11n
71
(K11n
71
)
A knot diagram
1
Linearized knot diagam
4 1 7 2 11 9 3 6 8 1 6
Solving Sequence
3,7
4
8,9 1,10
2 5 6 11
c
3
c
7
c
9
c
2
c
4
c
6
c
11
c
1
, c
5
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h481u
12
− 3744u
11
+ ··· + 245268d − 61940, −4057u
12
− 5862u
11
+ ··· + 163512c − 19528,
− 664u
12
− 4959u
11
+ ··· + 122634b + 22418, 15485u
12
+ 31932u
11
+ ··· + 490536a − 416896,
u
13
+ 2u
12
+ 5u
11
+ 6u
10
+ 6u
9
+ 6u
8
− u
7
− 4u
6
− 10u
5
− 12u
4
+ 24u
3
− 4u
2
+ 8i
I
u
2
= h−u
3
+ au + 2u
2
+ d − 4u + 3, 2u
4
a − 4u
3
a − u
4
+ 8u
2
a + 3u
3
− 6au − 6u
2
+ 2c + 2a + 7u − 4,
− u
4
a + 2u
3
a − 5u
2
a + 3au + u
2
+ b − 2a − u + 2,
3u
4
a − 9u
3
a − u
4
+ 16u
2
a + 3u
3
+ 2a
2
− 17au − 6u
2
+ 4a + 7u − 2, u
5
− 3u
4
+ 6u
3
− 7u
2
+ 4u − 2i
I
u
3
= hu
2
+ d, −u
2
+ c − 1, 2au − u
2
+ b + a − u, 4u
2
a + a
2
+ au − 3u
2
+ 6a − u − 5, u
3
+ u
2
+ 2u + 1i
I
u
4
= hu
2
c + cu − u
2
+ d + 2c − u − 1, u
2
c + c
2
− u
2
+ c − 1, b − u, a + u, u
3
+ u
2
+ 2u + 1i
I
u
5
= hu
2
+ d, −u
2
+ c − 1, b − u, a + u, u
3
+ u
2
+ 2u + 1i
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
* 8 irreducible components of dim
C
= 0, with total 41 representations.
* 1 irreducible components of dim
C
= 1
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).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
=
h481u
12
− 3744u
11
+ · · · + 2.45 × 10
5
d − 6.19 × 10
4
, −4057u
12
− 5862u
11
+ · · · +
1.64×10
5
c−1.95×10
4
, −664u
12
−4959u
11
+· · ·+1.23×10
5
b+2.24×10
4
, 1.55×
10
4
u
12
+3.19×10
4
u
11
+· · ·+4.91×10
5
a−4.17×10
5
, u
13
+2u
12
+· · ·−4u
2
+8i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
u
a
9
=
0.0248116u
12
+ 0.0358506u
11
+ ··· − 1.16261u + 0.119429
−0.00196112u
12
+ 0.0152649u
11
+ ··· + 0.849879u + 0.252540
a
1
=
−0.0315675u
12
− 0.0650961u
11
+ ··· − 0.166977u + 0.849879
0.00541449u
12
+ 0.0404374u
11
+ ··· + 0.371969u − 0.182804
a
10
=
−0.00479679u
12
− 0.0550051u
11
+ ··· − 0.979802u + 0.162744
0.0276473u
12
+ 0.106121u
11
+ ··· + 0.667074u + 0.209224
a
2
=
−0.0177948u
12
− 0.0521797u
11
+ ··· − 0.286405u + 1.04837
0.00289479u
12
+ 0.0135036u
11
+ ··· + 0.261787u − 0.0657730
a
5
=
−0.0261530u
12
− 0.0246587u
11
+ ··· + 0.204992u + 0.667074
0.0454115u
12
+ 0.0564362u
11
+ ··· − 0.162744u − 0.0383743
a
6
=
−0.0228505u
12
− 0.0511155u
11
+ ··· + 0.312727u − 0.371969
−0.00196112u
12
+ 0.0152649u
11
+ ··· + 0.849879u + 0.252540
a
11
=
−0.00615449u
12
− 0.0166593u
11
+ ··· − 0.562364u + 0.739289
0.0254497u
12
+ 0.0984515u
11
+ ··· + 0.788525u + 0.0840387
a
11
=
−0.00615449u
12
− 0.0166593u
11
+ ··· − 0.562364u + 0.739289
0.0254497u
12
+ 0.0984515u
11
+ ··· + 0.788525u + 0.0840387
