11a
51
(K11a
51
)
A knot diagram
1
Linearized knot diagam
5 1 8 2 4 10 3 7 11 6 9
Solving Sequence
3,7
8 4
1,9
2 5 11 10 6
c
7
c
3
c
8
c
2
c
4
c
11
c
9
c
6
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5u
14
+ 23u
13
+ ··· + 4b − 28,
2u
14
− 7u
13
+ 9u
12
+ 6u
11
− 33u
10
+ 42u
9
− 6u
8
− 42u
7
+ 53u
6
− 19u
5
− 7u
4
+ 6u
3
+ 11u
2
+ 4a − 10u + 2,
u
15
− 5u
14
+ 10u
13
− 5u
12
− 18u
11
+ 44u
10
− 40u
9
− 3u
8
+ 49u
7
− 55u
6
+ 26u
5
− u
4
+ 2u
3
− 12u
2
+ 12u − 4i
I
u
2
= h2u
22
a + 8u
22
+ ··· − 4a − 16, −2u
21
a + 7u
22
+ ··· + 6a − 11, u
23
+ 2u
22
+ ··· − 5u − 2i
I
v
1
= ha, b
2
− b + 1, v + 1i
I
v
2
= ha, b − v, v
2
− v + 1i
* 4 irreducible components of dim
C
= 0, with total 65 representations.
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
=
h−5u
14
+23u
13
+· · ·+4b−28, 2u
14
−7u
13
+· · ·+4a+2, u
15
−5u
14
+· · ·+12u−4i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
1
=
−
1
2
u
14
+
7
4
u
13
+ ··· +
5
2
u −
1
2
5
4
u
14
−
23
4
u
13
+ ··· −
27
2
u + 7
a
9
=
−u
2
+ 1
−u
2
a
2
=
−
1
4
u
14
+ u
13
+ ··· +
3
2
u −
1
2
−
1
4
u
14
+
3
4
u
13
+ ··· − u
2
+
3
2
u
a
5
=
3
4
u
14
− 4u
13
+ ··· − 9u +
9
2
7
4
u
14
−
29
4
u
13
+ ··· −
25
2
u + 5
a
11
=
−
5
4
u
14
+
9
2
u
13
+ ··· + 6u −
5
2
−
1
4
u
14
−
1
4
u
13
+ ··· −
9
2
u + 3
a
10
=
−
1
2
u
14
+
7
4
u
13
+ ··· + 2u +
1
2
−
1
4
u
14
+
3
4
u
13
+ ··· − 2u
2
+
1
2
u
a
6
=
7
4
u
14
−
15
2
u
13
+ ··· − 16u +
15
2
3
4
u
14
−
11
4
u
13
+ ··· −
11
2
u + 2
a
6
=
7
4
u
14
−
15
2
u
13
+ ··· − 16u +
15
2
3
4
u
14
−
11
4
u
13
+ ··· −
11
2
u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 13u
14
− 58u
13
+ 91u
12
+ 9u
11
− 253u
10
+ 402u
9
− 196u
8
−
247u
7
+ 488u
6
− 328u
5
+ 45u
4
+ 37u
3
+ 59u
2
− 114u + 58
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
15
+ u
14
+ ··· + 2u − 1
c
2
, c
5
, c
9
c
11
u
15
+ 5u
14
+ ··· + 18u
2
− 1
c
3
, c
7
u
15
− 5u
14
+ ··· + 12u − 4
c
8
u
15
− 5u
14
+ ··· + 48u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
15
+ 5y
14
+ ··· + 18y
2
− 1
c
2
, c
5
, c
9
c
11
y
15
+ 13y
14
+ ··· + 36y −1
c
3
, c
7
y
15
− 5y
14
+ ··· + 48y −16
c
8
y
15
+ 3y
14
+ ··· − 1024y −256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.297110 + 1.013620I
a = −0.987350 − 0.311397I
b = −0.738671 + 0.490241I
3.26489 + 2.24335I 7.04256 − 3.44027I
u = 0.297110 − 1.013620I
a = −0.987350 + 0.311397I
b = −0.738671 − 0.490241I
3.26489 − 2.24335I 7.04256 + 3.44027I
u = 0.843039 + 0.715120I
a = 0.718904 − 0.735528I
b = −0.47287 − 1.47924I
−6.27477 + 2.71677I −5.40032 − 3.41816I
u = 0.843039 − 0.715120I
a = 0.718904 + 0.735528I
