10
114
(K10a
77
)
A knot diagram
1
Linearized knot diagam
5 6 8 7 9 10 4 1 2 3
Solving Sequence
3,8 1,4
9 7 5 10 6 2
c
3
c
8
c
7
c
4
c
10
c
6
c
2
c
1
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h149u
22
622u
21
+ ··· + 293b 2738, 2738u
22
+ 12647u
21
+ ··· + 2051a + 19961,
u
23
5u
22
+ ··· 46u + 7i
I
u
2
= h−u
14
3u
13
+ ··· + b + 1, u
14
a + u
14
+ ··· a 4,
u
15
+ 3u
14
+ 12u
13
+ 25u
12
+ 52u
11
+ 78u
10
+ 104u
9
+ 109u
8
+ 94u
7
+ 58u
6
+ 24u
5
2u
4
8u
3
4u
2
+ 1i
I
u
3
= hu
5
+ 2u
4
+ 4u
3
+ 4u
2
+ b + 3u + 1, u
7
2u
6
6u
5
7u
4
9u
3
5u
2
+ a 3u + 1,
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1i
I
v
1
= ha, b + 1, v 1i
* 4 irreducible components of dim
C
= 0, with total 62 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
= h149u
22
622u
21
+ · · · + 293b 2738, 2738u
22
+ 12647u
21
+ · · · +
2051a + 19961, u
23
5u
22
+ · · · 46u + 7i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
1
=
1.33496u
22
6.16626u
21
+ ··· + 74.2716u 9.73233
0.508532u
22
+ 2.12287u
21
+ ··· 51.6758u + 9.34471
a
4
=
1
u
2
a
9
=
3.13701u
22
+ 14.7157u
21
+ ··· 146.794u + 20.1351
0.969283u
22
4.75768u
21
+ ··· + 125.167u 21.9590
a
7
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
2u
2
a
10
=
0.826426u
22
4.04339u
21
+ ··· + 22.5958u 0.387616
0.508532u
22
+ 2.12287u
21
+ ··· 51.6758u + 9.34471
a
6
=
1.11555u
22
4.72111u
21
+ ··· + 61.6090u 12.8684
0.436860u
22
0.890785u
21
+ ··· 12.6007u + 4.75085
a
2
=
0.689907u
22
3.07752u
21
+ ··· + 27.7835u 2.87226
0.136519u
22
+ 0.965870u
21
+ ··· 24.8123u + 3.51536
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1041
293
u
22
5380
293
u
21
+ ··· +
116025
293
u
22191
293
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
23
2u
22
+ ··· 2u 1
c
2
, c
5
u
23
u
22
+ ··· u 1
c
3
, c
4
, c
7
u
23
+ 5u
22
+ ··· 46u 7
c
8
, c
10
u
23
+ 2u
22
+ ··· + 14u 1
c
9
u
23
+ 14u
22
+ ··· 43u 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
23
+ 2y
22
+ ··· 12y 1
c
2
, c
5
y
23
9y
22
+ ··· + 25y 1
c
3
, c
4
, c
7
y
23
+ 23y
22
+ ··· + 198y 49
c
8
, c
10
y
23
18y
22
+ ··· + 68y 1
c
9
y
23
+ 26y
21
+ ··· + 225y 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.746057 + 0.716204I
a = 0.944626 + 0.309140I
b = 0.926152 + 0.445909I
1.41145 5.79407I 0.88331 + 5.20349I
u = 0.746057 0.716204I
a = 0.944626 0.309140I
b = 0.926152 0.445909I
1.41145 + 5.79407I 0.88331 5.20349I
u = 0.838014 + 0.461206I
a = 0.68916 + 1.31806I
b = 1.18542 0.78671I
0.67120 + 11.14210I 1.22299 8.55675I
u = 0.838014 0.461206I
a = 0.68916 1.31806I
b = 1.18542 + 0.78671I
0.67120 11.14210I 1.22299 + 8.55675I
u = 0.638103 + 0.842766I
a = 0.134410 + 0.113744I
b = 0.181627 0.040696I
