12n
0067
(K12n
0067
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 10 11 5 8 6 7
Solving Sequence
5,9 6,10,11
12 4 3 2 1 8 7
c
9
c
11
c
4
c
3
c
2
c
1
c
8
c
7
c
5
, c
6
, c
10
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h5.68457 × 10
17
u
17
+ 8.64985 × 10
17
u
16
+ ··· + 1.24822 × 10
20
d + 1.55459 × 10
19
,
2.99690 × 10
17
u
17
+ 2.72458 × 10
17
u
16
+ ··· + 2.49645 × 10
20
c − 2.46906 × 10
20
,
− 4.18893 × 10
15
u
17
+ 2.24411 × 10
18
u
16
+ ··· + 1.24822 × 10
20
b − 4.97576 × 10
19
,
− 3.58259 × 10
17
u
17
− 3.47344 × 10
18
u
16
+ ··· + 2.49645 × 10
20
a − 2.35898 × 10
20
,
u
18
+ 3u
17
+ ··· + 32u + 32i
I
u
2
= h−1447u
9
c − 65u
9
+ ··· + 7346c + 3206, −22391u
9
c + 7563u
9
+ ··· + 121770c − 50482,
− 378u
9
+ 149u
8
+ ··· + 857b + 1781, 7265u
9
− 363u
8
+ ··· + 13712a − 20806,
u
10
− u
9
− 7u
8
+ 8u
7
+ 13u
6
− 14u
5
− 2u
4
− 2u
3
+ 13u
2
− 12u + 4i
I
v
1
= ha, d, c − 1, b − 1, v
2
− v + 1i
I
v
2
= ha, d + 1, c + a, b − 1, v
2
− v + 1i
I
v
3
= hc, d + 1, b, a + 1, v + 1i
I
v
4
= hc, d + 1, −v
2
ba − v
2
b + av + c + v, b
2
v
2
− bv + 1i
* 5 irreducible components of dim
C
= 0, with total 43 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
= h5.68 × 10
17
u
17
+ 8.65× 10
17
u
16
+ · · · + 1.25 × 10
20
d +1.55 × 10
19
, 3.00 ×
10
17
u
17
+ 2.72 × 10
17
u
16
+ · · · + 2.50 × 10
20
c − 2.47 × 10
20
, −4.19 × 10
15
u
17
+
2.24 × 10
18
u
16
+ · · · + 1.25 × 10
20
b − 4.98 × 10
19
, −3.58 × 10
17
u
17
− 3.47 ×
10
18
u
16
+ · · · + 2.50 × 10
20
a − 2.36 × 10
20
, u
18
+ 3u
17
+ · · · + 32u + 32i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
6
=
0.00143508u
17
+ 0.0139135u
16
+ ··· − 0.714624u + 0.944936
0.0000335592u
17
− 0.0179784u
16
+ ··· + 1.37888u + 0.398628
a
10
=
1
−u
2
a
11
=
−0.00120047u
17
− 0.00109138u
16
+ ··· − 0.0893825u + 0.989028
−0.00455413u
17
− 0.00692973u
16
+ ··· − 0.245124u − 0.124544
a
12
=
−0.00490067u
17
− 0.0153878u
16
+ ··· + 0.466611u + 1.14967
0.00513528u
17
+ 0.0282099u
16
+ ··· − 1.27062u − 0.215706
a
4
=
−u
u
a
3
=
0.000371161u
17
+ 0.0231129u
16
+ ··· + 0.350709u − 0.584653
0.0295819u
17
+ 0.0399851u
16
+ ··· + 2.27781u + 1.67132
a
2
=
0.000371161u
17
+ 0.0231129u
16
+ ··· + 0.350709u − 0.584653
0.0113208u
17
+ 0.00191842u
16
+ ··· + 1.56195u + 0.967341
a
1
=
−0.00146864u
17
+ 0.00406488u
16
+ ··· − 0.664258u − 1.34356
0.0141649u
17
+ 0.00737088u
16
+ ··· + 1.60295u + 0.669693
a
8
=
−0.00120047u
17
− 0.00109138u
16
+ ··· − 0.0893825u + 0.989028
0.00756978u
17
+ 0.0124143u
16
+ ··· + 0.287029u + 0.204865
a
7
=
−0.00575459u
17
− 0.00802111u
16
+ ··· − 0.334506u + 0.864484
0.0164592u
17
+ 0.0311513u
16
+ ··· + 0.356742u + 0.420310
(ii) Obstruction class = −1
(iii) Cusp Shapes =
1881106086253954753
31205580083057755580
u
17
+
5887773742508132609
62411160166115511160
u
16
+ ··· +
57261478582730965292