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
3739
13626
u
12
−
4675
13626
u
11
−
4243
4542
u
10
−
6761
13626
u
9
−
812
6813
u
8
−
59
757
u
7
+
14825
13626
u
6
−
1951
13626
u
5
−
811
757
u
4
−
10702
6813
u
3
−
80432
6813
u
2
+
22922
6813
u −
4756
2271
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
u
13
− 2u
12
+ 4u
10
− 8u
8
+ 7u
7
+ 7u
6
− 8u
5
− 3u
4
+ 9u
3
+ u
2
− u + 1
c
2
, c
9
u
13
+ 4u
12
+ ··· − u + 1
c
3
, c
7
u
13
+ 2u
12
+ ··· − 4u
2
+ 8
c
5
, c
11
u
13
+ 2u
12
+ ··· + 8u + 4
c
10
u
13
− 14u
12
+ ··· + 88u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
8
y
13
− 4y
12
+ ··· − y − 1
c
2
, c
9
y
13
+ 16y
12
+ ··· − 25y − 1
c
3
, c
7
y
13
+ 6y
12
+ ··· + 64y − 64
c
5
, c
11
y
13
− 14y
12
+ ··· + 88y − 16
c
10
y
13
− 30y
12
+ ··· + 2848y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.917056 + 0.260692I
a = 0.504975 + 0.125247I
b = −0.535060 + 0.800968I
c = −0.740548 + 0.715066I
d = 0.430439 + 0.246501I
−1.87851 + 3.16005I −8.32269 − 6.37622I
u = 0.917056 − 0.260692I
a = 0.504975 − 0.125247I
b = −0.535060 − 0.800968I
c = −0.740548 − 0.715066I
d = 0.430439 − 0.246501I
−1.87851 − 3.16005I −8.32269 + 6.37622I
u = 0.300918 + 0.625488I
a = 1.038000 − 0.500200I
b = 0.094351 + 0.164390I
c = −0.352870 − 0.518553I
d = 0.625222 + 0.498737I
1.70980 + 0.77307I 3.13297 − 1.88722I
u = 0.300918 − 0.625488I
a = 1.038000 + 0.500200I
b = 0.094351 − 0.164390I
c = −0.352870 + 0.518553I
d = 0.625222 − 0.498737I
1.70980 − 0.77307I 3.13297 + 1.88722I
u = −0.613875
a = 0.608171
b = −0.415090
c = 1.04952
d = −0.373341
−1.13096 −8.32650
u = −1.37082 + 0.38920I
a = 0.437589 − 0.166249I
b = −0.41839 − 1.51286I
c = 0.527632 + 0.703269I
d = −0.535153 + 0.398209I
4.46546 − 5.94244I −3.19547 + 4.81410I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.37082 − 0.38920I
a = 0.437589 + 0.166249I
b = −0.41839 + 1.51286I
c = 0.527632 − 0.703269I
d = −0.535153 − 0.398209I
4.46546 + 5.94244I −3.19547 − 4.81410I
u = 0.54282 + 1.32018I
a = −0.163933 + 1.389820I
b = −0.67082 − 1.53809I
c = 0.748510 − 0.513111I
d = −1.92380 + 0.53800I
1.53986 − 8.66555I −5.43123 + 7.16460I
u = 0.54282 − 1.32018I
a = −0.163933 − 1.389820I
b = −0.67082 + 1.53809I
c = 0.748510 + 0.513111I
d = −1.92380 − 0.53800I
1.53986 + 8.66555I −5.43123 − 7.16460I
u = −0.79330 + 1.40153I
a = −0.397741 − 1.239110I
b = −0.98955 + 1.80695I
c = −0.773067 − 0.443499I
d = 2.05217 + 0.42554I
7.6949 + 13.5931I −3.46569 − 7.45820I
u = −0.79330 − 1.40153I
a = −0.397741 + 1.239110I
b = −0.98955 − 1.80695I
c = −0.773067 + 0.443499I
d = 2.05217 − 0.42554I
7.6949 − 13.5931I −3.46569 + 7.45820I
u = −0.28973 + 1.63988I
a = 0.277026 + 0.842714I
b = 0.72701 − 1.38782I
c = 0.565582 − 0.495050I
