10
96
(K10a
24
)
A knot diagram
1
Linearized knot diagam
9 6 1 7 3 10 4 2 8 5
Solving Sequence
2,8
9 10
1,4
3 7 5 6
c
8
c
9
c
1
c
3
c
7
c
4
c
6
c
2
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−5272122u
17
+ 4798544u
16
+ ··· + 51537967b + 28315457,
38859701u
17
+ 11491400u
16
+ ··· + 206151868a − 139434563,
u
18
+ 4u
16
+ 9u
14
− u
13
+ 12u
12
− 3u
11
+ 11u
10
− 5u
9
+ 8u
8
+ 4u
7
+ 2u
6
+ 6u
5
+ 8u
4
+ 7u
3
+ u
2
+ 3u + 4i
I
u
2
= hu
14
a − 2u
14
+ ··· − 2a − 1, 2u
14
a + 2u
14
+ ··· + a
2
+ 4a,
u
15
− u
14
+ 4u
13
− 3u
12
+ 8u
11
− 6u
10
+ 10u
9
− 7u
8
+ 8u
7
− 6u
6
+ 6u
5
− 4u
4
+ 4u
3
− 2u
2
+ 2u − 1i
I
u
3
= hb − 1, 2a + 2u + 3, u
2
+ u + 1i
* 3 irreducible components of dim
C
= 0, with total 50 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−5.27 × 10
6
u
17
+ 4.80 × 10
6
u
16
+ · · · + 5.15 × 10
7
b + 2.83 × 10
7
, 3.89 ×
10
7
u
17
+1.15×10
7
u
16
+· · ·+2.06×10
8
a−1.39×10
8
, u
18
+4u
16
+· · ·+3u +4i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
10
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
−0.188500u
17
− 0.0557424u
16
+ ··· + 0.154930u + 0.676368
0.102296u
17
− 0.0931070u
16
+ ··· − 0.813721u − 0.549410
a
3
=
−0.166761u
17
− 0.0607885u
16
+ ··· + 0.283272u + 1.04603
0.0148237u
17
− 0.207715u
16
+ ··· − 0.870244u − 0.939258
a
7
=
0.234815u
17
+ 0.0148237u
16
+ ··· − 0.790765u − 0.165801
−0.0607885u
17
+ 0.189164u
16
+ ··· + 1.54632u + 0.667045
a
5
=
−0.373129u
17
− 0.128980u
16
+ ··· + 0.922103u + 1.59149
0.128980u
17
− 0.289335u
16
+ ··· − 2.71088u − 1.49252
a
6
=
0.137352u
17
+ 0.102296u
16
+ ··· − 0.248070u − 0.401663
−0.0557424u
17
+ 0.123431u
16
+ ··· + 1.24187u + 0.754001
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
23479367
51537967
u
17
−
127343919
206151868
u
16
+ ··· +
657635827
206151868
u +
414460539
51537967
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
18
+ 4u
16
+ ··· − 3u + 4
c
2
, c
4
, c
5
c
7
u
18
− 2u
17
+ ··· − u + 1
c
3
, c
6
4(4u
18
− 6u
17
+ ··· + u + 1)
c
9
u
18
+ 8u
17
+ ··· − u + 16
c
10
u
18
+ 3u
17
+ ··· + 120u + 32
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
18
+ 8y
17
+ ··· − y + 16
c
2
, c
4
, c
5
c
7
y
18
+ 8y
17
+ ··· + 17y + 1
c
3
, c
6
16(16y
18
− 28y
17
+ ··· + 11y + 1)
c
9
y
18
+ 4y
17
+ ··· + 735y + 256
c
10
y
18
− 5y
17
+ ··· − 4288y + 1024
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.954364 + 0.371541I
a = −0.854485 + 0.746417I
b = 0.527077 − 1.253950I
−3.68268 − 9.36876I −0.27355 + 5.71519I
u = 0.954364 − 0.371541I
a = −0.854485 − 0.746417I
b = 0.527077 + 1.253950I
−3.68268 + 9.36876I −0.27355 − 5.71519I
u = 0.495157 + 0.969336I
a = 0.811360 − 1.129300I
b = −1.278490 + 0.262032I
1.41086 + 2.64017I −3.75807 − 9.26255I
u = 0.495157 − 0.969336I
a = 0.811360 + 1.129300I
b = −1.278490 − 0.262032I
1.41086 − 2.64017I −3.75807 + 9.26255I