0.67100 2.44356I 2.46207 5.34596I
u = 0.638103 0.842766I
a = 0.134410 0.113744I
b = 0.181627 + 0.040696I
0.67100 + 2.44356I 2.46207 + 5.34596I
u = 0.134358 + 1.265940I
a = 0.552051 + 0.174175I
b = 0.294667 0.675459I
2.55142 2.44221I 0.25016 + 2.15872I
u = 0.134358 1.265940I
a = 0.552051 0.174175I
b = 0.294667 + 0.675459I
2.55142 + 2.44221I 0.25016 2.15872I
u = 0.571973 + 0.376783I
a = 0.67318 1.94063I
b = 1.116240 + 0.856342I
1.92126 + 3.42239I 4.06899 7.96024I
u = 0.571973 0.376783I
a = 0.67318 + 1.94063I
b = 1.116240 0.856342I
1.92126 3.42239I 4.06899 + 7.96024I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.024762 + 1.413530I
a = 0.463614 0.845353I
b = 1.206410 + 0.634398I
6.65304 0.20600I 5.87376 0.49624I
u = 0.024762 1.413530I
a = 0.463614 + 0.845353I
b = 1.206410 0.634398I
6.65304 + 0.20600I 5.87376 + 0.49624I
u = 0.26611 + 1.40784I
a = 0.095717 0.962667I
b = 1.380760 + 0.121423I
7.16412 + 2.89840I 6.40584 0.61240I
u = 0.26611 1.40784I
a = 0.095717 + 0.962667I
b = 1.380760 0.121423I
7.16412 2.89840I 6.40584 + 0.61240I
u = 0.541870
a = 0.563072
b = 0.305112
1.26878 7.95590
u = 0.476919 + 0.256901I
a = 1.77295 0.55054I
b = 0.986987 0.192913I
1.97196 0.18097I 4.00287 0.43243I
u = 0.476919 0.256901I
a = 1.77295 + 0.55054I
b = 0.986987 + 0.192913I
1.97196 + 0.18097I 4.00287 + 0.43243I
u = 0.21309 + 1.44798I
a = 0.594646 1.149250I
b = 1.53737 + 1.10594I
7.80750 + 6.31614I 8.73055 7.98600I
u = 0.21309 1.44798I
a = 0.594646 + 1.149250I
b = 1.53737 1.10594I
7.80750 6.31614I 8.73055 + 7.98600I
u = 0.30585 + 1.51255I
a = 0.399853 + 1.070490I
b = 1.49687 0.93220I
7.0586 + 15.3049I 1.91417 8.23545I
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.30585 1.51255I
a = 0.399853 1.070490I
b = 1.49687 + 0.93220I
7.0586 15.3049I 1.91417 + 8.23545I
u = 0.15014 + 1.58348I
a = 0.068059 + 0.631954I
b = 0.990467 0.202654I
9.33057 2.66158I 5.53368 + 3.29637I
u = 0.15014 1.58348I
a = 0.068059 0.631954I
b = 0.990467 + 0.202654I
9.33057 + 2.66158I 5.53368 3.29637I
7
II.
I
u
2
= h−u
14
3u
13
+· · ·+b+1, u
14
a+u
14
+· · ·a4, u
15
+3u
14
+· · ·4u
2
+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
1
=
a
u
14
+ 3u
13
+ ··· u 1
a
4
=
1
u
2
a
9
=
u
14
a + u
14
+ ··· a 1
1
a
7
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
2u
2
a
10
=
u
14
+ 3u
13
+ ··· + a 1
u
14
+ 3u
13
+ ··· u 1
a
6
=
u
14
+ 3u
13
+ ··· a 2
u
12
a 3u
11
a + ··· + 2u + 1
a
2
=
u
14
+ 3u
13
+ ··· + a 1
u
8
a + u
8
+ ··· + au 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
14
+ 4u
13
+ 24u
12
+ 12u
11
+ 32u
10
24u
9
56u
8
136u
7
172u
6
184u
5
124u
4
72u
3
8u
2
+ 16u + 10
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