7801395020764438895
u +
64355080374530213256
7801395020764438895
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
18
+ 5u
17
+ ··· − 136u + 16
c
2
, c
5
u
18
+ u
17
+ ··· − 12u + 4
c
3
u
18
− u
17
+ ··· − 756u + 1252
c
4
, c
9
u
18
+ 3u
17
+ ··· + 32u + 32
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
18
+ 5u
17
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
18
+ 17y
17
+ ··· − 38944y + 256
c
2
, c
5
y
18
+ 5y
17
+ ··· − 136y + 16
c
3
y
18
+ 29y
17
+ ··· − 3653960y + 1567504
c
4
, c
9
y
18
− 15y
17
+ ··· − 2048y + 1024
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
18
− 29y
17
+ ··· − 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.078440 + 0.216619I
a = 0.253388 − 1.028300I
b = −0.71841 + 2.42684I
c = 0.492205 − 0.156710I
d = −0.844681 − 0.587317I
3.61986 + 3.92600I 13.3379 − 5.7849I
u = −1.078440 − 0.216619I
a = 0.253388 + 1.028300I
b = −0.71841 − 2.42684I
c = 0.492205 + 0.156710I
d = −0.844681 + 0.587317I
3.61986 − 3.92600I 13.3379 + 5.7849I
u = 0.709201 + 0.274453I
a = −0.01264 + 1.59035I
b = 0.27741 − 3.38402I
c = 0.515734 + 0.082365I
d = −0.890761 + 0.301961I
3.12578 + 1.29944I 14.10514 − 0.79844I
u = 0.709201 − 0.274453I
a = −0.01264 − 1.59035I
b = 0.27741 + 3.38402I
c = 0.515734 − 0.082365I
d = −0.890761 − 0.301961I
3.12578 − 1.29944I 14.10514 + 0.79844I
u = −0.610909 + 0.417338I
a = 0.428235 + 0.847865I
b = −0.502581 − 0.271599I
c = 0.768504 + 0.302779I
d = −0.126387 + 0.443779I
−1.20916 − 1.63680I 1.95124 + 5.83411I
u = −0.610909 − 0.417338I
a = 0.428235 − 0.847865I
b = −0.502581 + 0.271599I
c = 0.768504 − 0.302779I
d = −0.126387 − 0.443779I
−1.20916 + 1.63680I 1.95124 − 5.83411I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.555399
a = 0.144993
b = 0.407093
c = 0.739573
d = −0.352132
0.726383 14.1310
u = −0.072203 + 0.503217I
a = 2.01283 + 0.53928I
b = 0.179243 + 0.151857I
c = 1.330050 + 0.161709I
d = 0.259101 + 0.090079I
0.39079 + 2.25423I 1.75748 − 3.62098I
u = −0.072203 − 0.503217I
a = 2.01283 − 0.53928I
b = 0.179243 − 0.151857I
c = 1.330050 − 0.161709I
d = 0.259101 − 0.090079I
0.39079 − 2.25423I 1.75748 + 3.62098I
u = −1.83506 + 0.34828I
a = 0.808325 + 0.623484I
b = −0.014393 − 0.834480I
c = −1.318640 − 0.296832I
d = 1.72178 − 0.16248I
11.72250 − 5.21750I 12.21552 + 2.94469I
u = −1.83506 − 0.34828I
a = 0.808325 − 0.623484I
b = −0.014393 + 0.834480I
c = −1.318640 + 0.296832I
d = 1.72178 + 0.16248I
11.72250 + 5.21750I 12.21552 − 2.94469I
u = −1.70473 + 1.04671I
a = −0.230730 + 0.966273I
b = −0.03020 − 2.29892I
c = −0.961354 − 0.702659I
d = 1.67800 − 0.49555I
−19.5607 − 13.8899I 13.2954 + 6.2001I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.70473 − 1.04671I
a = −0.230730 − 0.966273I
b = −0.03020 + 2.29892I
c = −0.961354 + 0.702659I
d = 1.67800 + 0.49555I
−19.5607 + 13.8899I 13.2954 − 6.2001I