b = −0.47287 + 1.47924I
−6.27477 − 2.71677I −5.40032 + 3.41816I
u = 0.528547 + 1.045590I
a = 1.235390 + 0.154632I
b = 0.915557 − 0.882680I
1.75577 − 8.71874I 3.93323 + 7.24615I
u = 0.528547 − 1.045590I
a = 1.235390 − 0.154632I
b = 0.915557 + 0.882680I
1.75577 + 8.71874I 3.93323 − 7.24615I
u = −0.548950 + 0.445559I
a = −0.294279 − 0.663565I
b = −0.232624 − 0.217433I
−1.34006 − 1.53790I −1.51731 + 5.00908I
u = −0.548950 − 0.445559I
a = −0.294279 + 0.663565I
b = −0.232624 + 0.217433I
−1.34006 + 1.53790I −1.51731 − 5.00908I
u = 0.700518
a = −0.240121
b = 0.561665
0.940705 11.2760
u = 1.194600 + 0.597734I
a = 0.209836 + 0.830578I
b = 1.56955 + 0.92220I
6.11311 + 3.45523I 8.74146 − 0.79948I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.194600 − 0.597734I
a = 0.209836 − 0.830578I
b = 1.56955 − 0.92220I
6.11311 − 3.45523I 8.74146 + 0.79948I
u = −1.338190 + 0.093539I
a = −0.043731 − 1.064360I
b = −0.043240 − 0.609135I
9.46149 − 5.98215I 9.71265 + 5.53392I
u = −1.338190 − 0.093539I
a = −0.043731 + 1.064360I
b = −0.043240 + 0.609135I
9.46149 + 5.98215I 9.71265 − 5.53392I
u = 1.173580 + 0.723559I
a = −0.218707 − 1.141120I
b = −1.77854 − 1.21305I
3.8210 + 15.1159I 4.84980 − 10.19781I
u = 1.173580 − 0.723559I
a = −0.218707 + 1.141120I
b = −1.77854 + 1.21305I
3.8210 − 15.1159I 4.84980 + 10.19781I
6
II. I
u
2
= h2u
22
a + 8u
22
+ · · · − 4a − 16, −2u
21
a + 7u
22
+ · · · + 6a − 11, u
23
+
2u
22
+ · · · − 5u − 2i
(i) Arc colorings
a
3
=
0
u
a
7
=
1
0
a
8
=
1
−u
2
a
4
=
u
−u
3
+ u
a
1
=
a
−u
22
a − 4u
22
+ ··· + 2a + 8
a
9
=
−u
2
+ 1
−u
2
a
2
=
1
2
u
22
a +
3
2
u
22
+ ··· − 6u −
7
2
−
7
2
u
22
a −
5
2
u
22
+ ··· + 8a + 8
a
5
=
−u
22
a − 4u
22
+ ··· + a + 8
−
1
2
u
22
−
1
2
u
21
+ ··· + au +
3
2
u
a
11
=
−
1
2
u
19
+ 2u
17
+ ··· + a − 1
−u
22
a −
7
2
u
22
+ ··· + 2a + 7
a
10
=
3u
22
+
5
2
u
21
+ ··· − 10u −
9
2
7
2
u
22
a +
5
2
u
22
+ ··· − 7a − 6
a
6
=
−u
22
a − 4u
22
+ ··· + a + 8
−
1
2
u
22
−
1
2
u
21
+ ··· + au +
3
2
u
a
6
=
−u
22
a − 4u
22
+ ··· + a + 8
−
1
2
u
22
−
1
2
u
21
+ ··· + au +
3
2
u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −3u
22
−6u
21
+13u
20
+32u
19
−22u
18
−86u
17
+9u
16
+146u
15
+52u
14
−172u
13
−134u
12
+
142u
11
+ 194u
10
− 86u
9
− 185u
8
+ 26u
7
+ 133u
6
+ 16u
5
− 53u
4
− 28u
3
+ 4u
2
+ 14u + 15
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
6
c
10
u
46
+ 2u
45
+ ··· + 3u + 1
c
2
, c
5
, c
9
c
11
u
46
+ 16u
45
+ ··· − 7u + 1
c
3
, c
7
(u
23
+ 2u
22
+ ··· − 5u − 2)
2
c
8
(u
23
− 10u
22
+ ··· + 9u − 4)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
y
46
+ 16y
45
+ ··· − 7y + 1
