − 1.51945I
d = −2.42854 − 1.67823I
2.90411 − 9.45510I 9.09507 + 6.28090I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.324650 + 0.201985I
a = −0.528390 − 0.500497I
b = 1.47880 − 0.09640I
c = 1.63860 + 0.03463I
d = −0.086473 + 0.947361I
13.75320 − 2.16453I 16.4022 + 0.8027I
u = −1.324650 − 0.201985I
a = −0.528390 + 0.500497I
b = 1.47880 + 0.09640I
c = 1.63860 − 0.03463I
d = −0.086473 − 0.947361I
13.75320 + 2.16453I 16.4022 − 0.8027I
u = 1.140080 + 0.732610I
a = −0.00237 + 1.63419I
b = 1.39022 + 0.35769I
c = −1.51711 + 0.10256I
d = −1.19387 + 2.89111I
7.42067 + 10.78250I 12.9034 − 6.4003I
u = 1.140080 − 0.732610I
a = −0.00237 − 1.63419I
b = 1.39022 − 0.35769I
c = −1.51711 − 0.10256I
d = −1.19387 − 2.89111I
7.42067 − 10.78250I 12.9034 + 6.4003I
u = 1.315590 + 0.366431I
a = −0.378349 + 0.860467I
b = 1.47476 + 0.17549I
c = −1.61416 + 0.05615I
d = −0.05780 + 1.68875I
12.6616 + 7.9478I 14.6243 − 6.1519I
u = 1.315590 − 0.366431I
a = −0.378349 − 0.860467I
b = 1.47476 − 0.17549I
c = −1.61416 − 0.05615I
d = −0.05780 − 1.68875I
12.6616 − 7.9478I 14.6243 + 6.1519I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.618010
a = 0.115785
b = −0.535478
c = 0.463967
d = −0.579693
0.841351 11.7320
u = −1.130850 + 0.817356I
a = 0.14112 − 1.69304I
b = 1.38677 − 0.40113I
c = 1.49067 + 0.09360I
d = 1.38113 + 3.14130I
4.3220 − 16.2949I 9.65915 + 9.61437I
u = −1.130850 − 0.817356I
a = 0.14112 + 1.69304I
b = 1.38677 + 0.40113I
c = 1.49067 − 0.09360I
d = 1.38113 − 3.14130I
4.3220 + 16.2949I 9.65915 − 9.61437I
u = 0.237558 + 0.464767I
a = 1.232230 − 0.506488I
b = 0.141301 − 0.223079I
c = 0.1335290 + 0.0041366I
d = 0.413099 + 0.410875I
−1.63449 − 0.53093I −3.85466 + 0.92872I
u = 0.237558 − 0.464767I
a = 1.232230 + 0.506488I
b = 0.141301 + 0.223079I
c = 0.1335290 − 0.0041366I
d = 0.413099 − 0.410875I
−1.63449 + 0.53093I −3.85466 − 0.92872I
9
II. I
u
2
= h−4u
3
a − 6u
3
+ · · · + 2a + 10, −2u
3
a − 3u
3
+ · · · + a + 5, u
3
a +
5u
3
+ · · · − 4a + 1, −u
3
a − 2u
3
+ · · · + a
2
+ 1, u
4
− 2u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
4
=
2
7
u
3
a +
3
7
u
3
+ ··· −
1
7
a −
5
7
4
7
u
3
a +
6
7
u
3
+ ··· −
2
7
a −
10
7
a
6
=
u
−u
3
+ u
a
7
=
−
4
7
u
3
a +
1
7
u
3
+ ··· +
2
7
a −
4
7
−au + u − 1
a
12
=
−u
2
+ 1
−u
2
a
1
=
a
−
1
7
u
3
a −
5
7
u
3
+ ··· +
4
7
a −
1
7
a
3
=
4
7
u
3
a −
1
7
u
3
+ ··· −
2
7
a −
3
7
5
7
u
3
a −
3
7
u
3
+ ··· +
1
7
a −
9
7
a
9
=
−
2
7
u
3
a +
11
7
u
3
+ ··· +
1
7
a +
5
7
−
3
7
u
3
a +
6
7
u
3
+ ··· −
2
7
a +
4
7
a
8
=
1
7
u
3
a +
5
7
u
3
+ ··· +
3
7
a +
1
7
1
7
u
3
a +
5
7
u
3
+ ··· −
4
7
a +
1
7
a
2
=
8
7
u
3
a −
2
7
u
3
+ ··· +
3
7
a +
1
7
2
7
u
3
a −
4
7
u
3
+ ··· +
6
7
a −
5
7
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
+ 4u
2
− 8u + 10
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 3u
3
+ 5u
2
+ 3u + 1)
2
c
2
, c
7
(u
4
− u
3
− u
2
+ u + 1)
2
c
3
, c
4
, c
6
c
8
, c
9
, c
12
u
8
+ u
7
− 2u
6
− 2u
5
− u
3
+ u
2
+ 2u + 1
c
5
, c
10