u = −0.16477 + 2.05598I
a = 0.905061 − 0.066880I
b = 0.464341 + 0.377003I
c = 0.354039 − 0.009486I
d = −1.82253 − 0.07562I
15.4858 + 3.5329I 13.90580 − 2.19457I
u = −0.16477 − 2.05598I
a = 0.905061 + 0.066880I
b = 0.464341 − 0.377003I
c = 0.354039 + 0.009486I
d = −1.82253 + 0.07562I
15.4858 − 3.5329I 13.90580 + 2.19457I
u = 2.12691
a = 0.609160
b = 0.619389
c = −1.17023
d = 1.85453
16.6053 15.4680
u = 1.91575 + 0.96837I
a = −0.041545 − 0.774296I
b = 0.33135 + 2.10179I
c = −0.965214 + 0.561225I
d = 1.77427 + 0.45020I
−18.1284 + 6.9769I 14.6320 − 1.8700I
u = 1.91575 − 0.96837I
a = −0.041545 + 0.774296I
b = 0.33135 − 2.10179I
c = −0.965214 − 0.561225I
d = 1.77427 − 0.45020I
−18.1284 − 6.9769I 14.6320 + 1.8700I
7
II. I
u
2
= h−1447cu
9
− 65u
9
+ · · · + 7346c + 3206, −2.24 × 10
4
cu
9
+ 7563u
9
+
· · · + 1.22 × 10
5
c − 5.05 × 10
4
, −378u
9
+ 149u
8
+ · · · + 857b + 1781, 7265u
9
−
363u
8
+ · · · + 1.37 × 10
4
a − 2.08 × 10
4
, u
10
− u
9
+ · · · − 12u + 4i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
6
=
−0.529828u
9
+ 0.0264732u
8
+ ··· − 4.18035u + 1.51736
0.441074u
9
− 0.173862u
8
+ ··· + 4.90898u − 2.07818
a
10
=
1
−u
2
a
11
=
c
0.422112cu
9
+ 0.0189615u
9
+ ··· − 2.14294c − 0.935239
a
12
=
−0.0189615cu
9
− 0.529828u
9
+ ··· + 0.935239c + 1.51736
0.199533cu
9
+ 0.460035u
9
+ ··· − 0.487748c − 3.01342
a
4
=
−u
u
a
3
=
0.893451u
9
− 0.113258u
8
+ ··· + 6.74818u − 3.90621
−0.258897u
9
+ 0.0170653u
8
+ ··· − 1.24023u + 1.07730
a
2
=
0.893451u
9
− 0.113258u
8
+ ··· + 6.74818u − 3.90621
0.381418u
9
− 0.120916u
8
+ ··· + 4.54828u − 2.04347
a
1
=
0.0887544u
9
+ 0.147389u
8
+ ··· − 0.728632u + 0.560823
0.145566u
9
− 0.271004u
8
+ ··· + 2.43028u − 1.13361
a
8
=
c
−0.422112cu
9
− 0.0189615u
9
+ ··· + 2.14294c + 0.935239
a
7
=
0.422112cu
9
+ 0.0189615u
9
+ ··· − 1.14294c − 0.935239
−0.387106cu
9
− 0.218495u
9
+ ··· + 2.72404c + 1.42299
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
3875
1714
u
9
−
183
1714
u
8
−
26957
1714
u
7
+
2248
857
u
6
+
51811
1714
u
5
+
541
857
u
4
−
185
857
u
3
−
9943
857
u
2
+
27495
1714
u +
882
857
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
10
+ 2u
9
+ 9u
8
+ 14u
7
+ 28u
6
+ 31u
5
+ 35u
4
+ 20u
3
+ 15u
2
+ 5u + 1)
2
c
2
, c
5
(u
10
+ 2u
9
+ 3u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 3u
4
+ 3u
2
+ u + 1)
2
c
3
(u
10
− 2u
9
+ ··· + 21u + 17)
2
c
4
, c
9
(u
10
− u
9
− 7u
8
+ 8u
7
+ 13u
6
− 14u
5
− 2u
4
− 2u
3
+ 13u
2
− 12u + 4)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
20
+ 3u
19
+ ··· − 8u + 16
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
10
+ 14y
9
+ ··· + 5y + 1)
2
c
2
, c
5
(y
10
+ 2y
9
+ 9y
8
+ 14y
7
+ 28y
6
+ 31y
5
+ 35y
4
+ 20y
3
+ 15y
2
+ 5y + 1)
2
c
3
(y
10
+ 26y
9
+ ··· + 2925y + 289)
2
c
4
, c
9
(y
10
− 15y
9
+ ··· − 40y + 16)
2
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
