11a
292
(K11a
292
)
A knot diagram
1
Linearized knot diagam
8 5 1 9 2 11 10 3 6 7 4
Solving Sequence
6,11 2,7
5 3 10 8 1 9 4
c
6
c
5
c
2
c
10
c
7
c
1
c
9
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h14579744602u
24
+ 15331471056u
23
+ ··· + 396477743843b − 332846474137,
362005963341u
24
− 27656036296u
23
+ ··· + 1585910975372a − 1558403855541,
u
25
+ 11u
23
+ ··· + 5u − 4i
I
u
2
= h8u
20
a − 2u
20
+ ··· − a − 2, −2u
20
a + 3u
20
+ ··· + a
2
+ 10, u
21
+ u
20
+ ··· − u − 1i
I
u
3
= hb + 1, 2u
2
+ 2a − 2u + 5, u
3
− u
2
+ 2u − 1i
* 3 irreducible components of dim
C
= 0, with total 70 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
=
h1.46×10
10
u
24
+1.53×10
10
u
23
+· · ·+3.96×10
11
b−3.33×10
11
, 3.62×10
11
u
24
−
2.77 × 10
10
u
23
+ · · · + 1.59 × 10
12
a − 1.56 × 10
12
, u
25
+ 11u
23
+ · · · + 5u − 4i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−0.228264u
24
+ 0.0174386u
23
+ ··· − 4.67501u + 0.982655
−0.0367732u
24
− 0.0386692u
23
+ ··· − 1.61229u + 0.839509
a
7
=
1
u
2
a
5
=
0.244682u
24
− 0.0104806u
23
+ ··· + 4.92670u − 0.639254
0.0214093u
24
+ 0.0107022u
23
+ ··· + 2.37619u − 0.880534
a
3
=
−0.454939u
24
+ 0.0416564u
23
+ ··· − 8.69816u + 2.21103
−0.0416564u
24
− 0.0575212u
23
+ ··· − 4.48573u + 1.81976
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−0.220134u
24
+ 0.0214093u
23
+ ··· − 4.11288u + 1.27552
−0.0104806u
24
− 0.00911491u
23
+ ··· − 1.86266u + 0.978727
a
9
=
u
3
+ 2u
u
3
+ u
a
4
=
0.209877u
24
− 0.0367732u
23
+ ··· + 4.36887u − 0.562901
0.0174386u
24
+ 0.0197581u
23
+ ··· + 2.12397u − 0.913055
a
4
=
0.209877u
24
− 0.0367732u
23
+ ··· + 4.36887u − 0.562901
0.0174386u
24
+ 0.0197581u
23
+ ··· + 2.12397u − 0.913055
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
318615294651
396477743843
u
24
−
34664114752
396477743843
u
23
+ ··· +
10688164272079
1585910975372
u −
7965281676665
396477743843
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
8(8u
25
− 4u
24
+ ··· + 2u + 1)
c
2
, c
3
, c
5
c
11
u
25
+ 3u
24
+ ··· + 3u + 1
c
6
, c
7
, c
10
u
25
+ 11u
23
+ ··· + 5u + 4
c
8
u
25
+ 3u
24
+ ··· + 352u + 128
c
9
u
25
− u
23
+ ··· + 797u + 292
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
64(64y
25
+ 240y
24
+ ··· + 16y −1)
c
2
, c
3
, c
5
c
11
y
25
+ 11y
24
+ ··· + 3y −1
c
6
, c
7
, c
10
y
25
+ 22y
24
+ ··· + 241y −16
c
8
y
25
+ 7y
24
+ ··· − 84992y −16384
c
9
y
25
− 2y
24
+ ··· + 1188257y −85264
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.548894 + 0.797398I
a = −0.101206 − 0.491260I
b = −0.474580 − 1.242550I
5.61589 − 7.41862I −5.99307 + 4.17618I
u = −0.548894 − 0.797398I
a = −0.101206 + 0.491260I
b = −0.474580 + 1.242550I
5.61589 + 7.41862I −5.99307 − 4.17618I
u = 0.706370 + 0.548812I
a = 0.798029 − 0.174639I
b = 0.263483 + 0.886965I
0.86744 − 3.46984I −11.3753 + 9.7737I
u = 0.706370 − 0.548812I