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
2
c
11
(u
4
+ 2u
2
+ 3u + 1)
2
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ y
3
+ 9y
2
+ y + 1)
2
c
2
, c
7
(y
4
− 3y
3
+ 5y
2
− 3y + 1)
2
c
3
, c
4
, c
6
c
8
, c
9
, c
12
y
8
− 5y
7
+ 8y
6
− 10y
4
+ 3y
3
+ 5y
2
− 2y + 1
c
5
, c
10
(y
4
+ 2y
2
+ 3y + 1)
2
c
11
(y
4
+ 4y
3
+ 6y
2
− 5y + 1)
2
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.070696 + 0.758745I
a = −0.762101 − 0.037785I
b = −1.213740 − 0.031383I
c = −0.457945 + 0.239806I
d = −1.13826 + 1.05122I
2.21227 + 1.41376I 7.79581 − 4.79737I
u = −0.070696 + 0.758745I
a = 1.88384 + 1.34441I
b = 0.521295 + 0.349531I
c = 0.07969 + 1.93284I
d = −0.18895 + 1.45474I
2.21227 + 1.41376I 7.79581 − 4.79737I
u = −0.070696 − 0.758745I
a = −0.762101 + 0.037785I
b = −1.213740 + 0.031383I
c = −0.457945 − 0.239806I
d = −1.13826 − 1.05122I
2.21227 − 1.41376I 7.79581 + 4.79737I
u = −0.070696 − 0.758745I
a = 1.88384 − 1.34441I
b = 0.521295 − 0.349531I
c = 0.07969 − 1.93284I
d = −0.18895 − 1.45474I
2.21227 − 1.41376I 7.79581 + 4.79737I
u = 1.070700 + 0.758745I
a = 0.366524 − 1.338260I
b = −0.162537 − 0.919710I
c = −1.49950 + 0.12150I
d = −1.45261 + 2.85433I
−0.56734 + 11.56320I 6.20419 − 8.26147I
u = 1.070700 + 0.758745I
a = 0.01173 + 1.77886I
b = 1.354980 + 0.371832I
c = 0.377761 − 0.546931I
d = −0.220186 − 0.348363I
−0.56734 + 11.56320I 6.20419 − 8.26147I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.070700 − 0.758745I
a = 0.366524 + 1.338260I
b = −0.162537 + 0.919710I
c = −1.49950 − 0.12150I
d = −1.45261 − 2.85433I
−0.56734 − 11.56320I 6.20419 + 8.26147I
u = 1.070700 − 0.758745I
a = 0.01173 − 1.77886I
b = 1.354980 − 0.371832I
c = 0.377761 + 0.546931I
d = −0.220186 + 0.348363I
−0.56734 − 11.56320I 6.20419 + 8.26147I
14
III. I
u
3
= hu
7
+ u
6
+ · · · + d − 1, u
6
− u
4
+ 2u
2
+ c − 1, −22u
7
a − 20u
7
+
· · · + 7a + 40, −4u
7
a + 2u
7
+ · · · + 8a − 2, u
8
+ u
7
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
4
=
−u
6
+ u
4
− 2u
2
+ 1
−u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
− 2u
2
+ 2u + 1
a
6
=
u
−u
3
+ u
a
7
=
−u
4
+ u
2
− 1
−u
4
a
12
=
−u
2
+ 1
−u
2
a
1
=
a
0.594595au
7
+ 0.540541u
7
+ ··· − 0.189189a − 1.08108
a
3
=
−u
2
+ 1
−u
2
a
9
=
−0.540541au
7
− 0.945946u
7
+ ··· + 1.08108a + 1.89189
0.0540541au
7
− 0.405405u
7
+ ··· − 0.108108a + 0.810811
a
8
=
−0.594595au
7
− 0.540541u
7
+ ··· + 1.18919a + 1.08108
−0.594595au
7
− 0.540541u
7
+ ··· + 0.189189a + 1.08108
a
2
=
0.540541au
7
− 0.0540541u
7
+ ··· + 0.918919a + 0.108108
1.08108au
7
+ 0.891892u
7
+ ··· − 0.162162a − 1.78378
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
+ 4u
4
− 8u
3
− 4u
2
+ 4u + 14
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 9u
15
+ ··· − 8u
2
+ 1
c
2
, c
7
, c
8
c
9
, c
12
u
16
− u
15
+ ··· + 2u − 1
c
3
, c
4
, c
6
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
2
c
5
, c
10
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
2
c
11