20
− 19y
19
+ ··· + 1248y + 256
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.620250 + 0.748934I
a = −0.676664 + 0.412835I
b = −0.425803 + 0.101141I
c = 0.448932 − 0.060647I
d = −1.187590 − 0.295523I
4.43566 − 1.46073I 14.6593 + 3.2864I
u = −0.620250 + 0.748934I
a = −0.676664 + 0.412835I
b = −0.425803 + 0.101141I
c = −0.77388 − 2.52919I
d = 1.110620 − 0.361536I
4.43566 − 1.46073I 14.6593 + 3.2864I
u = −0.620250 − 0.748934I
a = −0.676664 − 0.412835I
b = −0.425803 − 0.101141I
c = 0.448932 + 0.060647I
d = −1.187590 + 0.295523I
4.43566 + 1.46073I 14.6593 − 3.2864I
u = −0.620250 − 0.748934I
a = −0.676664 − 0.412835I
b = −0.425803 − 0.101141I
c = −0.77388 + 2.52919I
d = 1.110620 + 0.361536I
4.43566 + 1.46073I 14.6593 − 3.2864I
u = 0.793271 + 0.121626I
a = −1.18565 − 0.94130I
b = 0.064264 + 0.396481I
c = 0.549929 + 0.112131I
d = −0.745831 + 0.355977I
2.87696 − 2.81207I 12.88002 + 4.64391I
u = 0.793271 + 0.121626I
a = −1.18565 − 0.94130I
b = 0.064264 + 0.396481I
c = −4.13892 + 0.99173I
d = 1.228490 + 0.054749I
2.87696 − 2.81207I 12.88002 + 4.64391I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.793271 − 0.121626I
a = −1.18565 + 0.94130I
b = 0.064264 − 0.396481I
c = 0.549929 − 0.112131I
d = −0.745831 − 0.355977I
2.87696 + 2.81207I 12.88002 − 4.64391I
u = 0.793271 − 0.121626I
a = −1.18565 + 0.94130I
b = 0.064264 − 0.396481I
c = −4.13892 − 0.99173I
d = 1.228490 − 0.054749I
2.87696 + 2.81207I 12.88002 − 4.64391I
u = 0.413972 + 0.524496I
a = −0.490625 + 0.051502I
b = 0.987479 + 0.430021I
c = 0.920372 − 0.380673I
d = 0.072202 − 0.383745I
1.39065 − 0.79591I 7.22040 − 0.81155I
u = 0.413972 + 0.524496I
a = −0.490625 + 0.051502I
b = 0.987479 + 0.430021I
c = 0.475648 + 0.039205I
d = −1.088210 + 0.172121I
1.39065 − 0.79591I 7.22040 − 0.81155I
u = 0.413972 − 0.524496I
a = −0.490625 − 0.051502I
b = 0.987479 − 0.430021I
c = 0.920372 + 0.380673I
d = 0.072202 + 0.383745I
1.39065 + 0.79591I 7.22040 + 0.81155I
u = 0.413972 − 0.524496I
a = −0.490625 − 0.051502I
b = 0.987479 − 0.430021I
c = 0.475648 − 0.039205I
d = −1.088210 − 0.172121I
1.39065 + 0.79591I 7.22040 + 0.81155I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.88200 + 0.46774I
a = 0.111563 + 0.952024I
b = 0.18395 − 2.32396I
c = −1.236340 + 0.360963I
d = 1.74531 + 0.21760I
12.6890 + 7.4068I 12.74326 − 4.41038I
u = 1.88200 + 0.46774I
a = 0.111563 + 0.952024I
b = 0.18395 − 2.32396I
c = 0.385819 − 0.297883I
d = −0.623883 − 1.253760I
12.6890 + 7.4068I 12.74326 − 4.41038I
u = 1.88200 − 0.46774I
a = 0.111563 − 0.952024I
b = 0.18395 + 2.32396I
c = −1.236340 − 0.360963I
d = 1.74531 − 0.21760I
12.6890 − 7.4068I 12.74326 + 4.41038I
u = 1.88200 − 0.46774I
a = 0.111563 − 0.952024I
b = 0.18395 + 2.32396I
c = 0.385819 + 0.297883I
d = −0.623883 + 1.253760I
12.6890 − 7.4068I 12.74326 + 4.41038I