u = −0.567357 + 0.706169I
a = −0.421889 − 0.044039I
b = 0.123272 + 0.375141I
0.11776 − 1.42471I 0.46661 + 2.50425I
u = −0.567357 − 0.706169I
a = −0.421889 + 0.044039I
b = 0.123272 − 0.375141I
0.11776 + 1.42471I 0.46661 − 2.50425I
u = 0.501769 + 0.662267I
a = 1.69141 − 0.67535I
b = −1.010020 − 0.434093I
2.35859 + 1.45777I 5.68941 + 2.64543I
u = 0.501769 − 0.662267I
a = 1.69141 + 0.67535I
b = −1.010020 + 0.434093I
2.35859 − 1.45777I 5.68941 − 2.64543I
u = −0.881883 + 0.896090I
a = −0.838759 + 0.128282I
b = 0.278239 − 0.862332I
−0.64162 − 4.35809I 2.09542 + 8.94470I
u = −0.881883 − 0.896090I
a = −0.838759 − 0.128282I
b = 0.278239 + 0.862332I
−0.64162 + 4.35809I 2.09542 − 8.94470I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.715844 + 0.165207I
a = 0.153155 + 0.140793I
b = −0.254607 + 0.632963I
0.38947 − 1.38737I 5.20835 + 5.01616I
u = −0.715844 − 0.165207I
a = 0.153155 − 0.140793I
b = −0.254607 − 0.632963I
0.38947 + 1.38737I 5.20835 − 5.01616I
u = 0.644327 + 1.178320I
a = −1.77812 + 0.47961I
b = 0.57190 + 1.33178I
−6.1478 + 15.1779I −2.47148 − 8.89088I
u = 0.644327 − 1.178320I
a = −1.77812 − 0.47961I
b = 0.57190 − 1.33178I
−6.1478 − 15.1779I −2.47148 + 8.89088I
u = 0.123550 + 1.355420I
a = −0.009343 − 0.587707I
b = 0.343795 − 1.275010I
−9.80486 − 5.84779I −6.18830 + 4.95030I
u = 0.123550 − 1.355420I
a = −0.009343 + 0.587707I
b = 0.343795 + 1.275010I
−9.80486 + 5.84779I −6.18830 − 4.95030I
u = −0.554083 + 1.298630I
a = 0.871664 + 0.626444I
b = −0.301163 + 1.054570I
−3.73889 − 6.36829I −2.64340 + 9.34206I
u = −0.554083 − 1.298630I
a = 0.871664 − 0.626444I
b = −0.301163 − 1.054570I
−3.73889 + 6.36829I −2.64340 − 9.34206I
6
II. I
u
2
=
hu
14
a−2u
14
+· · ·−2a−1, 2u
14
a+2u
14
+· · ·+a
2
+4a, u
15
−u
14
+· · ·+2u−1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
10
=
u
2
+ 1
−u
2
a
1
=
−u
u
3
+ u
a
4
=
a
−u
14
a + 2u
14
+ ··· + 2a + 1
a
3
=
3u
13
a − 3u
14
+ ··· − 2a − 2
−2u
14
a + 2u
14
+ ··· + 2a + 2
a
7
=
−2u
14
a + 4u
13
a + ··· − a + 5
−3u
14
a − u
14
+ ··· − 4u + 1
a
5
=
u
14
+ 3u
12
+ 6u
10
+ 7u
8
+ 6u
6
+ 4u
4
+ 2u
2
+ 1
−u
14
+ u
13
+ ··· + u − 1
a
6
=
−2u
14
a − u
14
+ ··· − 2u + 4
2u
14
− 2u
13
+ ··· − au − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
13
−4u
12
+12u
11
−12u
10
+20u
9
−24u
8
+20u
7
−24u
6
+16u
5
−16u
4
+16u
3
−8u
2
+8u−6
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
(u
15
+ u
14
+ ··· + 2u + 1)
2
c
2
, c
4
, c
5
c
7
u
30
+ 5u
29
+ ··· + 2u + 1
c
3
, c
6
u
30
+ u
29
+ ··· − 162u + 29
c
9
(u
15
+ 7u
14
+ ··· + 4u
2
− 1)
2
c
10
(u
15
− u
14
+ ··· + 2u − 1)
2
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
15
+ 7y
14
+ ··· + 4y
2
− 1)
2
c
2
, c
4
, c
5
c
7
y
30
+ 19y
29
+ ··· − 20y
2
+ 1
c
3
, c
6
y
30
− 13y
29
+ ··· + 21316y + 841
c
9
(y
15
+ 3y
14
+ ··· + 8y −1)
2
c
10