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 5y
15
+ ··· − 16y + 1
c
2
, c
7
, c
8
c
9
, c
12
y
16
− 9y
15
+ ··· − 8y
2
+ 1
c
3
, c
4
, c
6
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
2
c
5
, c
10
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
2
c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = 0.85267 + 1.13323I
b = 0.097535 + 0.616980I
c = 0.33804 + 1.54318I
d = −1.43432 + 0.96489I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 + 0.730671I
a = 0.43836 − 3.06608I
b = 1.082580 − 0.348383I
c = 0.33804 + 1.54318I
d = −1.43432 + 0.96489I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 − 0.730671I
a = 0.85267 − 1.13323I
b = 0.097535 − 0.616980I
c = 0.33804 − 1.54318I
d = −1.43432 − 0.96489I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = −0.570868 − 0.730671I
a = 0.43836 + 3.06608I
b = 1.082580 + 0.348383I
c = 0.33804 − 1.54318I
d = −1.43432 − 0.96489I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 0.855237 + 0.665892I
a = −0.683988 + 0.514398I
b = −1.134620 + 0.424735I
c = 0.306664 − 0.427719I
d = 0.233537 − 0.170925I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.855237 + 0.665892I
a = −0.24547 + 2.30190I
b = 1.242710 + 0.322774I
c = 0.306664 − 0.427719I
d = 0.233537 − 0.170925I
−2.15941 + 2.57849I 4.27708 − 3.56796I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.855237 − 0.665892I
a = −0.683988 − 0.514398I
b = −1.134620 − 0.424735I
c = 0.306664 + 0.427719I
d = 0.233537 + 0.170925I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 0.855237 − 0.665892I
a = −0.24547 − 2.30190I
b = 1.242710 − 0.322774I
c = 0.306664 + 0.427719I
d = 0.233537 + 0.170925I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 1.09818
a = −0.166989 + 0.837022I
b = −0.685501 + 0.640105I
c = −1.71160
d = −0.895847
6.50273 13.8640
u = 1.09818
a = −0.166989 − 0.837022I
b = −0.685501 − 0.640105I
c = −1.71160
d = −0.895847
6.50273 13.8640
u = −1.031810 + 0.655470I
a = −0.688737 − 0.639006I
b = −1.130780 − 0.529217I
c = 1.53294 + 0.14882I
d = 1.41965 + 2.49301I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.031810 + 0.655470I
a = 0.351395 + 1.239290I
b = −0.203747 + 0.848147I
c = 1.53294 + 0.14882I
d = 1.41965 + 2.49301I
2.37968 − 6.44354I 9.42845 + 5.29417I
19
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031810 − 0.655470I
a = −0.688737 + 0.639006I
b = −1.130780 + 0.529217I
c = 1.53294 − 0.14882I
d = 1.41965 − 2.49301I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −1.031810 − 0.655470I
a = 0.351395 − 1.239290I
b = −0.203747 − 0.848147I
c = 1.53294 − 0.14882I
d = 1.41965 − 2.49301I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −0.603304
a = −0.0902138
b = −0.684028
c = 0.356309
d = −0.541881
0.845036 11.8940
u = −0.603304
a = −5.62425
b = 1.14767
c = 0.356309
d = −0.541881
0.845036 11.8940
20
IV. I
u
4
= hu
7
c − 2u
7
+ · · · − 3c + 3, 2u
7
c − u
7
+ · · · − 3c + 2, −u
5
+ u
3
+ b −
u, u
3
+ a, u
8
+ u
7
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
