11a
130
(K11a
130
)
A knot diagram
1
Linearized knot diagam
6 1 11 10 2 9 3 5 7 4 8
Solving Sequence
3,11 4,7
8 1 2 10 5 9 6
c
3
c
7
c
11
c
2
c
10
c
4
c
9
c
6
c
1
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h1.08589 × 10
65
u
61
− 2.14541 × 10
65
u
60
+ ··· + 1.37317 × 10
65
b + 1.63028 × 10
65
,
1.15709 × 10
65
u
61
− 2.34918 × 10
65
u
60
+ ··· + 1.37317 × 10
65
a + 1.55380 × 10
65
, u
62
− 2u
61
+ ··· + 2u − 1i
I
u
2
= h3b + 1, 3a + 1, u − 1i
* 2 irreducible components of dim
C
= 0, with total 63 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
= h1.09 × 10
65
u
61
− 2.15 × 10
65
u
60
+ · · · + 1.37 × 10
65
b + 1.63 × 10
65
, 1.16 ×
10
65
u
61
−2.35×10
65
u
60
+· · ·+1.37×10
65
a+1.55×10
65
, u
62
−2u
61
+· · ·+2u−1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
u
a
4
=
1
−u
2
a
7
=
−0.842640u
61
+ 1.71077u
60
+ ··· − 2.66212u − 1.13154
−0.790788u
61
+ 1.56238u
60
+ ··· + 2.05964u − 1.18724
a
8
=
−0.0518518u
61
+ 0.148389u
60
+ ··· − 4.72176u + 0.0556948
−0.790788u
61
+ 1.56238u
60
+ ··· + 2.05964u − 1.18724
a
1
=
0.341402u
61
− 0.580498u
60
+ ··· − 0.691103u + 0.320601
−0.235284u
61
+ 0.469850u
60
+ ··· − 1.26969u − 0.112987
a
2
=
0.252650u
61
− 0.150172u
60
+ ··· + 0.0795973u + 1.03377
−0.109160u
61
− 0.0358719u
60
+ ··· − 0.212253u + 0.116597
a
10
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−0.792952u
61
+ 1.65665u
60
+ ··· − 4.07865u − 1.02885
−0.744507u
61
+ 1.47164u
60
+ ··· + 3.24890u − 1.22506
a
6
=
−0.183781u
61
+ 0.268627u
60
+ ··· + 1.82401u − 0.309920
−0.100621u
61
+ 0.180677u
60
+ ··· − 1.14699u + 0.0882537
a
6
=
−0.183781u
61
+ 0.268627u
60
+ ··· + 1.82401u − 0.309920
−0.100621u
61
+ 0.180677u
60
+ ··· − 1.14699u + 0.0882537
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.87855u
61
+ 4.80262u
60
+ ··· + 9.92096u − 3.84759
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
62
− 2u
61
+ ··· − 2u + 1
c
2
u
62
+ 22u
61
+ ··· − 8u + 1
c
3
, c
4
, c
10
u
62
+ 2u
61
+ ··· − 2u − 1
c
6
, c
9
u
62
+ 2u
61
+ ··· − 4u − 9
c
7
3(3u
62
− 52u
61
+ ··· + 308u + 49)
c
8
3(3u
62
+ 43u
61
+ ··· + 708u − 62)
c
11
u
62
+ 5u
61
+ ··· + 36u + 18
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
62
+ 22y
61
+ ··· − 8y + 1
c
2
y
62
+ 30y
61
+ ··· − 352y + 1
c
3
, c
4
, c
10
y
62
+ 58y
61
+ ··· − 8y + 1
c
6
, c
9
y
62
− 38y
61
+ ··· + 524y + 81
c
7
9(9y
62
− 1042y
61
+ ··· − 72128y + 2401)
c
8
9(9y
62
− 1081y
61
+ ··· + 151348y + 3844)
c
11
y
62
− 9y
61
+ ··· − 180y + 324
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.854708 + 0.475494I
a = −0.501387 + 0.218656I
b = −0.766880 − 1.014110I
5.21542 − 5.84748I 0. + 5.18141I
u = −0.854708 − 0.475494I