c
2
, c
5
, c
9
c
11
y
46
+ 28y
45
+ ··· − 31y + 1
c
3
, c
7
(y
23
− 10y
22
+ ··· + 9y − 4)
2
c
8
(y
23
+ 6y
22
+ ··· + 81y − 16)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.639801 + 0.747481I
a = 0.727893 − 0.688432I
b = 0.26465 − 1.54953I
−2.85626 − 3.41905I −2.17452 + 2.62575I
u = 0.639801 + 0.747481I
a = 1.368810 + 0.331230I
b = 0.347272 − 0.897201I
−2.85626 − 3.41905I −2.17452 + 2.62575I
u = 0.639801 − 0.747481I
a = 0.727893 + 0.688432I
b = 0.26465 + 1.54953I
−2.85626 + 3.41905I −2.17452 − 2.62575I
u = 0.639801 − 0.747481I
a = 1.368810 − 0.331230I
b = 0.347272 + 0.897201I
−2.85626 + 3.41905I −2.17452 − 2.62575I
u = 0.892339 + 0.406575I
a = −0.099975 − 1.361930I
b = −0.81309 − 2.02727I
0.68141 + 1.67196I 4.30301 − 3.03015I
u = 0.892339 + 0.406575I
a = 1.245900 + 0.653876I
b = −0.365826 − 0.883644I
0.68141 + 1.67196I 4.30301 − 3.03015I
u = 0.892339 − 0.406575I
a = −0.099975 + 1.361930I
b = −0.81309 + 2.02727I
0.68141 − 1.67196I 4.30301 + 3.03015I
u = 0.892339 − 0.406575I
a = 1.245900 − 0.653876I
b = −0.365826 + 0.883644I
0.68141 − 1.67196I 4.30301 + 3.03015I
u = 1.050370 + 0.349306I
a = 0.291173 + 0.949009I
b = 1.18138 + 1.14414I
3.69234 + 0.67223I 9.57904 − 0.98278I
u = 1.050370 + 0.349306I
a = −0.472020 − 0.128106I
b = 0.866881 + 0.515908I
3.69234 + 0.67223I 9.57904 − 0.98278I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.050370 − 0.349306I
a = 0.291173 − 0.949009I
b = 1.18138 − 1.14414I
3.69234 − 0.67223I 9.57904 + 0.98278I
u = 1.050370 − 0.349306I
a = −0.472020 + 0.128106I
b = 0.866881 − 0.515908I
3.69234 − 0.67223I 9.57904 + 0.98278I
u = −0.423739 + 1.023080I
a = 0.901532 − 0.308315I
b = 0.646872 + 0.688817I
2.61521 + 3.21096I 5.70075 − 2.17483I
u = −0.423739 + 1.023080I
a = −1.263400 + 0.094664I
b = −0.912235 − 0.683061I
2.61521 + 3.21096I 5.70075 − 2.17483I
u = −0.423739 − 1.023080I
a = 0.901532 + 0.308315I
b = 0.646872 − 0.688817I
2.61521 − 3.21096I 5.70075 + 2.17483I
u = −0.423739 − 1.023080I
a = −1.263400 − 0.094664I
b = −0.912235 + 0.683061I
2.61521 − 3.21096I 5.70075 + 2.17483I
u = −0.649214 + 0.610986I
a = −0.654087 − 0.683089I
b = −0.163180 − 1.021730I
−1.56921 − 1.42863I 0.37479 + 3.46803I
u = −0.649214 + 0.610986I
a = 0.540359 − 0.440252I
b = −0.111799 + 0.519787I
−1.56921 − 1.42863I 0.37479 + 3.46803I
u = −0.649214 − 0.610986I
a = −0.654087 + 0.683089I
b = −0.163180 + 1.021730I
−1.56921 + 1.42863I 0.37479 − 3.46803I
u = −0.649214 − 0.610986I
a = 0.540359 + 0.440252I
b = −0.111799 − 0.519787I
−1.56921 + 1.42863I 0.37479 − 3.46803I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.857444 + 0.223332I