4
=
c
−u
7
c + 2u
7
+ ··· + 3c − 3
a
6
=
u
−u
3
+ u
a
7
=
−u
7
c + 2u
7
+ ··· + 2c − 3
u
7
+ u
4
c − u
5
− u
2
c + 2u
3
− cu + 2c − u − 2
a
12
=
−u
2
+ 1
−u
2
a
1
=
−u
3
u
5
− u
3
+ u
a
3
=
u
7
c − u
7
− u
5
c − u
6
+ u
5
+ 2u
3
c + 2u
4
− u
3
− cu − u
2
+ 1
−u
7
c + u
7
+ ··· + 3c − 2
a
9
=
u
7
− 2u
5
+ 2u
3
− 2u
u
7
− u
5
+ 2u
3
− u
a
8
=
−u
u
3
− u
a
2
=
c
−u
7
c + 2u
7
+ ··· + 3c − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
+ 4u
4
− 8u
3
− 4u
2
+ 4u + 14
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
16
+ 9u
15
+ ··· − 8u
2
+ 1
c
2
, c
3
, c
4
c
6
, c
7
u
16
− u
15
+ ··· + 2u − 1
c
5
, c
10
(u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1)
2
c
8
, c
9
, c
12
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
2
c
11
(u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
2
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
16
− 5y
15
+ ··· − 16y + 1
c
2
, c
3
, c
4
c
6
, c
7
y
16
− 9y
15
+ ··· − 8y
2
+ 1
c
5
, c
10
(y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
2
c
8
, c
9
, c
12
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
2
c
11
(y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
2
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = −0.728286 − 0.324264I
b = −1.180120 − 0.268597I
c = 1.338630 + 0.392019I
d = 2.30490 + 2.27899I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 + 0.730671I
a = −0.728286 − 0.324264I
b = −1.180120 − 0.268597I
c = −0.348718 − 0.235508I
d = −0.684355 − 0.082854I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 − 0.730671I
a = −0.728286 + 0.324264I
b = −1.180120 + 0.268597I
c = 1.338630 − 0.392019I
d = 2.30490 − 2.27899I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = −0.570868 − 0.730671I
a = −0.728286 + 0.324264I
b = −1.180120 + 0.268597I
c = −0.348718 + 0.235508I
d = −0.684355 + 0.082854I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 0.855237 + 0.665892I
a = 0.512122 − 1.165900I
b = −0.108090 − 0.747508I
c = −0.259529 + 1.329030I
d = 1.91420 + 0.28957I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.855237 + 0.665892I
a = 0.512122 − 1.165900I
b = −0.108090 − 0.747508I
c = −1.50305 + 0.23227I
d = −1.89317 + 2.34673I
−2.15941 + 2.57849I 4.27708 − 3.56796I
24
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.855237 − 0.665892I
a = 0.512122 + 1.165900I
b = −0.108090 + 0.747508I
c = −0.259529 − 1.329030I
d = 1.91420 − 0.28957I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 0.855237 − 0.665892I
a = 0.512122 + 1.165900I
b = −0.108090 + 0.747508I
c = −1.50305 − 0.23227I
d = −1.89317 − 2.34673I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 1.09818
a = −1.32440
b = 1.37100
c = −0.054797 + 0.799128I
d = 0.635504 − 0.747497I
6.50273 13.8640
u = 1.09818
a = −1.32440
b = 1.37100
c = −0.054797 − 0.799128I
d = 0.635504 + 0.747497I
6.50273 13.8640
u = −1.031810 + 0.655470I
a = −0.23143 − 1.81188I
b = 1.334530 − 0.318930I