30
+ u
29
+ ··· + 16u + 1
c
2
, c
5
u
30
+ u
29
+ ··· 6u 1
c
3
, c
4
, c
7
(u
15
3u
14
+ ··· + 4u
2
1)
2
c
8
, c
10
u
30
u
29
+ ··· 6u 11
c
9
(u
15
7u
14
+ ··· + 4u
2
1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
30
+ 3y
29
+ ··· 92y + 1
c
2
, c
5
y
30
+ 7y
29
+ ··· 48y + 1
c
3
, c
4
, c
7
(y
15
+ 15y
14
+ ··· + 8y 1)
2
c
8
, c
10
y
30
+ 3y
29
+ ··· 1972y + 121
c
9
(y
15
y
14
+ ··· + 8y 1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.825834 + 0.538674I
a = 0.428447 + 0.718077I
b = 0.476814 0.494120I
1.13071 2.72262I 11.6934 + 8.2204I
u = 0.825834 + 0.538674I
a = 0.131251 0.683941I
b = 0.740636 + 0.362219I
1.13071 2.72262I 11.6934 + 8.2204I
u = 0.825834 0.538674I
a = 0.428447 0.718077I
b = 0.476814 + 0.494120I
1.13071 + 2.72262I 11.6934 8.2204I
u = 0.825834 0.538674I
a = 0.131251 + 0.683941I
b = 0.740636 0.362219I
1.13071 + 2.72262I 11.6934 8.2204I
u = 0.000696 + 1.255430I
a = 0.900707 0.205837I
b = 1.247670 0.599225I
1.82383 2.53738I 2.44510 + 1.72215I
u = 0.000696 + 1.255430I
a = 0.476757 + 0.994088I
b = 0.259040 1.130630I
1.82383 2.53738I 2.44510 + 1.72215I
u = 0.000696 1.255430I
a = 0.900707 + 0.205837I
b = 1.247670 + 0.599225I
1.82383 + 2.53738I 2.44510 1.72215I
u = 0.000696 1.255430I
a = 0.476757 0.994088I
b = 0.259040 + 1.130630I
1.82383 + 2.53738I 2.44510 1.72215I
u = 0.374558 + 0.641779I
a = 0.471003 + 0.871968I
b = 0.877609 0.842947I
1.31377 3.39671I 3.52800 + 8.19673I
u = 0.374558 + 0.641779I
a = 0.38443 1.59182I
b = 0.736028 + 0.024323I
1.31377 3.39671I 3.52800 + 8.19673I
11
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.374558 0.641779I
a = 0.471003 0.871968I
b = 0.877609 + 0.842947I
1.31377 + 3.39671I 3.52800 8.19673I
u = 0.374558 0.641779I
a = 0.38443 + 1.59182I
b = 0.736028 0.024323I
1.31377 + 3.39671I 3.52800 8.19673I
u = 0.678314
a = 1.44772
b = 0.327578
1.01641 9.27190
u = 0.678314
a = 0.482930
b = 0.982011
1.01641 9.27190
u = 0.100337 + 1.375660I
a = 0.268106 0.521008I
b = 0.27520 + 2.16220I
3.32174 + 5.59550I 0.66951 7.79345I
u = 0.100337 + 1.375660I
a = 1.57796 + 0.08496I
b = 0.689826 + 0.421097I
3.32174 + 5.59550I 0.66951 7.79345I
u = 0.100337 1.375660I
a = 0.268106 + 0.521008I
b = 0.27520 2.16220I
3.32174 5.59550I 0.66951 + 7.79345I
u = 0.100337 1.375660I
a = 1.57796 0.08496I
b = 0.689826 0.421097I
3.32174 5.59550I 0.66951 + 7.79345I
u = 0.15235 + 1.51729I
a = 0.516022 1.130560I
b = 0.789858 + 0.466052I
8.32063 5.47678I 8.29813 + 5.38780I
u = 0.15235 + 1.51729I
a = 0.252346 + 0.545908I
b = 1.63678 0.95520I
8.32063 5.47678I 8.29813 + 5.38780I
12
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.15235 1.51729I
a = 0.516022 + 1.130560I