a = −0.434590 + 1.081100I
b = −1.15099 + 1.59199I
1.26940 + 3.50227I 6.61882 − 3.38553I
u = −0.857444 + 0.223332I
a = −1.20976 + 0.81324I
b = 0.500178 − 0.598051I
1.26940 + 3.50227I 6.61882 − 3.38553I
u = −0.857444 − 0.223332I
a = −0.434590 − 1.081100I
b = −1.15099 − 1.59199I
1.26940 − 3.50227I 6.61882 + 3.38553I
u = −0.857444 − 0.223332I
a = −1.20976 − 0.81324I
b = 0.500178 + 0.598051I
1.26940 − 3.50227I 6.61882 + 3.38553I
u = −0.975157 + 0.564788I
a = −0.742547 − 0.767125I
b = 0.918100 − 1.023970I
−0.57975 − 3.22642I 2.48526 + 3.26705I
u = −0.975157 + 0.564788I
a = −0.313926 + 0.810399I
b = −1.47433 + 1.18838I
−0.57975 − 3.22642I 2.48526 + 3.26705I
u = −0.975157 − 0.564788I
a = −0.742547 + 0.767125I
b = 0.918100 + 1.023970I
−0.57975 + 3.22642I 2.48526 − 3.26705I
u = −0.975157 − 0.564788I
a = −0.313926 − 0.810399I
b = −1.47433 − 1.18838I
−0.57975 + 3.22642I 2.48526 − 3.26705I
u = −1.058660 + 0.462903I
a = 0.115203 − 1.237340I
b = 0.99587 − 1.50991I
2.96583 − 6.20103I 7.62650 + 6.52033I
u = −1.058660 + 0.462903I
a = 0.507084 − 0.155808I
b = −0.806153 + 0.696216I
2.96583 − 6.20103I 7.62650 + 6.52033I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.058660 − 0.462903I
a = 0.115203 + 1.237340I
b = 0.99587 + 1.50991I
2.96583 + 6.20103I 7.62650 − 6.52033I
u = −1.058660 − 0.462903I
a = 0.507084 + 0.155808I
b = −0.806153 − 0.696216I
2.96583 + 6.20103I 7.62650 − 6.52033I
u = 1.017600 + 0.636625I
a = 0.744768 − 0.749497I
b = −1.04484 − 1.24551I
−1.67882 + 8.70149I 0.49306 − 7.84909I
u = 1.017600 + 0.636625I
a = −0.217050 − 1.226050I
b = −1.50533 − 1.64405I
−1.67882 + 8.70149I 0.49306 − 7.84909I
u = 1.017600 − 0.636625I
a = 0.744768 + 0.749497I
b = −1.04484 + 1.24551I
−1.67882 − 8.70149I 0.49306 + 7.84909I
u = 1.017600 − 0.636625I
a = −0.217050 + 1.226050I
b = −1.50533 + 1.64405I
−1.67882 − 8.70149I 0.49306 + 7.84909I
u = 1.33812
a = 0.075989 + 1.040970I
b = 0.300733 + 0.595751I
9.53870 9.98620
u = 1.33812
a = 0.075989 − 1.040970I
b = 0.300733 − 0.595751I
9.53870 9.98620
u = −1.183710 + 0.666071I
a = 0.195146 − 1.147490I
b = 1.61477 − 1.17057I
5.02301 − 9.28326I 6.87076 + 5.60434I
u = −1.183710 + 0.666071I
a = −0.206318 + 0.804811I
b = −1.66505 + 0.97289I
5.02301 − 9.28326I 6.87076 + 5.60434I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.183710 − 0.666071I
a = 0.195146 + 1.147490I
b = 1.61477 + 1.17057I
5.02301 + 9.28326I 6.87076 − 5.60434I
u = −1.183710 − 0.666071I
a = −0.206318 − 0.804811I
b = −1.66505 − 0.97289I
5.02301 + 9.28326I 6.87076 − 5.60434I
