10
90
(K10a
92
)
A knot diagram
1
Linearized knot diagam
5 7 10 8 2 9 1 6 4 3
Solving Sequence
4,9
10 3
1,7
2 6 5 8
c
9
c
3
c
10
c
2
c
6
c
5
c
8
c
1
, c
4
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.45798 × 10
19
u
39
− 4.51348 × 10
19
u
38
+ ··· + 2.27356 × 10
21
b + 2.73076 × 10
21
,
− 7.03658 × 10
21
u
39
+ 1.13904 × 10
22
u
38
+ ··· + 6.82068 × 10
21
a + 1.48581 × 10
21
, u
40
− 2u
39
+ ··· − 2u + 1i
I
u
2
= hb + 1, 3a − 2u + 1, u
2
− u + 1i
* 2 irreducible components of dim
C
= 0, with total 42 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−3.46×10
19
u
39
−4.51×10
19
u
38
+· · ·+2.27×10
21
b+2.73×10
21
, −7.04×
10
21
u
39
+1.14×10
22
u
38
+· · ·+6.82×10
21
a+1.49×10
21
, u
40
−2u
39
+· · ·−2u+1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
1.03165u
39
− 1.66999u
38
+ ··· − 9.20228u − 0.217839
0.0152095u
39
+ 0.0198520u
38
+ ··· + 0.294657u − 1.20110
a
2
=
−1.20596u
39
+ 2.67703u
38
+ ··· − 4.75631u − 2.57467
0.765706u
39
− 1.55826u
38
+ ··· + 3.94732u − 1.22640
a
6
=
1.04686u
39
− 1.65014u
38
+ ··· − 8.90762u − 1.41894
0.0152095u
39
+ 0.0198520u
38
+ ··· + 0.294657u − 1.20110
a
5
=
−0.829665u
39
+ 2.71973u
38
+ ··· − 11.3323u − 2.16330
0.136920u
39
− 0.520550u
38
+ ··· + 3.27950u − 1.01464
a
8
=
1.00098u
39
− 1.67814u
38
+ ··· − 9.29825u − 0.212902
−0.101227u
39
+ 0.144212u
38
+ ··· − 0.00592179u − 1.04475
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
23709189092098357085641
20462029573507327146753
u
39
+
5967042122571150693039
2273558841500814127417
u
38
+ ··· −
151009571647058399841037
6820676524502442382251
u +
36425712582025581848210
20462029573507327146753
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
40
− 2u
39
+ ··· − 2u + 1
c
2
3(3u
40
+ 19u
39
+ ··· + 64u + 32)
c
3
, c
9
, c
10
u
40
− 2u
39
+ ··· − 2u + 1
c
4
3(3u
40
− 10u
39
+ ··· − 192u + 103)
c
6
, c
8
u
40
− 3u
39
+ ··· − 31u + 9
c
7
u
40
− 3u
39
+ ··· − 156u + 36
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
40
− 22y
39
+ ··· − 4y + 1
c
2
9(9y
40
− 181y
39
+ ··· − 13312y + 1024)
c
3
, c
9
, c
10
y
40
+ 38y
39
+ ··· − 4y + 1
c
4
9(9y
40
+ 38y
39
+ ··· + 78084y + 10609)
c
6
, c
8
y
40
− 21y
39
+ ··· + 389y + 81
c
7
y
40
− 15y
39
+ ··· − 7416y + 1296
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.718542 + 0.684654I
a = −0.109960 − 0.256762I
b = 1.052260 − 0.485181I
1.29563 + 4.66233I −0.05723 − 4.37430I
u = 0.718542 − 0.684654I
a = −0.109960 + 0.256762I
b = 1.052260 + 0.485181I
1.29563 − 4.66233I −0.05723 + 4.37430I
u = −0.875135 + 0.400189I
a = 0.674482 + 0.656422I
b = 1.057710 − 0.370943I
−2.73210 + 3.80447I −3.64129 − 6.83498I
u = −0.875135 − 0.400189I
a = 0.674482 − 0.656422I
b = 1.057710 + 0.370943I
−2.73210 − 3.80447I −3.64129 + 6.83498I
u = 0.812016 + 0.457171I
a = 0.695937 − 0.974226I