u = −1.96899 + 0.18613I
a = −0.008629 − 0.881122I
b = −0.30989 + 2.24439I
c = −1.262570 − 0.138704I
d = 1.78259 − 0.08597I
13.15130 − 0.50253I 13.49701 − 0.08773I
u = −1.96899 + 0.18613I
a = −0.008629 − 0.881122I
b = −0.30989 + 2.24439I
c = 0.381016 + 0.259317I
d = −0.79370 + 1.22078I
13.15130 − 0.50253I 13.49701 − 0.08773I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.96899 − 0.18613I
a = −0.008629 + 0.881122I
b = −0.30989 − 2.24439I
c = −1.262570 + 0.138704I
d = 1.78259 + 0.08597I
13.15130 + 0.50253I 13.49701 + 0.08773I
u = −1.96899 − 0.18613I
a = −0.008629 + 0.881122I
b = −0.30989 − 2.24439I
c = 0.381016 − 0.259317I
d = −0.79370 − 1.22078I
13.15130 + 0.50253I 13.49701 + 0.08773I
14
III. I
v
1
= ha, d, c − 1, b − 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
6
=
0
1
a
10
=
1
0
a
11
=
1
0
a
12
=
1
−1
a
4
=
v
0
a
3
=
v
−v
a
2
=
v − 1
−v
a
1
=
0
−1
a
8
=
1
0
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 7
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
(u + 1)
2
c
11
, c
12
(u − 1)
2
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = 1.00000
d = 0
1.64493 − 2.02988I 9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 1.00000
d = 0
1.64493 + 2.02988I 9.00000 − 3.46410I
18
IV. I
v
2
= ha, d + 1, c + a, b − 1, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
6
=
0
1
a
10
=
1
0
a
11
=
0
−1
a
12
=
0
−1
a
4
=
v
0
a
3
=
v
−v
a
2
=
v − 1
−v
a
1
=
0
−1
a
8
=
1
1
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 7
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
9
c
11
, c
12
u
2
c
7
, c
8
(u + 1)
2
c
10
(u − 1)
2
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
9
c
11
, c
12
y
2
c
7
, c
8
, c
10
(y − 1)
2
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
1.64493 − 2.02988I 9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 1.00000
c = 0
d = −1.00000
1.64493 + 2.02988I 9.00000 − 3.46410I
22
V. I
v
3
= hc, d + 1, b, a + 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
9
=
1
0
a
6
=
−1
0
a
10
=
1
0
a
11
=
0
−1
a
12
=
−1
−1
a
4
=
−1
0
a
3
=
−1
0
a
2
=
−1
0
a
1
=
−1
0
a
8
=
1
1
a
7
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
23
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
u
c
6
, c
10
u − 1
c
7
, c
8
, c
11
c
12
u + 1
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
y
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y − 1
25
(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
3.28987 12.0000
26
VI. I
v
4
= hc, d + 1, −v
2
ba − v
2
b + av + c + v, b
2
v
2
− bv + 1i
(i) Arc colorings
a
5
=
v
0
a
9
=
1
0
a
6
=
−1
b
a
10
=
1
0
a
11
=
0
−1
a
12
=
−1
b − 1
a
4
=
v
0
a
3
=
bv + v
−b
2
v
a
2
=
v
2
b + bv
−b
2
v
a
1
=
1
−b
a
8
=
1
1
a
7
=
0
1
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
3
v + 4bv − v
2
+ 12
(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.