c = 0.164531 + 1.264480I
d = −2.19900 − 0.17735I
2.37968 − 6.44354I 9.42845 + 5.29417I
u = −1.031810 + 0.655470I
a = −0.23143 − 1.81188I
b = 1.334530 − 0.318930I
c = −0.316450 − 0.535989I
d = 0.096756 − 0.127406I
2.37968 − 6.44354I 9.42845 + 5.29417I
25
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031810 − 0.655470I
a = −0.23143 + 1.81188I
b = 1.334530 + 0.318930I
c = 0.164531 − 1.264480I
d = −2.19900 + 0.17735I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −1.031810 − 0.655470I
a = −0.23143 + 1.81188I
b = 1.334530 + 0.318930I
c = −0.316450 + 0.535989I
d = 0.096756 + 0.127406I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −0.603304
a = 0.219587
b = −0.463640
c = 0.775554
d = −0.640533
0.845036 11.8940
u = −0.603304
a = 0.219587
b = −0.463640
c = 2.18322
d = 3.29089
0.845036 11.8940
26
V. I
u
5
= hu
7
+ u
6
+ · · · + d − 1, u
6
− u
4
+ 2u
2
+ c − 1, −u
5
+ u
3
+ b −
u, u
3
+ a, u
8
+ u
7
+ · · · − 2u − 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
4
=
−u
6
+ u
4
− 2u
2
+ 1
−u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
− 2u
2
+ 2u + 1
a
6
=
u
−u
3
+ u
a
7
=
−u
4
+ u
2
− 1
−u
4
a
12
=
−u
2
+ 1
−u
2
a
1
=
−u
3
u
5
− u
3
+ u
a
3
=
−u
2
+ 1
−u
2
a
9
=
u
7
− 2u
5
+ 2u
3
− 2u
u
7
− u
5
+ 2u
3
− u
a
8
=
−u
u
3
− u
a
2
=
−u
6
+ u
4
− 2u
2
+ 1
−u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
− 2u
2
+ 2u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
7
+ 8u
5
+ 4u
4
− 8u
3
− 4u
2
+ 4u + 14
27
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
8
+ 7u
7
+ 19u
6
+ 22u
5
+ 3u
4
− 14u
3
− 6u
2
+ 4u + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
12
u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1
c
5
, c
10
u
8
− u
7
− u
6
+ 2u
5
+ u
4
− 2u
3
+ 2u − 1
c
11
u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1
28
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
8
− 11y
7
+ 59y
6
− 186y
5
+ 343y
4
− 370y
3
+ 154y
2
− 28y + 1
c
2
, c
3
, c
4
c
6
, c
7
, c
8
c
9
, c
12
y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1
c
5
, c
10
y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1
c
11
y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1
29
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570868 + 0.730671I
a = −0.728286 − 0.324264I
b = −1.180120 − 0.268597I
c = 0.33804 + 1.54318I
d = −1.43432 + 0.96489I
1.04066 + 1.13123I 7.41522 − 0.51079I
u = −0.570868 − 0.730671I
a = −0.728286 + 0.324264I
b = −1.180120 + 0.268597I
c = 0.33804 − 1.54318I
d = −1.43432 − 0.96489I
1.04066 − 1.13123I 7.41522 + 0.51079I
u = 0.855237 + 0.665892I
a = 0.512122 − 1.165900I
b = −0.108090 − 0.747508I
c = 0.306664 − 0.427719I
d = 0.233537 − 0.170925I
−2.15941 + 2.57849I 4.27708 − 3.56796I
u = 0.855237 − 0.665892I
a = 0.512122 + 1.165900I
b = −0.108090 + 0.747508I
c = 0.306664 + 0.427719I
d = 0.233537 + 0.170925I
−2.15941 − 2.57849I 4.27708 + 3.56796I
u = 1.09818
a = −1.32440
b = 1.37100
c = −1.71160
d = −0.895847
6.50273 13.8640