a = −0.501387 − 0.218656I
b = −0.766880 + 1.014110I
5.21542 + 5.84748I 0. − 5.18141I
u = 0.786648 + 0.683133I
a = 0.435125 − 0.646494I
b = −0.564398 − 0.724669I
3.00308 − 6.49550I 0
u = 0.786648 − 0.683133I
a = 0.435125 + 0.646494I
b = −0.564398 + 0.724669I
3.00308 + 6.49550I 0
u = 0.828519 + 0.476769I
a = 0.527967 + 0.318651I
b = 0.93975 − 1.10440I
3.57519 + 11.87880I 5.00000 − 8.97401I
u = 0.828519 − 0.476769I
a = 0.527967 − 0.318651I
b = 0.93975 + 1.10440I
3.57519 − 11.87880I 5.00000 + 8.97401I
u = 0.834218 + 0.349760I
a = 0.205591 + 0.243605I
b = 0.939722 − 0.468213I
−2.11951 + 4.18883I 1.15636 − 7.37516I
u = 0.834218 − 0.349760I
a = 0.205591 − 0.243605I
b = 0.939722 + 0.468213I
−2.11951 − 4.18883I 1.15636 + 7.37516I
u = −0.858558 + 0.732202I
a = −0.324943 − 0.468199I
b = 0.329628 − 0.628618I
4.56334 + 0.20821I 0
u = −0.858558 − 0.732202I
a = −0.324943 + 0.468199I
b = 0.329628 + 0.628618I
4.56334 − 0.20821I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.19372
a = −0.137031
b = −0.442772
3.07751 0
u = 0.489192 + 0.594790I
a = −0.182908 − 1.042450I
b = −0.692845 + 0.109180I
−3.46490 + 0.19843I −2.36990 − 1.02428I
u = 0.489192 − 0.594790I
a = −0.182908 + 1.042450I
b = −0.692845 − 0.109180I
−3.46490 − 0.19843I −2.36990 + 1.02428I
u = 0.017185 + 1.247160I
a = 0.162682 − 0.287701I
b = −0.013266 + 1.237940I
1.05860 + 2.54967I 0
u = 0.017185 − 1.247160I
a = 0.162682 + 0.287701I
b = −0.013266 − 1.237940I
1.05860 − 2.54967I 0
u = 0.537923 + 0.421196I
a = −0.66395 − 1.42924I
b = −0.874587 + 0.713367I
−0.54466 + 6.46296I 3.86014 − 8.94603I
u = 0.537923 − 0.421196I
a = −0.66395 + 1.42924I
b = −0.874587 − 0.713367I
−0.54466 − 6.46296I 3.86014 + 8.94603I
u = 0.126822 + 1.321270I
a = 1.46059 − 0.50935I
b = 0.169563 + 0.083121I
−0.24430 + 1.55160I 0
u = 0.126822 − 1.321270I
a = 1.46059 + 0.50935I
b = 0.169563 − 0.083121I
−0.24430 − 1.55160I 0
u = −0.146235 + 1.336670I
a = −1.61705 − 0.58737I
b = −0.154694 − 0.262432I
−0.85413 − 6.64291I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.146235 − 1.336670I
a = −1.61705 + 0.58737I
b = −0.154694 + 0.262432I
−0.85413 + 6.64291I 0
u = 0.056128 + 1.345530I
a = 1.61787 + 0.49934I
b = 1.11617 + 1.02320I
−2.08593 + 1.24865I 0
u = 0.056128 − 1.345530I
a = 1.61787 − 0.49934I
b = 1.11617 − 1.02320I
−2.08593 − 1.24865I 0
u = −0.479881 + 0.382241I
a = 0.86897 − 1.13609I
b = 0.593189 + 0.758731I
0.78887 − 1.60795I 6.50613 + 4.85102I
u = −0.479881 − 0.382241I
a = 0.86897 + 1.13609I
b = 0.593189 − 0.758731I
0.78887 + 1.60795I 6.50613 − 4.85102I
u = −0.024388 + 1.403660I
a = −8.25761 + 1.43088I
b = −8.06787 + 1.51488I
−3.33744 + 1.94948I 0
u = −0.024388 − 1.403660I