27
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
3.28987 − 2.02988I 16.0361 + 3.3760I
28
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
· (u
10
+ 2u
9
+ 9u
8
+ 14u
7
+ 28u
6
+ 31u
5
+ 35u
4
+ 20u
3
+ 15u
2
+ 5u + 1)
2
· (u
18
+ 5u
17
+ ··· − 136u + 16)
c
2
u(u
2
+ u + 1)
2
· (u
10
+ 2u
9
+ 3u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 3u
4
+ 3u
2
+ u + 1)
2
· (u
18
+ u
17
+ ··· − 12u + 4)
c
3
u(u
2
− u + 1)
2
(u
10
− 2u
9
+ ··· + 21u + 17)
2
· (u
18
− u
17
+ ··· − 756u + 1252)
c
4
, c
9
u
5
(u
10
− u
9
+ ··· − 12u + 4)
2
· (u
18
+ 3u
17
+ ··· + 32u + 32)
c
5
u(u
2
− u + 1)
2
· (u
10
+ 2u
9
+ 3u
8
+ 2u
7
+ 4u
6
+ 3u
5
+ 3u
4
+ 3u
2
+ u + 1)
2
· (u
18
+ u
17
+ ··· − 12u + 4)
c
6
u
2
(u − 1)(u + 1)
2
(u
18
+ 5u
17
+ ··· − 2u − 1)(u
20
+ 3u
19
+ ··· − 8u + 16)
c
7
, c
8
u
2
(u + 1)
3
(u
18
+ 5u
17
+ ··· − 2u − 1)(u
20
+ 3u
19
+ ··· − 8u + 16)
c
10
u
2
(u − 1)
3
(u
18
+ 5u
17
+ ··· − 2u − 1)(u
20
+ 3u
19
+ ··· − 8u + 16)
c
11
, c
12
u
2
(u − 1)
2
(u + 1)(u
18
+ 5u
17
+ ··· − 2u − 1)(u
20
+ 3u
19
+ ··· − 8u + 16)
29
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
10
+ 14y
9
+ ··· + 5y + 1)
2
· (y
18
+ 17y
17
+ ··· − 38944y + 256)
c
2
, c
5
y(y
2
+ y + 1)
2
· (y
10
+ 2y
9
+ 9y
8
+ 14y
7
+ 28y
6
+ 31y
5
+ 35y
4
+ 20y
3
+ 15y
2
+ 5y + 1)
2
· (y
18
+ 5y
17
+ ··· − 136y + 16)
c
3
y(y
2
+ y + 1)
2
(y
10
+ 26y
9
+ ··· + 2925y + 289)
2
· (y
18
+ 29y
17
+ ··· − 3653960y + 1567504)
c
4
, c
9
y
5
(y
10
− 15y
9
+ ··· − 40y + 16)
2
(y
18
− 15y
17
+ ··· − 2048y + 1024)
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
2
(y − 1)
3
(y
18
− 29y
17
+ ··· − 26y + 1)
· (y
20
− 19y
19
+ ··· + 1248y + 256)
30