d = −1.46221 + 0.21013I
11.70800 + 0.17366I 0.445368 + 1.147630I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.28973 − 1.63988I
a = 0.277026 − 0.842714I
b = 0.72701 + 1.38782I
c = 0.565582 + 0.495050I
d = −1.46221 − 0.21013I
11.70800 − 0.17366I 0.445368 − 1.147630I
7
II. I
u
2
= h−u
3
+ 2u
2
+ · · · + d + 3, 2u
4
a − u
4
+ · · · + 2a − 4, −u
4
a + 2u
3
a +
· · · − 2a + 2, 3u
4
a − u
4
+ · · · + 4a − 2, u
5
− 3u
4
+ · · · + 4u − 2i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
u
a
9
=
−u
4
a +
1
2
u
4
+ ··· − a + 2
u
3
− au − 2u
2
+ 4u − 3
a
1
=
a
u
4
a − 2u
3
a + 5u
2
a − 3au − u
2
+ 2a + u − 2
a
10
=
u
3
a −
1
2
u
4
+
1
2
u
3
+ au − u
2
+ a −
1
2
u
−u
4
a + u
3
a + u
4
− 4u
2
a − u
3
+ au + 2u
2
− 2a + u − 1
a
2
=
−u
4
a + 2u
3
a − 4u
2
a + 3au + u
2
− a − u + 2
u
4
− u
3
− au + u
2
+ u − 2
a
5
=
u
4
a − 2u
3
a + 5u
2
a − 3au − u
2
+ 3a + u − 2
u
4
a − u
4
+ u
2
a + u
3
+ au − u
2
− u + 2
a
6
=
u
4
a −
1
2
u
4
+ ··· + a + 1
u
3
− au − 2u
2
+ 4u − 3
a
11
=
u
4
a −
1
2
u
4
+ ··· + 2a −
1
2
u
u
4
a − 3u
3
a + 6u
2
a + u
3
− 4au − 3u
2
+ 2a + 4u − 3
a
11
=
u
4
a −
1
2
u
4
+ ··· + 2a −
1
2
u
u
4
a − 3u
3
a + 6u
2
a + u
3
− 4au − 3u
2
+ 2a + 4u − 3
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2u
3
− 6u
2
+ 12u − 12
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
8
u
10
− u
9
− u
8
+ 3u
7
− 2u
5
+ u
4
+ 4u
3
− 3u
2
− 4u + 4
c
2
, c
9
u
10
+ 3u
9
+ ··· + 40u + 16
c
3
, c
7
(u
5
− 3u
4
+ 6u
3
− 7u
2
+ 4u − 2)
2
c
5
, c
11
(u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1)
2
c
10
(u
5
− 7u
4
+ 17u
3
− 14u
2
− 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
8
y
10
− 3y
9
+ ··· − 40y + 16
c
2
, c
9
y
10
+ 5y
9
+ ··· − 32y + 256
c
3
, c
7
(y
5
+ 3y
4
+ 2y
3
− 13y
2
− 12y − 4)
2
c
5
, c
11
(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
2
c
10
(y
5
− 15y
4
+ 93y
3
− 210y
2
− 28y − 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.225231 + 0.702914I
a = 0.456786 + 0.020682I
b = −1.393800 + 0.234385I
c = 0.723513 − 0.982142I
d = −1.62313 + 1.61232I
−2.91669 − 1.13882I −7.28192 + 6.05450I
u = 0.225231 + 0.702914I
a = 1.40917 + 2.76067I
b = −0.645580 − 0.490417I
c = −0.36215 + 1.56941I
d = 0.088345 + 0.325740I
−2.91669 − 1.13882I −7.28192 + 6.05450I
u = 0.225231 − 0.702914I
a = 0.456786 − 0.020682I
b = −1.393800 − 0.234385I
c = 0.723513 + 0.982142I
d = −1.62313 − 1.61232I
−2.91669 + 1.13882I −7.28192 − 6.05450I
u = 0.225231 − 0.702914I
a = 1.40917 − 2.76067I
b = −0.645580 + 0.490417I
c = −0.36215 − 1.56941I
d = 0.088345 − 0.325740I
−2.91669 + 1.13882I −7.28192 − 6.05450I
u = 1.36478
a = 0.467454 + 0.220835I
b = 0.121768 + 1.237560I
c = −0.548749 − 0.605393I
d = 0.637971 − 0.301391I