u = −1.031810 + 0.655470I
a = −0.23143 − 1.81188I
b = 1.334530 − 0.318930I
c = 1.53294 + 0.14882I
d = 1.41965 + 2.49301I
2.37968 − 6.44354I 9.42845 + 5.29417I
30
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −1.031810 − 0.655470I
a = −0.23143 + 1.81188I
b = 1.334530 + 0.318930I
c = 1.53294 − 0.14882I
d = 1.41965 − 2.49301I
2.37968 + 6.44354I 9.42845 − 5.29417I
u = −0.603304
a = 0.219587
b = −0.463640
c = 0.356309
d = −0.541881
0.845036 11.8940
31
VI. I
u
6
= hu
4
a − 3u
5
+ · · · + 2a + 5, 2u
5
a − u
5
+ · · · − 2a + 4, u
4
a − u
5
+
· · · + b + 2, −3u
5
a − u
5
+ · · · + 4a − 2, u
6
− u
5
+ · · · − 2u + 2i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
−u
2
a
4
=
−u
5
a +
1
2
u
5
+ ··· + a − 2
−u
4
a + 3u
5
− u
3
a − u
4
+ u
2
a − 4u
3
− au + 5u
2
− 2a + u − 5
a
6
=
u
−u
3
+ u
a
7
=
3
2
u
5
−
1
2
u
4
+ ··· − a − 3
2u
5
− 3u
3
− au + 3u
2
+ u − 3
a
12
=
−u
2
+ 1
−u
2
a
1
=
a
−u
4
a + u
5
− u
4
− u
3
− au + 2u
2
− u − 2
a
3
=
1
2
u
5
+
1
2
u
4
+ ··· + a +
1
2
u
−u
5
a + u
5
+ u
3
a − u
2
a − u
3
− au + u
2
− 1
a
9
=
−u
5
a + u
4
a − 2u
5
+ 2u
3
a + u
4
− 2u
2
a + 2u
3
− 4u
2
+ 3a + 4
−u
5
a − u
5
+ 2u
3
a − 2u
2
a + u
3
− au − 2u
2
+ 2a − u + 2
a
8
=
u
4
a − u
5
+ u
4
− u
2
a + u
3
+ au − 2u
2
+ a + u + 2
u
4
a − u
5
+ u
4
− u
2
a + u
3
+ au − 2u
2
+ u + 2
a
2
=
1
2
u
5
−
1
2
u
4
+ ··· + 2a −
1
2
u
−u
5
a + u
5
+ 2u
3
a − u
4
− 2u
2
a − u
3
− 2au + u
2
+ 2a − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2u
5
− 4u
4
+ 8u
3
− 8u + 16
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 2u
5
+ 3u
4
+ u
3
+ u
2
− u + 1)
2
c
2
, c
7
(u
6
− u
4
+ u
3
+ u
2
− u + 1)
2
c
3
, c
4
, c
6
c
8
, c
9
, c
12
u
12
− 5u
10
+ 2u
9
+ 9u
8
− 7u
7
− 4u
6
+ 7u
5
− 4u
4
+ 2u
3
+ u
2
− 4u + 4
c
5
, c
10
(u
6
+ u
5
− u
4
− 3u
3
− u
2
+ 2u + 2)
2
c
11
(u
6
− 3u
5
+ 5u
4
− 7u
3
+ 9u
2
− 8u + 4)
2
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
+ 2y
5
+ 7y
4
+ 11y
3
+ 9y
2
+ y + 1)
2
c
2
, c
7
(y
6
− 2y
5
+ 3y
4
− y
3
+ y
2
+ y + 1)
2
c
3
, c
4
, c
6
c
8
, c
9
, c
12
y
12
− 10y
11
+ ··· − 8y + 16
c
5
, c
10
(y
6
− 3y
5
+ 5y
4
− 7y
3
+ 9y
2
− 8y + 4)
2
c
11
(y
6
+ y
5
+ y
4
+ y
3
+ 9y
2
+ 8y + 16)
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = 0.954425 + 0.469441I
a = −0.543939 + 0.599164I
b = −1.013300 + 0.485889I
c = −1.61874 + 0.18698I
d = −1.52081 + 1.85766I
4.85214 + 1.71504I 13.36090 − 1.32670I
u = 0.954425 + 0.469441I
a = −0.84764 + 1.84095I
b = 1.297290 + 0.224098I
c = −0.258456 + 1.158850I
d = 1.61170 − 0.24019I
4.85214 + 1.71504I 13.36090 − 1.32670I
u = 0.954425 − 0.469441I
a = −0.543939 − 0.599164I
b = −1.013300 − 0.485889I
c = −1.61874 − 0.18698I
d = −1.52081 − 1.85766I
4.85214 − 1.71504I 13.36090 + 1.32670I
u = 0.954425 − 0.469441I
a = −0.84764 − 1.84095I
b = 1.297290 − 0.224098I
c = −0.258456 − 1.158850I
d = 1.61170 + 0.24019I
4.85214 − 1.71504I 13.36090 + 1.32670I
u = −1.130290 + 0.224113I
a = 0.003531 + 0.984620I
b = −0.529009 + 0.730272I
c = 1.67457 + 0.07044I