b = 0.789858 0.466052I
8.32063 + 5.47678I 8.29813 5.38780I
u = 0.15235 1.51729I
a = 0.252346 0.545908I
b = 1.63678 + 0.95520I
8.32063 + 5.47678I 8.29813 5.38780I
u = 0.29798 + 1.53037I
a = 0.439615 0.718620I
b = 1.181030 + 0.498484I
5.55973 6.84757I 1.00546 + 10.27446I
u = 0.29798 + 1.53037I
a = 0.169055 + 0.804639I
b = 0.968761 0.886910I
5.55973 6.84757I 1.00546 + 10.27446I
u = 0.29798 1.53037I
a = 0.439615 + 0.718620I
b = 1.181030 0.498484I
5.55973 + 6.84757I 1.00546 10.27446I
u = 0.29798 1.53037I
a = 0.169055 0.804639I
b = 0.968761 + 0.886910I
5.55973 + 6.84757I 1.00546 10.27446I
u = 0.388845 + 0.104061I
a = 0.40559 2.33647I
b = 0.51204 + 1.36623I
1.42898 + 3.92960I 9.71569 7.98755I
u = 0.388845 + 0.104061I
a = 2.10625 2.94990I
b = 0.400846 + 0.866321I
1.42898 + 3.92960I 9.71569 7.98755I
u = 0.388845 0.104061I
a = 0.40559 + 2.33647I
b = 0.51204 1.36623I
1.42898 3.92960I 9.71569 + 7.98755I
u = 0.388845 0.104061I
a = 2.10625 + 2.94990I
b = 0.400846 0.866321I
1.42898 3.92960I 9.71569 + 7.98755I
13
III. I
u
3
=
hu
5
+2u
4
+4u
3
+4u
2
+b+3u+1, u
7
2u
6
+· · ·+a+1, u
8
+2u
7
+· · ·+2u+1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
1
=
u
7
+ 2u
6
+ 6u
5
+ 7u
4
+ 9u
3
+ 5u
2
+ 3u 1
u
5
2u
4
4u
3
4u
2
3u 1
a
4
=
1
u
2
a
9
=
u
7
2u
6
5u
5
7u
4
8u
3
7u
2
5u 2
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u + 1
a
7
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
2u
2
a
10
=
u
7
+ 2u
6
+ 5u
5
+ 5u
4
+ 5u
3
+ u
2
2
u
5
2u
4
4u
3
4u
2
3u 1
a
6
=
u
7
2u
6
6u
5
8u
4
11u
3
8u
2
6u
u
3
+ u
2
+ 2u + 1
a
2
=
u
7
+ 2u
6
+ 5u
5
+ 6u
4
+ 6u
3
+ 3u
2
+ u 1
u
6
2u
5
5u
4
6u
3
6u
2
4u 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
7
u
6
3u
5
+ 8u
4
+ 17u
3
+ 19u
2
+ 18u + 5
14
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
8
u
7
+ 2u
6
u
5
+ 2u
4
u
3
+ 2u
2
+ 1
c
2
, c
5
u
8
+ 2u
6
+ u
5
+ 2u
4
+ u
3
+ 2u
2
+ u + 1
c
3
, c
4
u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1
c
7
u
8
2u
7
+ 6u
6
8u
5
+ 11u
4
9u
3
+ 7u
2
2u + 1
c
8
, c
10
u
8
3u
7
+ 6u
6
9u
5
+ 12u
4
11u
3
+ 8u
2
4u + 1
c
9
u
8
+ 5u
7
+ 13u
6
+ 20u
5
+ 22u
4
+ 18u
3
+ 12u
2
+ 5u + 1
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
8
+ 3y
7
+ 6y
6
+ 9y
5
+ 12y
4
+ 11y
3
+ 8y
2
+ 4y + 1
c
2
, c
5
y
8
+ 4y
7
+ 8y
6
+ 11y
5
+ 12y
4
+ 9y
3
+ 6y
2
+ 3y + 1
c
3
, c
4
, c
7
y
8
+ 8y
7
+ 26y
6
+ 46y
5
+ 55y
4
+ 53y
3
+ 35y
2
+ 10y + 1
c
8
, c
10
y
8
+ 3y
7
+ 6y
6
+ 13y
5
+ 20y
4
+ 11y
3
+ 1
c
9
y
8
+ y
7
+ 13y
6
+ 16y
5
+ 28y
4
+ 30y
3
+ 8y
2
y + 1
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
1(vol +
1CS) Cusp shape
u = 0.768546 + 0.720795I
a = 0.216551 + 0.549851I
b = 0.562759 0.266496I
0.48271 2.83701I 5.21159 + 10.60912I