a = 0.798029 + 0.174639I
b = 0.263483 − 0.886965I
0.86744 + 3.46984I −11.3753 − 9.7737I
u = 0.858910 + 0.133092I
a = −0.566243 − 0.452994I
b = −0.131692 − 0.750408I
−0.421269 − 1.124170I −15.1711 + 4.4746I
u = 0.858910 − 0.133092I
a = −0.566243 + 0.452994I
b = −0.131692 + 0.750408I
−0.421269 + 1.124170I −15.1711 − 4.4746I
u = −0.809123 + 0.315012I
a = −1.88500 + 0.57325I
b = −0.546754 + 1.295430I
4.07653 + 12.13020I −8.33349 − 8.34430I
u = −0.809123 − 0.315012I
a = −1.88500 − 0.57325I
b = −0.546754 − 1.295430I
4.07653 − 12.13020I −8.33349 + 8.34430I
u = −0.156187 + 1.202150I
a = 1.122910 + 0.745988I
b = 0.946754 − 0.548140I
0.27538 + 2.19318I −11.91071 + 0.36993I
u = −0.156187 − 1.202150I
a = 1.122910 − 0.745988I
b = 0.946754 + 0.548140I
0.27538 − 2.19318I −11.91071 − 0.36993I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.223868 + 1.253510I
a = −0.470162 + 0.030904I
b = −0.238848 + 0.287288I
2.68775 − 2.30692I −5.11682 + 1.56003I
u = 0.223868 − 1.253510I
a = −0.470162 − 0.030904I
b = −0.238848 − 0.287288I
2.68775 + 2.30692I −5.11682 − 1.56003I
u = 0.471042 + 1.205750I
a = −0.864543 + 0.069126I
b = −0.306312 − 0.956199I
3.65181 − 5.92897I −7.49144 + 10.01248I
u = 0.471042 − 1.205750I
a = −0.864543 − 0.069126I
b = −0.306312 + 0.956199I
3.65181 + 5.92897I −7.49144 − 10.01248I
u = −0.223600 + 1.354960I
a = 0.469907 + 0.958847I
b = 1.330580 + 0.239812I
1.78338 + 3.43475I −2.55385 − 7.61768I
u = −0.223600 − 1.354960I
a = 0.469907 − 0.958847I
b = 1.330580 − 0.239812I
1.78338 − 3.43475I −2.55385 + 7.61768I
u = −0.583764 + 0.120670I
a = 2.27131 + 0.85488I
b = 1.134100 + 0.298870I
−2.92328 + 0.50544I −12.3574 − 10.8616I
u = −0.583764 − 0.120670I
a = 2.27131 − 0.85488I
b = 1.134100 − 0.298870I
−2.92328 − 0.50544I −12.3574 + 10.8616I
u = −0.32151 + 1.44044I
a = −1.66224 − 0.76899I
b = −0.57182 + 1.34966I
9.6840 + 16.2255I −4.63027 − 8.78327I
u = −0.32151 − 1.44044I
a = −1.66224 + 0.76899I
b = −0.57182 − 1.34966I
9.6840 − 16.2255I −4.63027 + 8.78327I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.29535 + 1.50905I
a = 0.856616 − 0.740944I
b = 0.284532 + 1.100380I
7.47014 − 7.28043I −3.70614 + 9.00978I
u = 0.29535 − 1.50905I
a = 0.856616 + 0.740944I
b = 0.284532 − 1.100380I
7.47014 + 7.28043I −3.70614 − 9.00978I
u = −0.05465 + 1.54501I
a = 0.003062 + 0.744056I
b = −0.323896 − 1.309710I
13.5945 − 5.6631I −1.19159 + 4.67130I
u = −0.05465 − 1.54501I
a = 0.003062 − 0.744056I
b = −0.323896 + 1.309710I
13.5945 + 5.6631I −1.19159 − 4.67130I
u = 0.284375
a = −0.694884
b = 0.268925
−0.608310 −16.5880
7
II. I
u
2
=
h8u
20
a−2u
20
+· · ·−a−2, −2u
20
a+3u
20
+· · ·+a
2
+10, u
21
+u
20
+· · ·−u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
a
−
8
9
u
20
a +
2
9
u
20
+ ··· +
1
9
a +
2
9
a
7
=
1
u
2
a
5
=
2
9
u
20
a −
14
9
u
20
+ ··· +
2
9
a −
5
9
−
4
9
u
20
a −
8
9
u
20
+ ··· +
5
9
a +