d = 0.781173 + 0.975415I
6.01369 − 4.89103I 12.12173 + 6.59162I
u = −1.130290 + 0.224113I
a = −1.023270 − 0.773208I
b = 1.385610 − 0.106695I
c = −0.085338 − 0.700500I
d = −0.199297 + 0.648369I
6.01369 − 4.89103I 12.12173 + 6.59162I
35
Solutions to I
u
6
√
−1(vol +
√
−1CS) Cusp shape
u = −1.130290 − 0.224113I
a = 0.003531 − 0.984620I
b = −0.529009 − 0.730272I
c = 1.67457 − 0.07044I
d = 0.781173 − 0.975415I
6.01369 + 4.89103I 12.12173 − 6.59162I
u = −1.130290 − 0.224113I
a = −1.023270 + 0.773208I
b = 1.385610 + 0.106695I
c = −0.085338 + 0.700500I
d = −0.199297 − 0.648369I
6.01369 + 4.89103I 12.12173 − 6.59162I
u = 0.675862 + 0.935235I
a = −0.855739 + 0.390801I
b = −1.284560 + 0.329038I
c = 0.476837 − 0.318716I
d = 0.762506 − 0.547149I
−1.81870 − 5.32947I 4.51738 + 4.54389I
u = 0.675862 + 0.935235I
a = 0.76705 − 1.38346I
b = 0.143970 − 0.800673I
c = −0.18887 + 1.51212I
d = 2.06473 + 1.31344I
−1.81870 − 5.32947I 4.51738 + 4.54389I
u = 0.675862 − 0.935235I
a = −0.855739 − 0.390801I
b = −1.284560 − 0.329038I
c = 0.476837 + 0.318716I
d = 0.762506 + 0.547149I
−1.81870 + 5.32947I 4.51738 − 4.54389I
u = 0.675862 − 0.935235I
a = 0.76705 + 1.38346I
b = 0.143970 + 0.800673I
c = −0.18887 − 1.51212I
d = 2.06473 − 1.31344I
−1.81870 + 5.32947I 4.51738 − 4.54389I
36
VII. I
v
1
= ha, d + 1, c − a + 1, b + 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
10
=
1
0
a
11
=
1
0
a
4
=
−1
−1
a
6
=
−1
0
a
7
=
0
1
a
12
=
1
0
a
1
=
0
−1
a
3
=
0
−1
a
9
=
1
1
a
8
=
0
1
a
2
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
37
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
, c
11
u
c
3
, c
4
, c
8
c
9
u + 1
c
6
, c
12
u − 1
38
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
10
, c
11
y
c
3
, c
4
, c
6
c
8
, c
9
, c
12
y −1
39
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
c = −1.00000
d = −1.00000
3.28987 12.0000
40
VIII. I
v
2
= ha, d, c − 1, b + 1, v − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
1
0
a
11
=
1
0
a
4
=
1
0
a
6
=
1
0
a
7
=
1
0
a
12
=
1
0
a
1
=
0
−1
a
3
=
1
0
a
9
=
1
1
a
8
=
0
1
a
2
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
41
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
12
u − 1
c
3
, c
4
, c
5
c
6
, c
10
, c
11
u
c
7
, c
8
, c
9
u + 1
42
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
, c
9
, c
12
y −1
c
3
, c
4
, c
5
c
6
, c
10
, c
11
y
43
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 0
b = −1.00000
c = 1.00000
d = 0
0 0
44
IX. I
v
3
= hc, d − 1, b, a − 1, v − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
1
0
a
11
=
1
0
a
4
=
0
1
a
6
=
1
0
a
7
=
1
−1
a
12
=
1
0
a
1
=
1
0
a
3
=
−1
1
a
9
=
1
0
a
8
=
1
0
a
2
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
45
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u − 1
c
2
, c
3
, c
4
u + 1
c
5
, c
8
, c
9
c
10
, c
11
, c
12
u
46
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
6
, c
7
y −1
c
5
, c
8
, c
9
c
10
, c
11
, c
12
y
47
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