a = −8.25761 − 1.43088I
b = −8.06787 − 1.51488I
−3.33744 − 1.94948I 0
u = −0.099048 + 1.403400I
a = −1.84560 − 0.69536I
b = −1.172890 − 0.762039I
−4.73418 − 2.70185I 0
u = −0.099048 − 1.403400I
a = −1.84560 + 0.69536I
b = −1.172890 + 0.762039I
−4.73418 + 2.70185I 0
u = 0.356454 + 1.365780I
a = −0.896048 − 0.640586I
b = −0.915691 − 0.086245I
−4.97349 − 0.07836I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356454 − 1.365780I
a = −0.896048 + 0.640586I
b = −0.915691 + 0.086245I
−4.97349 + 0.07836I 0
u = 0.484112 + 0.293337I
a = −0.371899 + 0.237707I
b = 0.942298 + 0.544052I
−0.34287 − 3.16265I 3.47830 + 1.04615I
u = 0.484112 − 0.293337I
a = −0.371899 − 0.237707I
b = 0.942298 − 0.544052I
−0.34287 + 3.16265I 3.47830 − 1.04615I
u = −0.516231 + 0.142983I
a = 2.34094 − 0.73876I
b = −0.092583 + 0.868567I
3.74985 − 4.26844I 11.92903 + 7.28144I
u = −0.516231 − 0.142983I
a = 2.34094 + 0.73876I
b = −0.092583 − 0.868567I
3.74985 + 4.26844I 11.92903 − 7.28144I
u = −0.17339 + 1.45631I
a = −1.57036 − 0.03554I
b = −0.906111 − 0.957483I
−5.19208 − 4.01888I 0
u = −0.17339 − 1.45631I
a = −1.57036 + 0.03554I
b = −0.906111 + 0.957483I
−5.19208 + 4.01888I 0
u = −0.07310 + 1.46676I
a = −0.785313 − 0.776260I
b = −0.523873 − 1.073670I
−4.86855 − 2.39184I 0
u = −0.07310 − 1.46676I
a = −0.785313 + 0.776260I
b = −0.523873 + 1.073670I
−4.86855 + 2.39184I 0
u = 0.19203 + 1.46284I
a = 1.65883 + 0.15373I
b = 1.03342 − 1.00736I
−6.64439 + 9.14751I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.19203 − 1.46284I
a = 1.65883 − 0.15373I
b = 1.03342 + 1.00736I
−6.64439 − 9.14751I 0
u = 0.506831 + 0.096686I
a = −2.48548 − 0.48498I
b = 0.165777 + 0.615510I
4.11698 − 0.69808I 13.39590 − 0.06993I
u = 0.506831 − 0.096686I
a = −2.48548 + 0.48498I
b = 0.165777 − 0.615510I
4.11698 + 0.69808I 13.39590 + 0.06993I
u = 0.17217 + 1.50217I
a = 1.180340 + 0.239805I
b = 0.973547 − 0.684251I
−10.23620 + 2.66149I 0
u = 0.17217 − 1.50217I
a = 1.180340 − 0.239805I
b = 0.973547 + 0.684251I
−10.23620 − 2.66149I 0
u = 0.30961 + 1.48362I
a = −1.62839 − 0.14045I
b = −1.38181 + 0.69978I
−8.08648 + 8.33462I 0
u = 0.30961 − 1.48362I
a = −1.62839 + 0.14045I
b = −1.38181 − 0.69978I
−8.08648 − 8.33462I 0
u = −0.37255 + 1.47837I
a = 1.073200 − 0.107474I
b = 0.847659 + 0.449176I
−2.26534 − 5.42283I 0
u = −0.37255 − 1.47837I
a = 1.073200 + 0.107474I
b = 0.847659 − 0.449176I
−2.26534 + 5.42283I 0
u = −0.345940 + 0.314360I
a = 0.691718 + 0.084915I
b = −0.339879 + 0.970968I
0.771077 − 1.084410I 6.64507 + 5.83005I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.345940 − 0.314360I
a = 0.691718 − 0.084915I
b = −0.339879 − 0.970968I