b = 1.221190 + 0.590650I
0.61792 − 9.83239I −1.42359 + 7.89553I
u = 0.812016 − 0.457171I
a = 0.695937 + 0.974226I
b = 1.221190 − 0.590650I
0.61792 + 9.83239I −1.42359 − 7.89553I
u = −0.668019 + 0.947602I
a = 0.128837 + 0.281540I
b = 0.847605 + 0.160546I
−1.20798 + 1.63374I 5.34484 + 3.65075I
u = −0.668019 − 0.947602I
a = 0.128837 − 0.281540I
b = 0.847605 − 0.160546I
−1.20798 − 1.63374I 5.34484 − 3.65075I
u = 0.548023 + 0.473980I
a = −0.128815 + 0.412875I
b = 0.217702 − 0.991146I
3.67375 − 4.20324I 2.19223 + 6.09439I
u = 0.548023 − 0.473980I
a = −0.128815 − 0.412875I
b = 0.217702 + 0.991146I
3.67375 + 4.20324I 2.19223 − 6.09439I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.042556 + 1.284610I
a = 0.906133 + 0.658831I
b = −1.55343 − 0.24102I
1.29749 − 1.62987I 0. + 3.54187I
u = 0.042556 − 1.284610I
a = 0.906133 − 0.658831I
b = −1.55343 + 0.24102I
1.29749 + 1.62987I 0. − 3.54187I
u = 0.635260 + 0.284826I
a = 1.38094 − 0.39057I
b = 0.418271 + 0.528348I
3.12136 + 0.50572I 2.23334 + 2.05026I
u = 0.635260 − 0.284826I
a = 1.38094 + 0.39057I
b = 0.418271 − 0.528348I
3.12136 − 0.50572I 2.23334 − 2.05026I
u = 0.088735 + 1.341390I
a = 0.61542 + 1.56781I
b = −1.177540 − 0.538211I
1.96980 − 1.69833I 0
u = 0.088735 − 1.341390I
a = 0.61542 − 1.56781I
b = −1.177540 + 0.538211I
1.96980 + 1.69833I 0
u = −0.145572 + 1.361910I
a = 0.63895 − 1.93494I
b = −0.97948 + 1.02345I
3.71762 + 5.12635I 0
u = −0.145572 − 1.361910I
a = 0.63895 + 1.93494I
b = −0.97948 − 1.02345I
3.71762 − 5.12635I 0
u = −0.054010 + 1.410140I
a = 1.50150 − 2.72344I
b = −0.809247 + 0.079779I
5.39390 + 0.19809I 0
u = −0.054010 − 1.410140I
a = 1.50150 + 2.72344I
b = −0.809247 − 0.079779I
5.39390 − 0.19809I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29805 + 1.43344I
a = 0.374682 − 1.281700I
b = 0.859448 + 0.587652I
8.54985 − 3.07602I 0
u = 0.29805 − 1.43344I
a = 0.374682 + 1.281700I
b = 0.859448 − 0.587652I
8.54985 + 3.07602I 0
u = −0.491071 + 0.191924I
a = −0.398403 − 1.001630I
b = −1.093680 + 0.645721I
−1.16688 + 2.84021I −5.40123 − 7.45362I
u = −0.491071 − 0.191924I
a = −0.398403 + 1.001630I
b = −1.093680 − 0.645721I
−1.16688 − 2.84021I −5.40123 + 7.45362I
u = −0.334189 + 0.406515I
a = 0.489517 − 0.524451I
b = −0.086689 + 0.335230I
−0.073174 + 1.047740I −1.21383 − 6.28305I
u = −0.334189 − 0.406515I
a = 0.489517 + 0.524451I
b = −0.086689 − 0.335230I
−0.073174 − 1.047740I −1.21383 + 6.28305I
u = −0.14754 + 1.48353I
a = −0.198631 − 1.161320I
b = 0.205553 + 0.846197I
6.24860 + 2.92553I 0
u = −0.14754 − 1.48353I
a = −0.198631 + 1.161320I
b = 0.205553 − 0.846197I
6.24860 − 2.92553I 0
u = 0.19425 + 1.47878I
a = −0.63962 + 1.50949I
b = 0.365197 − 1.279800I
10.00150 − 6.93788I 0
u = 0.19425 − 1.47878I
a = −0.63962 − 1.50949I
b = 0.365197 + 1.279800I