5.22495 −1.71420
u = 1.36478
a = 0.467454 − 0.220835I
b = 0.121768 − 1.237560I
c = −0.548749 + 0.605393I
d = 0.637971 + 0.301391I
5.22495 −1.71420
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.59238 + 1.52933I
a = 0.362296 − 0.720965I
b = 1.02960 + 0.98230I
c = 0.719342 − 0.464705I
d = −1.92040 + 0.39965I
10.17380 − 6.99719I −0.86096 + 3.54683I
u = 0.59238 + 1.52933I
a = −0.195707 + 1.179910I
b = −0.61199 − 1.87536I
c = −0.531954 − 0.496057I
d = 1.317210 + 0.126988I
10.17380 − 6.99719I −0.86096 + 3.54683I
u = 0.59238 − 1.52933I
a = 0.362296 + 0.720965I
b = 1.02960 − 0.98230I
c = 0.719342 + 0.464705I
d = −1.92040 − 0.39965I
10.17380 + 6.99719I −0.86096 − 3.54683I
u = 0.59238 − 1.52933I
a = −0.195707 − 1.179910I
b = −0.61199 + 1.87536I
c = −0.531954 + 0.496057I
d = 1.317210 − 0.126988I
10.17380 + 6.99719I −0.86096 − 3.54683I
12
III. I
u
3
=
hu
2
+d, −u
2
+c−1, 2au−u
2
+b+a−u, 4u
2
a−3u
2
+· · ·+6a−5, u
3
+u
2
+2u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
u
a
9
=
u
2
+ 1
−u
2
a
1
=
a
−2au + u
2
− a + u
a
10
=
1
0
a
2
=
u
2
a + 2au − u
2
+ 2a − u
−2u
2
a − 5au + 3u
2
− 2a + 2u
a
5
=
−2au + u
2
+ u
2u
2
a + 6au − 3u
2
+ 3a − 2u
a
6
=
−1
−u
2
a
11
=
u
2
a + 2au − u
2
+ 2a − u
−2u
2
a − 5au + 3u
2
− 2a + 2u
a
11
=
u
2
a + 2au − u
2
+ 2a − u
−2u
2
a − 5au + 3u
2
− 2a + 2u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
11
u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1
c
2
u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1
c
3
, c
7
, c
9
(u
3
+ u
2
+ 2u + 1)
2
c
6
, c
8
(u
3
− u
2
+ 1)
2
c
10
u
6
− 5u
5
+ 8u
4
− 6u
3
+ 8u
2
− 8u + 1
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
11
y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1
c
2
, c
10
y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1
c
3
, c
7
, c
9
(y
3
+ 3y
2
+ 2y − 1)
2
c
6
, c
8
(y
3
− y
2
+ 2y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.460426 + 0.958773I
b = 0.366694 − 1.005170I
c = −0.662359 − 0.562280I
d = 1.66236 + 0.56228I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 + 1.307140I
a = 0.404090 − 0.016796I
b = −2.15161 − 0.30197I
c = −0.662359 − 0.562280I
d = 1.66236 + 0.56228I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.460426 − 0.958773I
b = 0.366694 + 1.005170I
c = −0.662359 + 0.562280I
d = 1.66236 − 0.56228I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = 0.404090 + 0.016796I
b = −2.15161 + 0.30197I
c = −0.662359 + 0.562280I
d = 1.66236 − 0.56228I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.569840
a = 0.725017
b = −0.143852
c = 1.32472
d = −0.324718
−1.11345 −9.01950
u = −0.569840
a = −7.45405
b = −1.28631
c = 1.32472
d = −0.324718
−1.11345 −9.01950
16
IV.