u = 0.768546 0.720795I
a = 0.216551 0.549851I
b = 0.562759 + 0.266496I
0.48271 + 2.83701I 5.21159 10.60912I
u = 0.024235 + 1.274500I
a = 0.986575 0.224172I
b = 0.309617 + 1.251960I
2.47121 + 3.78237I 0.87896 6.92362I
u = 0.024235 1.274500I
a = 0.986575 + 0.224172I
b = 0.309617 1.251960I
2.47121 3.78237I 0.87896 + 6.92362I
u = 0.057100 + 0.488588I
a = 1.72754 + 0.48541I
b = 0.138522 0.871772I
0.43885 3.70343I 0.65225 + 5.99436I
u = 0.057100 0.488588I
a = 1.72754 0.48541I
b = 0.138522 + 0.871772I
0.43885 + 3.70343I 0.65225 5.99436I
u = 0.19859 + 1.50044I
a = 0.475588 + 0.801618I
b = 1.108340 0.872786I
6.67501 5.79166I 2.06170 + 5.06823I
u = 0.19859 1.50044I
a = 0.475588 0.801618I
b = 1.108340 + 0.872786I
6.67501 + 5.79166I 2.06170 5.06823I
17
IV. I
v
1
= ha, b + 1, v 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
1
0
a
1
=
0
1
a
4
=
1
0
a
9
=
1
1
a
7
=
1
0
a
5
=
1
0
a
10
=
1
1
a
6
=
2
1
a
2
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
, c
10
u + 1
c
3
, c
4
, c
7
c
9
u
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
6
, c
8
, c
10
y 1
c
3
, c
4
, c
7
c
9
y
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 0
b = 1.00000
1.64493 6.00000
21
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
(u + 1)(u
8
u
7
+ ··· + 2u
2
+ 1)(u
23
2u
22
+ ··· 2u 1)
· (u
30
+ u
29
+ ··· + 16u + 1)
c
2
, c
5
(u + 1)(u
8
+ 2u
6
+ ··· + u + 1)(u
23
u
22
+ ··· u 1)
· (u
30
+ u
29
+ ··· 6u 1)
c
3
, c
4
u(u
8
+ 2u
7
+ 6u
6
+ 8u
5
+ 11u
4
+ 9u
3
+ 7u
2
+ 2u + 1)
· ((u
15
3u
14
+ ··· + 4u
2
1)
2
)(u
23
+ 5u
22
+ ··· 46u 7)
c
7
u(u
8
2u
7
+ 6u
6
8u
5
+ 11u
4
9u
3
+ 7u
2
2u + 1)
· ((u
15
3u
14
+ ··· + 4u
2
1)
2
)(u
23
+ 5u
22
+ ··· 46u 7)
c
8
, c
10
(u + 1)(u
8
3u
7
+ 6u
6
9u
5
+ 12u
4
11u
3
+ 8u
2
4u + 1)
· (u
23
+ 2u
22
+ ··· + 14u 1)(u
30
u
29
+ ··· 6u 11)
c
9
u(u
8
+ 5u
7
+ 13u
6
+ 20u
5
+ 22u
4
+ 18u
3
+ 12u
2
+ 5u + 1)
· ((u
15
7u
14
+ ··· + 4u
2
1)
2
)(u
23
+ 14u
22
+ ··· 43u 7)
22
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y 1)(y
8
+ 3y
7
+ 6y
6
+ 9y
5
+ 12y
4
+ 11y
3
+ 8y
2
+ 4y + 1)
· (y
23
+ 2y
22
+ ··· 12y 1)(y
30
+ 3y
29
+ ··· 92y + 1)
c
2
, c
5
(y 1)(y
8
+ 4y
7
+ 8y
6
+ 11y
5
+ 12y
4
+ 9y
3
+ 6y
2
+ 3y + 1)
· (y
23
9y
22
+ ··· + 25y 1)(y
30
+ 7y
29
+ ··· 48y + 1)
c
3
, c
4
, c
7
y(y
8
+ 8y
7
+ 26y
6
+ 46y
5
+ 55y
4
+ 53y
3
+ 35y
2
+ 10y + 1)
· ((y
15
+ 15y
14
+ ··· + 8y 1)
2
)(y
23
+ 23y
22
+ ··· + 198y 49)
c
8
, c
10
(y 1)(y
8
+ 3y
7
+ 6y
6
+ 13y
5
+ 20y
4
+ 11y
3
+ 1)
· (y
23
18y
22
+ ··· + 68y 1)(y
30
+ 3y
29
+ ··· 1972y + 121)
c
9
y(y
8
+ y
7
+ 13y
6
+ 16y
5
+ 28y
4
+ 30y
3
+ 8y
2
y + 1)
· ((y
15
y
14
+ ··· + 8y 1)
2
)(y
23
+ 26y
21
+ ··· + 225y 49)
23