10
9
a
3
=
−u
20
− 9u
18
+ ··· − u
2
+ 1
−u
20
− u
19
+ ··· − u
2
+ 1
a
10
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−
5
9
u
20
a +
8
9
u
20
+ ··· +
4
9
a −
1
9
−
11
9
u
20
a +
5
9
u
20
+ ··· −
2
9
a −
4
9
a
9
=
u
3
+ 2u
u
3
+ u
a
4
=
−
1
9
u
20
a −
2
9
u
20
+ ··· +
8
9
a +
7
9
2u
20
+ 2u
19
+ ··· + 2u + 2
a
4
=
−
1
9
u
20
a −
2
9
u
20
+ ··· +
8
9
a +
7
9
2u
20
+ 2u
19
+ ··· + 2u + 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
19
− 4u
18
− 36u
17
− 32u
16
− 132u
15
− 100u
14
− 244u
13
−
140u
12
− 216u
11
− 52u
10
− 40u
9
+ 68u
8
+ 56u
7
+ 52u
6
− 12u
4
− 36u
3
− 12u
2
− 8u − 6
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
42
− u
41
+ ··· + 2496u + 1081
c
2
, c
3
, c
5
c
11
u
42
− 7u
41
+ ··· − 2u + 1
c
6
, c
7
, c
10
(u
21
− u
20
+ ··· − u + 1)
2
c
8
(u
21
− u
20
+ ··· + u − 1)
2
c
9
(u
21
+ u
20
+ ··· − 3u + 1)
2
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
42
+ 19y
41
+ ··· + 26506988y + 1168561
c
2
, c
3
, c
5
c
11
y
42
+ 27y
41
+ ··· + 26y
2
+ 1
c
6
, c
7
, c
10
(y
21
+ 19y
20
+ ··· + 3y −1)
2
c
8
(y
21
+ 7y
20
+ ··· + 3y −1)
2
c
9
(y
21
− y
20
+ ··· + 3y −1)
2
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.199184 + 0.953331I
a = −0.631854 − 0.459630I
b = −0.518967 + 0.275770I
1.91999 − 2.68588I −9.85070 + 3.67518I
u = 0.199184 + 0.953331I
a = 0.378897 + 0.152272I
b = 0.359361 + 0.936794I
1.91999 − 2.68588I −9.85070 + 3.67518I
u = 0.199184 − 0.953331I
a = −0.631854 + 0.459630I
b = −0.518967 − 0.275770I
1.91999 + 2.68588I −9.85070 − 3.67518I
u = 0.199184 − 0.953331I
a = 0.378897 − 0.152272I
b = 0.359361 − 0.936794I
1.91999 + 2.68588I −9.85070 − 3.67518I
u = −0.268883 + 0.739769I
a = −0.921198 − 0.860900I
b = −0.764352 + 0.086691I
2.12997 − 2.73152I −8.80842 + 2.00184I
u = −0.268883 + 0.739769I
a = −0.108391 + 0.403964I
b = 0.423673 + 1.154260I
2.12997 − 2.73152I −8.80842 + 2.00184I
u = −0.268883 − 0.739769I
a = −0.921198 + 0.860900I
b = −0.764352 − 0.086691I
2.12997 + 2.73152I −8.80842 − 2.00184I
u = −0.268883 − 0.739769I
a = −0.108391 − 0.403964I
b = 0.423673 − 1.154260I
2.12997 + 2.73152I −8.80842 − 2.00184I
u = −0.721828 + 0.253446I
a = −1.72355 − 0.58410I
b = −1.029770 − 0.113619I
0.38553 + 6.51836I −11.49661 − 6.69162I
u = −0.721828 + 0.253446I
a = 2.02082 − 0.78488I
b = 0.580475 − 1.281080I
0.38553 + 6.51836I −11.49661 − 6.69162I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.721828 − 0.253446I
a = −1.72355 + 0.58410I
b = −1.029770 + 0.113619I
0.38553 − 6.51836I −11.49661 + 6.69162I
u = −0.721828 − 0.253446I
a = 2.02082 + 0.78488I
b = 0.580475 + 1.281080I
0.38553 − 6.51836I −11.49661 + 6.69162I
u = 0.708881 + 0.196468I
a = −1.228480 − 0.496280I
b = −0.135993 − 0.853092I
−0.369814 − 0.901098I −13.44354 + 1.25880I
u = 0.708881 + 0.196468I
a = 0.072151 + 0.168216I
b = 0.193105 − 0.268938I
−0.369814 − 0.901098I −13.44354 + 1.25880I