(y
15
− 5y
14
+ ··· + 12y
3
− 1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.385605 + 0.867795I
a = 3.01190 + 0.62486I
b = −0.160281 − 0.896058I
−3.64104 − 1.66084I 1.51042 + 3.96405I
u = −0.385605 + 0.867795I
a = 0.98340 + 3.53440I
b = −0.081650 + 1.113800I
−3.64104 − 1.66084I 1.51042 + 3.96405I
u = −0.385605 − 0.867795I
a = 3.01190 − 0.62486I
b = −0.160281 + 0.896058I
−3.64104 + 1.66084I 1.51042 − 3.96405I
u = −0.385605 − 0.867795I
a = 0.98340 − 3.53440I
b = −0.081650 − 1.113800I
−3.64104 + 1.66084I 1.51042 − 3.96405I
u = 0.146928 + 1.062740I
a = −0.532247 + 0.803689I
b = −0.235764 + 1.349700I
−5.11062 − 2.07402I −3.82822 + 2.67122I
u = 0.146928 + 1.062740I
a = −0.336119 + 0.803807I
b = 0.789375 − 0.319437I
−5.11062 − 2.07402I −3.82822 + 2.67122I
u = 0.146928 − 1.062740I
a = −0.532247 − 0.803689I
b = −0.235764 − 1.349700I
−5.11062 + 2.07402I −3.82822 − 2.67122I
u = 0.146928 − 1.062740I
a = −0.336119 − 0.803807I
b = 0.789375 + 0.319437I
−5.11062 + 2.07402I −3.82822 − 2.67122I
u = −0.715401 + 0.518352I
a = −0.495626 + 0.162788I
b = 0.253544 + 0.465102I
0.24352 − 1.50523I 4.15133 + 2.74048I
u = −0.715401 + 0.518352I
a = 0.203961 − 0.302035I
b = −0.220274 + 0.713343I
0.24352 − 1.50523I 4.15133 + 2.74048I
10
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.715401 − 0.518352I
a = −0.495626 − 0.162788I
b = 0.253544 − 0.465102I
0.24352 + 1.50523I 4.15133 − 2.74048I
u = −0.715401 − 0.518352I
a = 0.203961 + 0.302035I
b = −0.220274 − 0.713343I
0.24352 + 1.50523I 4.15133 − 2.74048I
u = 0.758945 + 0.422629I
a = 0.732399 − 1.007910I
b = −0.549307 + 1.203290I
−0.27297 − 4.09199I 3.04427 + 3.15094I
u = 0.758945 + 0.422629I
a = −1.52820 + 0.36163I
b = 0.930770 + 0.153909I
−0.27297 − 4.09199I 3.04427 + 3.15094I
u = 0.758945 − 0.422629I
a = 0.732399 + 1.007910I
b = −0.549307 − 1.203290I
−0.27297 + 4.09199I 3.04427 − 3.15094I
u = 0.758945 − 0.422629I
a = −1.52820 − 0.36163I
b = 0.930770 − 0.153909I
−0.27297 + 4.09199I 3.04427 − 3.15094I
u = 0.426893 + 1.085670I
a = 0.497713 − 0.065950I
b = 0.38528 − 1.46920I
−7.49803 + 3.60340I −6.16372 − 4.47672I
u = 0.426893 + 1.085670I
a = −1.91914 + 0.58198I
b = 0.672463 + 1.225340I
−7.49803 + 3.60340I −6.16372 − 4.47672I
u = 0.426893 − 1.085670I
a = 0.497713 + 0.065950I
b = 0.38528 + 1.46920I
−7.49803 − 3.60340I −6.16372 + 4.47672I
u = 0.426893 − 1.085670I
a = −1.91914 − 0.58198I
b = 0.672463 − 1.225340I
−7.49803 − 3.60340I −6.16372 + 4.47672I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.594997 + 1.040830I
a = −1.57156 − 0.42279I
b = 0.212345 − 0.992556I
−1.30682 − 3.51852I 1.71302 + 2.59027I
u = −0.594997 + 1.040830I
a = 0.257459 − 0.239199I
b = −0.368301 − 0.106759I
−1.30682 − 3.51852I 1.71302 + 2.59027I
u = −0.594997 − 1.040830I
a = −1.57156 + 0.42279I
b = 0.212345 + 0.992556I