u = −0.121237 + 0.604443I
a = −1.76798 − 0.31454I
b = −0.373843 − 0.180509I
0.47190 + 2.34013I 2.62944 − 2.83732I
u = −0.121237 + 0.604443I
a = −0.082205 + 0.174275I
b = −0.250037 + 0.826429I
0.47190 + 2.34013I 2.62944 − 2.83732I
u = −0.121237 − 0.604443I
a = −1.76798 + 0.31454I
b = −0.373843 + 0.180509I
0.47190 − 2.34013I 2.62944 + 2.83732I
u = −0.121237 − 0.604443I
a = −0.082205 − 0.174275I
b = −0.250037 − 0.826429I
0.47190 − 2.34013I 2.62944 + 2.83732I
14
III. I
v
1
= ha, b
2
− b + 1, v + 1i
(i) Arc colorings
a
3
=
−1
0
a
7
=
1
0
a
8
=
1
0
a
4
=
−1
0
a
1
=
0
b
a
9
=
1
0
a
2
=
−1
b − 1
a
5
=
−b
−b
a
11
=
b
b
a
10
=
b
b − 1
a
6
=
0
−b
a
6
=
0
−b
(ii) Obstruction class = 1
(iii) Cusp Shapes = 8b − 4
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
u
2
+ u + 1
c
3
, c
7
, c
8
u
2
c
4
, c
9
, c
10
u
2
− u + 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
7
, c
8
y
2
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = 0.500000 + 0.866025I
− 4.05977I 0. + 6.92820I
v = −1.00000
a = 0
b = 0.500000 − 0.866025I
4.05977I 0. − 6.92820I
18
IV. I
v
2
= ha, b − v, v
2
− v + 1i
(i) Arc colorings
a
3
=
v
0
a
7
=
1
0
a
8
=
1
0
a
4
=
v
0
a
1
=
0
v
a
9
=
1
0
a
2
=
v
1
a
5
=
1
−v
a
11
=
v
v
a
10
=
v
v − 1
a
6
=
0
−v
a
6
=
0
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
11
u
2
+ u + 1
c
3
, c
7
, c
8
u
2
c
4
, c
9
, c
10
u
2
− u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
9
c
10
, c
11
y
2
+ y + 1
c
3
, c
7
, c
8
y
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 = 0.500000 + 0.866025I
0 3.00000
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
0 3.00000
22
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
((u
2
+ u + 1)
2
)(u
15
+ u
14
+ ··· + 2u − 1)(u
46
+ 2u
45
+ ··· + 3u + 1)
c
2
, c
5
, c
11
((u
2
+ u + 1)
2
)(u
15
+ 5u
14
+ ··· + 18u
2
− 1)(u
46
+ 16u
45
+ ··· − 7u + 1)
c
3
, c
7
u
4
(u
15
− 5u
14
+ ··· + 12u − 4)(u
23
+ 2u
22
+ ··· − 5u − 2)
2
c
4
, c
10
((u
2
− u + 1)
2
)(u
15
+ u
14
+ ··· + 2u − 1)(u
46
+ 2u
45
+ ··· + 3u + 1)
c
8
u
4
(u
15
− 5u
14
+ ··· + 48u − 16)(u
23
− 10u
22
+ ··· + 9u − 4)
2
c
9
((u
2
− u + 1)
2
)(u
15
+ 5u
14
+ ··· + 18u
2
− 1)(u
46
+ 16u
45
+ ··· − 7u + 1)
23
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
6
c
10
((y
2
+ y + 1)
2
)(y
15
+ 5y
14
+ ··· + 18y
2
− 1)(y
46
+ 16y
45
+ ··· − 7y + 1)
c
2
, c
5
, c
9
c
11
((y
2
+ y + 1)
2
)(y
15
+ 13y
14
+ ··· + 36y − 1)
· (y
46
+ 28y
45
+ ··· − 31y + 1)
c
3
, c
7
y
4
(y
15
− 5y
14
+ ··· + 48y − 16)(y
23
− 10y
22
+ ··· + 9y − 4)
2
c
8
y
4
(y
15
+ 3y
14
+ ··· − 1024y − 256)(y
23
+ 6y
22
+ ··· + 81y − 16)
2
24