u = 0.708881 − 0.196468I
a = −1.228480 + 0.496280I
b = −0.135993 + 0.853092I
−0.369814 + 0.901098I −13.44354 − 1.25880I
u = 0.708881 − 0.196468I
a = 0.072151 − 0.168216I
b = 0.193105 + 0.268938I
−0.369814 + 0.901098I −13.44354 − 1.25880I
u = 0.161237 + 1.327480I
a = 2.14675 − 0.60357I
b = 0.215364 − 0.842067I
6.68759 − 2.26276I −8.12423 + 3.11409I
u = 0.161237 + 1.327480I
a = 0.45038 − 2.86282I
b = 0.077855 + 1.154110I
6.68759 − 2.26276I −8.12423 + 3.11409I
u = 0.161237 − 1.327480I
a = 2.14675 + 0.60357I
b = 0.215364 + 0.842067I
6.68759 + 2.26276I −8.12423 − 3.11409I
u = 0.161237 − 1.327480I
a = 0.45038 + 2.86282I
b = 0.077855 − 1.154110I
6.68759 + 2.26276I −8.12423 − 3.11409I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.520195 + 0.340511I
a = −0.049542 − 1.209510I
b = −0.354858 − 1.344690I
5.31141 + 1.59690I −4.86726 − 4.73829I
u = −0.520195 + 0.340511I
a = −2.65329 + 0.61691I
b = −0.538046 + 1.172550I
5.31141 + 1.59690I −4.86726 − 4.73829I
u = −0.520195 − 0.340511I
a = −0.049542 + 1.209510I
b = −0.354858 + 1.344690I
5.31141 − 1.59690I −4.86726 + 4.73829I
u = −0.520195 − 0.340511I
a = −2.65329 − 0.61691I
b = −0.538046 − 1.172550I
5.31141 − 1.59690I −4.86726 + 4.73829I
u = 0.280467 + 1.374360I
a = 0.312181 + 0.269648I
b = 0.406166 − 0.029756I
4.61079 − 4.48385I −8.56586 + 2.47352I
u = 0.280467 + 1.374360I
a = −1.52575 + 0.72271I
b = −0.211636 − 1.044900I
4.61079 − 4.48385I −8.56586 + 2.47352I
u = 0.280467 − 1.374360I
a = 0.312181 − 0.269648I
b = 0.406166 + 0.029756I
4.61079 + 4.48385I −8.56586 − 2.47352I
u = 0.280467 − 1.374360I
a = −1.52575 − 0.72271I
b = −0.211636 + 1.044900I
4.61079 + 4.48385I −8.56586 − 2.47352I
u = −0.085311 + 1.403890I
a = −0.476783 − 0.880832I
b = 0.23480 + 1.42238I
8.43398 − 1.80763I −3.74093 + 2.73625I
u = −0.085311 + 1.403890I
a = −0.310639 − 0.651382I
b = −0.881295 − 0.383290I
8.43398 − 1.80763I −3.74093 + 2.73625I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.085311 − 1.403890I
a = −0.476783 + 0.880832I
b = 0.23480 − 1.42238I
8.43398 + 1.80763I −3.74093 − 2.73625I
u = −0.085311 − 1.403890I
a = −0.310639 + 0.651382I
b = −0.881295 + 0.383290I
8.43398 + 1.80763I −3.74093 − 2.73625I
u = −0.20569 + 1.41170I
a = 0.479429 + 0.350972I
b = −0.41262 − 1.50197I
10.87740 + 4.29720I −1.24857 − 3.93304I
u = −0.20569 + 1.41170I
a = −1.63387 − 0.79459I
b = −0.70246 + 1.26246I
10.87740 + 4.29720I −1.24857 − 3.93304I
u = −0.20569 − 1.41170I
a = 0.479429 − 0.350972I
b = −0.41262 + 1.50197I
10.87740 − 4.29720I −1.24857 + 3.93304I
u = −0.20569 − 1.41170I
a = −1.63387 + 0.79459I
b = −0.70246 − 1.26246I
10.87740 − 4.29720I −1.24857 + 3.93304I
u = −0.28719 + 1.40273I
a = −0.607054 − 0.791979I
b = −1.149010 − 0.072988I
5.66073 + 10.18330I −6.74618 − 7.21296I
u = −0.28719 + 1.40273I
a = 1.67005 + 0.78565I
b = 0.61911 − 1.37353I