−1.30682 + 3.51852I 1.71302 − 2.59027I
u = −0.594997 − 1.040830I
a = 0.257459 + 0.239199I
b = −0.368301 + 0.106759I
−1.30682 + 3.51852I 1.71302 − 2.59027I
u = 0.594032 + 1.095620I
a = −0.858900 + 0.821598I
b = 1.119760 − 0.096018I
−2.26357 + 9.21780I −0.14540 − 7.39135I
u = 0.594032 + 1.095620I
a = 1.85470 − 0.46519I
b = −0.61782 − 1.34369I
−2.26357 + 9.21780I −0.14540 − 7.39135I
u = 0.594032 − 1.095620I
a = −0.858900 − 0.821598I
b = 1.119760 + 0.096018I
−2.26357 − 9.21780I −0.14540 + 7.39135I
u = 0.594032 − 1.095620I
a = 1.85470 + 0.46519I
b = −0.61782 + 1.34369I
−2.26357 − 9.21780I −0.14540 + 7.39135I
u = 0.538411
a = −1.79974 + 1.43818I
b = 0.369866 − 1.187600I
−4.71415 −2.56340
u = 0.538411
a = −1.79974 − 1.43818I
b = 0.369866 + 1.187600I
−4.71415 −2.56340
12
III. I
u
3
= hb − 1, 2a + 2u + 3, u
2
+ u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
9
=
1
u + 1
a
10
=
−u
u + 1
a
1
=
−u
u + 1
a
4
=
−u −
3
2
1
a
3
=
−u − 1
1
2
u + 1
a
7
=
−u −
1
2
1
a
5
=
−2u − 2
2
a
6
=
−u − 1
−
1
2
u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
4
u + 2
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
2
− u + 1
c
2
, c
4
(u + 1)
2
c
3
4(4u
2
+ 2u + 1)
c
5
, c
7
(u − 1)
2
c
6
4(4u
2
− 2u + 1)
c
8
, c
9
u
2
+ u + 1
c
10
u
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
9
y
2
+ y + 1
c
2
, c
4
, c
5
c
7
(y −1)
2
c
3
, c
6
16(16y
2
+ 4y + 1)
c
10
y
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.500000 + 0.866025I
a = −1.000000 − 0.866025I
b = 1.00000
1.64493 − 2.02988I 1.87500 + 0.21651I
u = −0.500000 − 0.866025I
a = −1.000000 + 0.866025I
b = 1.00000
1.64493 + 2.02988I 1.87500 − 0.21651I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
− u + 1)(u
15
+ u
14
+ ··· + 2u + 1)
2
(u
18
+ 4u
16
+ ··· − 3u + 4)
c
2
, c
4
((u + 1)
2
)(u
18
− 2u
17
+ ··· − u + 1)(u
30
+ 5u
29
+ ··· + 2u + 1)
c
3
16(4u
2
+ 2u + 1)(4u
18
− 6u
17
+ ··· + u + 1)(u
30
+ u
29
+ ··· − 162u + 29)
c
5
, c
7
((u − 1)
2
)(u
18
− 2u
17
+ ··· − u + 1)(u
30
+ 5u
29
+ ··· + 2u + 1)
c
6
16(4u
2
− 2u + 1)(4u
18
− 6u
17
+ ··· + u + 1)(u
30
+ u
29
+ ··· − 162u + 29)
c
8
(u
2
+ u + 1)(u
15
+ u
14
+ ··· + 2u + 1)
2
(u
18
+ 4u
16
+ ··· − 3u + 4)
c
9
(u
2
+ u + 1)(u
15
+ 7u
14
+ ··· + 4u
2
− 1)
2
(u
18
+ 8u
17
+ ··· − u + 16)
c
10
u
2
(u
15
− u
14
+ ··· + 2u − 1)
2
(u
18
+ 3u
17
+ ··· + 120u + 32)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
(y
2
+ y + 1)(y
15
+ 7y
14
+ ··· + 4y
2
− 1)
2
(y
18
+ 8y
17
+ ··· − y + 16)
c
2
, c
4
, c
5
c
7
((y −1)
2
)(y
18
+ 8y
17
+ ··· + 17y + 1)(y
30
+ 19y
29
+ ··· − 20y
2
+ 1)
c
3
, c
6
256(16y
2
+ 4y + 1)(16y
18
− 28y
17
+ ··· + 11y + 1)
· (y
30
− 13y
29
+ ··· + 21316y + 841)
c
9
(y
2
+ y + 1)(y
15
+ 3y
14
+ ··· + 8y −1)
2
· (y
18
+ 4y
17
+ ··· + 735y + 256)
c
10
y
2
(y
15
− 5y
14
+ ··· + 12y
3
− 1)
2
(y
18
− 5y
17
+ ··· − 4288y + 1024)
18