I
u
4
= hu
2
c−u
2
+· · ·+2c−1, u
2
c+c
2
−u
2
+c−1, b−u, a+u, u
3
+u
2
+2u+1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
u
a
9
=
c
−u
2
c − cu + u
2
− 2c + u + 1
a
1
=
−u
u
a
10
=
−u
2
c − cu + u
2
+ c + u
−2c + 1
a
2
=
u
2
+ 1
−u
2
a
5
=
0
−u
a
6
=
u
2
c + cu − u
2
+ c − u − 1
−u
2
c − cu + u
2
− 2c + u + 1
a
11
=
c
−u
2
c − cu + u
2
− 2c + u + 1
a
11
=
c
−u
2
c − cu + u
2
− 2c + u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
17
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
(u
3
− u
2
+ 1)
2
c
2
, c
3
, c
7
(u
3
+ u
2
+ 2u + 1)
2
c
5
, c
6
, c
8
c
11
u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1
c
9
u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1
c
10
u
6
− 5u
5
+ 8u
4
− 6u
3
+ 8u
2
− 8u + 1
18
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y
3
− y
2
+ 2y − 1)
2
c
2
, c
3
, c
7
(y
3
+ 3y
2
+ 2y − 1)
2
c
5
, c
6
, c
8
c
11
y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1
c
9
, c
10
y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1
19
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.215080 − 1.307140I
b = −0.215080 + 1.307140I
c = 0.103733 + 1.107850I
d = −0.064957 + 0.531815I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 + 1.307140I
a = 0.215080 − 1.307140I
b = −0.215080 + 1.307140I
c = 0.558626 − 0.545571I
d = −1.352280 + 0.395629I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.215080 + 1.307140I
b = −0.215080 − 1.307140I
c = 0.103733 − 1.107850I
d = −0.064957 − 0.531815I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.215080 − 1.307140I
a = 0.215080 + 1.307140I
b = −0.215080 − 1.307140I
c = 0.558626 + 0.545571I
d = −1.352280 − 0.395629I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.569840
a = 0.569840
b = −0.569840
c = 0.665586
d = −0.413144
−1.11345 −9.01950
u = −0.569840
a = 0.569840
b = −0.569840
c = −1.99030
d = 4.24762
−1.11345 −9.01950
20
V. I
u
5
= hu
2
+ d, −u
2
+ c − 1, b − u, a + u, u
3
+ u
2
+ 2u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
4
=
1
u
2
a
8
=
−u
u
a
9
=
u
2
+ 1
−u
2
a
1
=
−u
u
a
10
=
1
0
a
2
=
u
2
+ 1
−u
2
a
5
=
0
−u
a
6
=
−1
−u
2
a
11
=
u
2
+ 1
−u
2
a
11
=
u
2
+ 1
−u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
2
− 4u − 10
21
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
11
u
3
− u
2
+ 1
c
2
, c
3
, c
7
c
9
u
3
+ u
2
+ 2u + 1
c
10
u
3
− u
2
+ 2u − 1
22
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
8
, c
11
y
3
− y
2
+ 2y − 1
c
2
, c
3
, c
7
c
9
, c
10
y
3
+ 3y
2
+ 2y − 1
23
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.215080 + 1.307140I
a = 0.215080 − 1.307140I
b = −0.215080 + 1.307140I
c = −0.662359 − 0.562280I
d = 1.66236 + 0.56228I
3.02413 + 2.82812I −2.49024 − 2.97945I
u = −0.215080 − 1.307140I
a = 0.215080 + 1.307140I
b = −0.215080 − 1.307140I
c = −0.662359 + 0.562280I
d = 1.66236 − 0.56228I
3.02413 − 2.82812I −2.49024 + 2.97945I
u = −0.569840
a = 0.569840
b = −0.569840
c = 1.32472
d = −0.324718
−1.11345 −9.01950
24
VI. I
v
1
= ha, d + 1, c − a + 1, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
−1
0
a
4
=
1
0
a
8
=
−1
0
a
9
=
−1
−1
a
1
=
0
−1
a
10
=
0
−1
a
2
=
1
−1
a
5
=
0
1
a
6
=
0
1
a
11
=
0
−1
a
11
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
25
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u − 1
c
2
, c
4
, c
8
c
9
u + 1
c
3
, c
5
, c
7
c
10
, c
11
u
26
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y − 1
c
3
, c
5
, c
7
c
10
, c
11
y
27
(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
28
VII. I
v
2
= ha, d, c − 1, b + 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
4
=
1
0
a
8
=
1
0
a
9
=
1
0
a
1
=
0
−1
a
10
=
1
0
a
2
=
1
−1
a
5
=
0
1
a
6
=
1
0
a
11
=
1
−1
a
11
=
1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
29
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u − 1
c
2
, c
4
, c
5
c
10
u + 1
c
3
, c
6
, c
7
c
8
, c
9
u
30
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
10
, c
11
y − 1
c
3
, c
6
, c
7
c
8
, c
9
y
31
(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
32
VIII. I
v
3
= hc, d − 1, b, a − 1, v − 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
1
0
a
4
=
1
0
a
8
=
1
0
a
9
=
0
1
a
1
=
1
0
a
10
=
−1
1
a
2
=
1
0
a
5
=
1
0
a
6
=
1
−1
a
11
=
0
1
a
11
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
33
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
c
5
, c
6
u − 1
c
8
, c
9
, c
10
c
11
u + 1
34
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
c
5
, c
6
, c
8
c
9
, c
10
, c
11
y − 1
35
(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
36
IX. I
v
4
= ha, da + c − v − 1, dv − 1, cv − v
2
+ a − v, b + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
v
0
a
4
=
1
0
a
8
=
v
0
a
9
=
v + 1
d
a
1
=
0
−1
a
10
=
1
d
a
2
=
1
−1
a
5
=
0
1
a
6
=
−1
−d
a
11
=
1
d − 1
a
11
=
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.