5.66073 + 10.18330I −6.74618 − 7.21296I
u = −0.28719 − 1.40273I
a = −0.607054 + 0.791979I
b = −1.149010 + 0.072988I
5.66073 − 10.18330I −6.74618 + 7.21296I
u = −0.28719 − 1.40273I
a = 1.67005 − 0.78565I
b = 0.61911 + 1.37353I
5.66073 − 10.18330I −6.74618 + 7.21296I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.478663
a = 5.33975 + 3.09458I
b = 0.089091 − 1.011840I
2.46606 −16.2150
u = 0.478663
a = 5.33975 − 3.09458I
b = 0.089091 + 1.011840I
2.46606 −16.2150
15
III. I
u
3
= hb + 1, 2u
2
+ 2a − 2u + 5, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
2
=
−u
2
+ u −
5
2
−1
a
7
=
1
u
2
a
5
=
−u
2
+ u −
3
2
−1
a
3
=
−2u
2
+ 2u − 4
−2
a
10
=
u
u
2
− u + 1
a
8
=
u
2
+ 1
u
2
− u + 1
a
1
=
−u
2
+ u − 2
1
2
u − 1
a
9
=
u
2
+ 1
u
2
− u + 1
a
4
=
−u
2
+ u − 2
−
1
2
u − 1
a
4
=
−u
2
+ u − 2
−
1
2
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =
1
4
u − 10
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
8(8u
3
− 4u
2
+ 1)
c
2
, c
11
(u − 1)
3
c
3
, c
5
(u + 1)
3
c
4
8(8u
3
+ 4u
2
− 1)
c
6
, c
7
u
3
− u
2
+ 2u − 1
c
8
u
3
c
9
u
3
− u
2
+ 1
c
10
u
3
+ u
2
+ 2u + 1
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
64(64y
3
− 16y
2
+ 8y −1)
c
2
, c
3
, c
5
c
11
(y −1)
3
c
6
, c
7
, c
10
y
3
+ 3y
2
+ 2y −1
c
8
y
3
c
9
y
3
− y
2
+ 2y −1
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.622561 + 0.744862I
b = −1.00000
1.37919 − 2.82812I −9.94623 + 0.32679I
u = 0.215080 − 1.307140I
a = −0.622561 − 0.744862I
b = −1.00000
1.37919 + 2.82812I −9.94623 − 0.32679I
u = 0.569840
a = −2.25488
b = −1.00000
−2.75839 −9.85750
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
64(8u
3
− 4u
2
+ 1)(8u
25
− 4u
24
+ ··· + 2u + 1)
· (u
42
− u
41
+ ··· + 2496u + 1081)
c
2
, c
11
((u − 1)
3
)(u
25
+ 3u
24
+ ··· + 3u + 1)(u
42
− 7u
41
+ ··· − 2u + 1)
c
3
, c
5
((u + 1)
3
)(u
25
+ 3u
24
+ ··· + 3u + 1)(u
42
− 7u
41
+ ··· − 2u + 1)
c
4
64(8u
3
+ 4u
2
− 1)(8u
25
− 4u
24
+ ··· + 2u + 1)
· (u
42
− u
41
+ ··· + 2496u + 1081)
c
6
, c
7
(u
3
− u
2
+ 2u − 1)(u
21
− u
20
+ ··· − u + 1)
2
(u
25
+ 11u
23
+ ··· + 5u + 4)
c
8
u
3
(u
21
− u
20
+ ··· + u − 1)
2
(u
25
+ 3u
24
+ ··· + 352u + 128)
c
9
(u
3
− u
2
+ 1)(u
21
+ u
20
+ ··· − 3u + 1)
2
(u
25
− u
23
+ ··· + 797u + 292)
c
10
(u
3
+ u
2
+ 2u + 1)(u
21
− u
20
+ ··· − u + 1)
2
(u
25
+ 11u
23
+ ··· + 5u + 4)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
4096(64y
3
− 16y
2
+ 8y −1)(64y
25
+ 240y
24
+ ··· + 16y −1)
· (y
42
+ 19y
41
+ ··· + 26506988y + 1168561)
c
2
, c
3
, c
5
c
11
((y −1)
3
)(y
25
+ 11y
24
+ ··· + 3y −1)(y
42
+ 27y
41
+ ··· + 26y
2
+ 1)
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y −1)(y
21
+ 19y
20
+ ··· + 3y −1)
2
· (y
25
+ 22y
24
+ ··· + 241y −16)
c
8
y
3
(y
21
+ 7y
20
+ ··· + 3y −1)
2
(y
25
+ 7y
24
+ ··· − 84992y −16384)
c
9
(y
3
− y
2
+ 2y −1)(y
21
− y
20
+ ··· + 3y −1)
2
· (y
25
− 2y
24
+ ··· + 1188257y −85264)
21