0 0
48
X. I
v
4
= ha, da + c − v − 1, dv − 1, cv − v
2
+ a − v, b + 1i
(i) Arc colorings
a
5
=
v
0
a
10
=
1
0
a
11
=
1
0
a
4
=
v + 1
d
a
6
=
v
0
a
7
=
−1
−d
a
12
=
1
0
a
1
=
0
−1
a
3
=
1
d
a
9
=
1
1
a
8
=
0
1
a
2
=
1
d − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −d
2
− v
2
+ 8
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
49
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
1.64493 8.90487 − 0.21066I
50
XI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u − 1)
2
(u
4
+ 3u
3
+ 5u
2
+ 3u + 1)
2
· (u
6
+ 2u
5
+ 3u
4
+ u
3
+ u
2
− u + 1)
2
· (u
8
+ 7u
7
+ 19u
6
+ 22u
5
+ 3u
4
− 14u
3
− 6u
2
+ 4u + 1)
· ((u
16
+ 9u
15
+ ··· − 8u
2
+ 1)
2
)(u
23
+ 10u
22
+ ··· + 88u + 16)
c
2
, c
7
u(u − 1)(u + 1)(u
4
− u
3
− u
2
+ u + 1)
2
(u
6
− u
4
+ u
3
+ u
2
− u + 1)
2
· (u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)(u
16
− u
15
+ ··· + 2u − 1)
2
· (u
23
− 2u
22
+ ··· + 8u − 4)
c
3
, c
4
, c
8
c
9
u(u + 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
3
· (u
8
+ u
7
− 2u
6
− 2u
5
− u
3
+ u
2
+ 2u + 1)
· (u
12
− 5u
10
+ 2u
9
+ 9u
8
− 7u
7
− 4u
6
+ 7u
5
− 4u
4
+ 2u
3
+ u
2
− 4u + 4)
· (u
16
− u
15
+ ··· + 2u − 1)(u
23
+ 2u
22
+ ··· − u − 1)
c
5
, c
10
u
3
(u
4
+ 2u
3
+ 2u
2
+ u + 1)
2
(u
6
+ u
5
− u
4
− 3u
3
− u
2
+ 2u + 2)
2
· ((u
8
− u
7
+ ··· + 2u − 1)
5
)(u
23
− 2u
22
+ ··· + 4u
2
− 8)
c
6
, c
12
u(u − 1)
2
(u
8
+ u
7
− 3u
6
− 2u
5
+ 3u
4
+ 2u − 1)
3
· (u
8
+ u
7
− 2u
6
− 2u
5
− u
3
+ u
2
+ 2u + 1)
· (u
12
− 5u
10
+ 2u
9
+ 9u
8
− 7u
7
− 4u
6
+ 7u
5
− 4u
4
+ 2u
3
+ u
2
− 4u + 4)
· (u
16
− u
15
+ ··· + 2u − 1)(u
23
+ 2u
22
+ ··· − u − 1)
c
11
u
3
(u
4
+ 2u
2
+ 3u + 1)
2
(u
6
− 3u
5
+ 5u
4
− 7u
3
+ 9u
2
− 8u + 4)
2
· (u
8
− 3u
7
+ 7u
6
− 10u
5
+ 11u
4
− 10u
3
+ 6u
2
− 4u + 1)
5
· (u
23
− 6u
22
+ ··· + 64u − 64)
51
XII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y − 1)
2
(y
4
+ y
3
+ 9y
2
+ y + 1)
2
· (y
6
+ 2y
5
+ 7y
4
+ 11y
3
+ 9y
2
+ y + 1)
2
· (y
8
− 11y
7
+ 59y
6
− 186y
5
+ 343y
4
− 370y
3
+ 154y
2
− 28y + 1)
· ((y
16
− 5y
15
+ ··· − 16y + 1)
2
)(y
23
+ 6y
22
+ ··· + 1824y −256)
c
2
, c
7
y(y − 1)
2
(y
4
− 3y
3
+ 5y
2
− 3y + 1)
2
· (y
6
− 2y
5
+ 3y
4
− y
3
+ y
2
+ y + 1)
2
· (y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
· ((y
16
− 9y
15
+ ··· − 8y
2
+ 1)
2
)(y
23
− 10y
22
+ ··· + 88y −16)
c
3
, c
4
, c
6
c
8
, c
9
, c
12
y(y − 1)
2
(y
8
− 7y
7
+ 19y
6
− 22y
5
+ 3y
4
+ 14y
3
− 6y
2
− 4y + 1)
3
· (y
8
− 5y
7
+ 8y
6
− 10y
4
+ 3y
3
+ 5y
2
− 2y + 1)
· (y
12
− 10y
11
+ ··· − 8y + 16)(y
16
− 9y
15
+ ··· − 8y
2
+ 1)
· (y
23
− 24y
22
+ ··· − 9y −1)
c
5
, c
10
y
3
(y
4
+ 2y
2
+ 3y + 1)
2
(y
6
− 3y
5
+ 5y
4
− 7y
3
+ 9y
2
− 8y + 4)
2
· (y
8
− 3y
7
+ 7y
6
− 10y
5
+ 11y
4
− 10y
3
+ 6y
2
− 4y + 1)
5
· (y
23
− 6y
22
+ ··· + 64y −64)
c
11
y
3
(y
4
+ 4y
3
+ 6y
2
− 5y + 1)
2
(y
6
+ y
5
+ y
4
+ y
3
+ 9y
2
+ 8y + 16)
2
· (y
8
+ 5y
7
+ 11y
6
+ 6y
5
− 17y
4
− 34y
3
− 22y
2
− 4y + 1)
5
· (y
23
+ 10y
22
+ ··· − 6144y −4096)
52