10.00150 + 6.93788I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.31725 + 1.49380I
a = −0.15513 + 1.42791I
b = 1.180340 − 0.563412I
3.39122 + 8.09434I 0
u = −0.31725 − 1.49380I
a = −0.15513 − 1.42791I
b = 1.180340 + 0.563412I
3.39122 − 8.09434I 0
u = 0.29587 + 1.50669I
a = −0.25279 − 1.73575I
b = 1.29708 + 0.71454I
6.9750 − 13.8661I 0
u = 0.29587 − 1.50669I
a = −0.25279 + 1.73575I
b = 1.29708 − 0.71454I
6.9750 + 13.8661I 0
u = 0.16112 + 1.56360I
a = −0.602788 + 0.551528I
b = 0.727804 − 0.598256I
8.93627 + 1.59631I 0
u = 0.16112 − 1.56360I
a = −0.602788 − 0.551528I
b = 0.727804 + 0.598256I
8.93627 − 1.59631I 0
u = 0.424864 + 0.027630I
a = −1.51964 + 0.31762I
b = −1.269680 − 0.070813I
−2.32372 − 0.01230I −6.85568 − 1.19794I
u = 0.424864 − 0.027630I
a = −1.51964 − 0.31762I
b = −1.269680 + 0.070813I
−2.32372 + 0.01230I −6.85568 + 1.19794I
u = −0.186501 + 0.360437I
a = 3.93271 − 1.95945I
b = −0.980417 − 0.195912I
−0.113312 − 0.691322I 2.03417 − 9.81182I
u = −0.186501 − 0.360437I
a = 3.93271 + 1.95945I
b = −0.980417 + 0.195912I
−0.113312 + 0.691322I 2.03417 + 9.81182I
8
II. I
u
2
= hb + 1, 3a − 2u + 1, u
2
− u + 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u − 1
a
3
=
u
u − 1
a
1
=
u
u − 2
a
7
=
2
3
u −
1
3
−1
a
2
=
u +
1
3
5
3
u −
4
3
a
6
=
2
3
u −
4
3
−1
a
5
=
1
3
u
4
3
u −
2
3
a
8
=
2
3
u −
1
3
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
20
3
u − 9
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
2
+ u + 1
c
2
3(3u
2
+ 1)
c
4
3(3u
2
− 3u + 1)
c
5
, c
9
, c
10
u
2
− u + 1
c
6
(u − 1)
2
c
7
u
2
c
8
(u + 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
9
, c
10
y
2
+ y + 1
c
2
9(3y + 1)
2
c
4
9(9y
2
− 3y + 1)
c
6
, c
8
(y −1)
2
c
7
y
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 0.577350I
b = −1.00000
−1.64493 − 2.02988I −5.66667 + 5.77350I
u = 0.500000 − 0.866025I
a = − 0.577350I
b = −1.00000
−1.64493 + 2.02988I −5.66667 − 5.77350I
12
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
2
+ u + 1)(u
40
− 2u
39
+ ··· − 2u + 1)
c
2
9(3u
2
+ 1)(3u
40
+ 19u
39
+ ··· + 64u + 32)
c
3
(u
2
+ u + 1)(u
40
− 2u
39
+ ··· − 2u + 1)
c
4
9(3u
2
− 3u + 1)(3u
40
− 10u
39
+ ··· − 192u + 103)
c
5
(u
2
− u + 1)(u
40
− 2u
39
+ ··· − 2u + 1)
c
6
((u − 1)
2
)(u
40
− 3u
39
+ ··· − 31u + 9)
c
7
u
2
(u
40
− 3u
39
+ ··· − 156u + 36)
c
8
((u + 1)
2
)(u
40
− 3u
39
+ ··· − 31u + 9)
c
9
, c
10
(u
2
− u + 1)(u
40
− 2u
39
+ ··· − 2u + 1)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y
2
+ y + 1)(y
40
− 22y
39
+ ··· − 4y + 1)
c
2
81(3y + 1)
2
(9y
40
− 181y
39
+ ··· − 13312y + 1024)
c
3
, c
9
, c
10
(y
2
+ y + 1)(y
40
+ 38y
39
+ ··· − 4y + 1)
c
4
81(9y
2
− 3y + 1)(9y
40
+ 38y
39
+ ··· + 78084y + 10609)
c
6
, c
8
((y −1)
2
)(y
40
− 21y
39
+ ··· + 389y + 81)
c
7
y
2
(y
40
− 15y
39
+ ··· − 7416y + 1296)
14