0.771077 + 1.084410I 6.64507 − 5.83005I
u = −0.362744 + 0.281740I
a = 1.140060 − 0.294583I
b = 0.206349 + 0.912447I
0.631390 − 1.069140I 6.33384 + 6.12642I
u = −0.362744 − 0.281740I
a = 1.140060 + 0.294583I
b = 0.206349 − 0.912447I
0.631390 + 1.069140I 6.33384 − 6.12642I
u = 0.30069 + 1.51433I
a = −1.84162 + 0.31312I
b = −1.34082 + 1.27068I
−2.8670 + 15.9906I 0
u = 0.30069 − 1.51433I
a = −1.84162 − 0.31312I
b = −1.34082 − 1.27068I
−2.8670 − 15.9906I 0
u = −0.30976 + 1.51386I
a = 1.67471 + 0.29668I
b = 1.18463 + 1.15509I
−1.20729 − 10.07420I 0
u = −0.30976 − 1.51386I
a = 1.67471 − 0.29668I
b = 1.18463 − 1.15509I
−1.20729 + 10.07420I 0
u = −0.061045 + 0.399084I
a = 0.245153 + 0.689749I
b = −0.01690 + 2.26843I
2.17222 + 2.29029I −6.76562 + 2.81680I
u = −0.061045 − 0.399084I
a = 0.245153 − 0.689749I
b = −0.01690 − 2.26843I
2.17222 − 2.29029I −6.76562 − 2.81680I
u = 0.10761 + 1.63393I
a = 0.225146 + 0.198889I
b = 0.322471 − 0.217860I
−5.19332 − 2.98425I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.10761 − 1.63393I
a = 0.225146 − 0.198889I
b = 0.322471 + 0.217860I
−5.19332 + 2.98425I 0
u = 0.336606
a = −2.26896
b = −0.768700
2.13260 1.50210
11
II. I
u
2
= h3b + 1, 3a + 1, u − 1i
(i) Arc colorings
a
3
=
1
0
a
11
=
0
1
a
4
=
1
−1
a
7
=
−0.333333
−0.333333
a
8
=
0
−0.333333
a
1
=
0
1
a
2
=
1
−1
a
10
=
−1
2
a
5
=
2
−3
a
9
=
−1.33333
1.66667
a
6
=
1
−2
a
6
=
1
−2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 19.1111
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
10
u + 1
c
2
, c
3
, c
4
c
5
, c
9
u − 1
c
7
3(3u − 1)
c
8
3(3u − 2)
c
11
u
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
9
, c
10
y −1
c
7
9(9y −1)
c
8
9(9y −4)
c
11
y
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −0.333333
b = −0.333333
3.28987 19.1110
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u + 1)(u
62
− 2u
61
+ ··· − 2u + 1)
c
2
(u − 1)(u
62
+ 22u
61
+ ··· − 8u + 1)
c
3
, c
4
(u − 1)(u
62
+ 2u
61
+ ··· − 2u − 1)
c
5
(u − 1)(u
62
− 2u
61
+ ··· − 2u + 1)
c
6
(u + 1)(u
62
+ 2u
61
+ ··· − 4u − 9)
c
7
9(3u − 1)(3u
62
− 52u
61
+ ··· + 308u + 49)
c
8
9(3u − 2)(3u
62
+ 43u
61
+ ··· + 708u − 62)
c
9
(u − 1)(u
62
+ 2u
61
+ ··· − 4u − 9)
c
10
(u + 1)(u
62
+ 2u
61
+ ··· − 2u − 1)
c
11
u(u
62
+ 5u
61
+ ··· + 36u + 18)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
(y −1)(y
62
+ 22y
61
+ ··· − 8y + 1)
c
2
(y −1)(y
62
+ 30y
61
+ ··· − 352y + 1)
c
3
, c
4
, c
10
(y −1)(y
62
+ 58y
61
+ ··· − 8y + 1)
c
6
, c
9
(y −1)(y
62
− 38y
61
+ ··· + 524y + 81)
c
7
81(9y −1)(9y
62
− 1042y
61
+ ··· − 72128y + 2401)
c
8
81(9y −4)(9y
62
− 1081y
61
+ ··· + 151348y + 3844)
c
11
y(y
62
− 9y
61
+ ··· − 180y + 324)
17