37
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
−1.64493 −7.39277 − 0.54214I
38
X. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u(u − 1)
2
(u
3
− u
2
+ 1)
3
(u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1)
· (u
10
− u
9
− u
8
+ 3u
7
− 2u
5
+ u
4
+ 4u
3
− 3u
2
− 4u + 4)
· (u
13
− 2u
12
+ 4u
10
− 8u
8
+ 7u
7
+ 7u
6
− 8u
5
− 3u
4
+ 9u
3
+ u
2
− u + 1)
c
2
, c
9
u(u + 1)
2
(u
3
+ u
2
+ 2u + 1)
3
(u
6
+ 5u
5
+ 8u
4
+ 6u
3
+ 8u
2
+ 8u + 1)
· (u
10
+ 3u
9
+ ··· + 40u + 16)(u
13
+ 4u
12
+ ··· − u + 1)
c
3
, c
7
u
3
(u
3
+ u
2
+ 2u + 1)
5
(u
5
− 3u
4
+ 6u
3
− 7u
2
+ 4u − 2)
2
· (u
13
+ 2u
12
+ ··· − 4u
2
+ 8)
c
4
, c
8
u(u + 1)
2
(u
3
− u
2
+ 1)
3
(u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1)
· (u
10
− u
9
− u
8
+ 3u
7
− 2u
5
+ u
4
+ 4u
3
− 3u
2
− 4u + 4)
· (u
13
− 2u
12
+ 4u
10
− 8u
8
+ 7u
7
+ 7u
6
− 8u
5
− 3u
4
+ 9u
3
+ u
2
− u + 1)
c
5
, c
11
u(u − 1)(u + 1)(u
3
− u
2
+ 1)(u
5
+ u
4
− 3u
3
− 2u
2
+ 2u − 1)
2
· ((u
6
+ u
5
− 2u
4
+ 2u
2
− 2u − 1)
2
)(u
13
+ 2u
12
+ ··· + 8u + 4)
c
10
u(u + 1)
2
(u
3
− u
2
+ 2u − 1)(u
5
− 7u
4
+ 17u
3
− 14u
2
− 1)
2
· ((u
6
− 5u
5
+ ··· − 8u + 1)
2
)(u
13
− 14u
12
+ ··· + 88u − 16)
39
XI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
8
y(y − 1)
2
(y
3
− y
2
+ 2y − 1)
3
(y
6
− 5y
5
+ 8y
4
− 6y
3
+ 8y
2
− 8y + 1)
· (y
10
− 3y
9
+ ··· − 40y + 16)(y
13
− 4y
12
+ ··· − y − 1)
c
2
, c
9
y(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)
3
· (y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
· (y
10
+ 5y
9
+ ··· − 32y + 256)(y
13
+ 16y
12
+ ··· − 25y − 1)
c
3
, c
7
y
3
(y
3
+ 3y
2
+ 2y − 1)
5
(y
5
+ 3y
4
+ 2y
3
− 13y
2
− 12y − 4)
2
· (y
13
+ 6y
12
+ ··· + 64y − 64)
c
5
, c
11
y(y − 1)
2
(y
3
− y
2
+ 2y − 1)(y
5
− 7y
4
+ 17y
3
− 14y
2
− 1)
2
· ((y
6
− 5y
5
+ ··· − 8y + 1)
2
)(y
13
− 14y
12
+ ··· + 88y − 16)
c
10
y(y − 1)
2
(y
3
+ 3y
2
+ 2y − 1)(y
5
− 15y
4
+ ··· − 28y − 1)
2
· (y
6
− 9y
5
+ 20y
4
+ 14y
3
− 16y
2
− 48y + 1)
2
· (y
13
− 30y
12
+ ··· + 2848y − 256)
40
