11n
129
(K11n
129
)
A knot diagram
1
Linearized knot diagam
7 1 10 8 9 2 11 5 1 7 4
Solving Sequence
7,11 4,8
5 1 2 6 10 3 9
c
7
c
4
c
11
c
1
c
6
c
10
c
3
c
9
c
2
, c
5
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.31440 × 10
35
u
29
− 4.29609 × 10
35
u
28
+ ··· + 1.17974 × 10
36
b − 3.84219 × 10
36
,
1.35861 × 10
37
u
29
+ 2.76955 × 10
37
u
28
+ ··· + 3.42123 × 10
37
a + 4.28134 × 10
38
,
u
30
+ 3u
29
+ ··· + 120u + 29i
I
u
2
= hu
6
− u
5
− u
2
+ b + 2u, −u
8
+ 2u
7
− 3u
5
+ 2u
4
− u
3
+ u
2
+ a + 2u − 3,
u
9
− 2u
8
− u
7
+ 4u
6
− u
5
− u
3
− 3u
2
+ 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 39 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−2.31 × 10
35
u
29
− 4.30 × 10
35
u
28
+ · · · + 1.18 × 10
36
b − 3.84 ×
10
36
, 1.36 × 10
37
u
29
+ 2.77 × 10
37
u
28
+ · · · + 3.42 × 10
37
a + 4.28 ×
10
38
, u
30
+ 3u
29
+ · · · + 120u + 29i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
−0.397110u
29
− 0.809517u
28
+ ··· − 36.6655u − 12.5140
0.196180u
29
+ 0.364157u
28
+ ··· + 15.5278u + 3.25682
a
8
=
1
−u
2
a
5
=
−0.559813u
29
− 1.18451u
28
+ ··· − 55.4393u − 20.3298
0.296144u
29
+ 0.567389u
28
+ ··· + 24.3826u + 6.53699
a
1
=
−0.434170u
29
− 0.988757u
28
+ ··· − 46.6121u − 16.4142
0.0403473u
29
+ 0.114621u
28
+ ··· + 7.11329u + 2.56728
a
2
=
−0.393822u
29
− 0.874135u
28
+ ··· − 39.4988u − 13.8469
0.0403473u
29
+ 0.114621u
28
+ ··· + 7.11329u + 2.56728
a
6
=
0.0125629u
29
− 0.00130980u
28
+ ··· − 1.04271u + 1.25453
−0.247561u
29
− 0.534045u
28
+ ··· − 24.8763u − 7.72880
a
10
=
−u
u
a
3
=
−0.550336u
29
− 1.10515u
28
+ ··· − 49.7304u − 17.0796
0.349405u
29
+ 0.659790u
28
+ ··· + 28.5927u + 7.82236
a
9
=
0.330131u
29
+ 0.777311u
28
+ ··· + 38.6348u + 14.8960
−0.0389985u
29
− 0.0361593u
28
+ ··· − 0.253016u − 0.364324
a
9
=
0.330131u
29
+ 0.777311u
28
+ ··· + 38.6348u + 14.8960
−0.0389985u
29
− 0.0361593u
28
+ ··· − 0.253016u − 0.364324
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.409930u
29
− 0.752927u
28
+ ··· − 34.5863u + 2.19818
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
30
+ u
29
+ ··· − 10u + 1
c
2
u
30
+ 37u
29
+ ··· + 78u + 1
c
3
u
30
+ 2u
29
+ ··· + 423u − 121
c
4
, c
5
, c
8
u
30
− 2u
29
+ ··· + 10u − 11
c
7
, c
10
u
30
− 3u
29
+ ··· − 120u + 29
c
9
u
30
− 4u
29
+ ··· + 1012u − 61
c
11
u
30
− 3u
29
+ ··· + 80u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
30
+ 37y
29
+ ··· + 78y + 1
c
2
y
30
− 79y
29
+ ··· + 2922y + 1
c
3
y
30
− 36y
29
+ ··· − 406651y + 14641
c
4
, c
5
, c
8
y
30
− 28y
29
+ ··· − 122y + 121
c
7
, c
10
y
30
− 15y
29
+ ··· − 7034y + 841
c
9
y
30
− 40y
29
+ ··· − 182466y + 3721
c
11
y
30
+ 15y
29
+ ··· − 5378y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.818507 + 0.418994I
a = 0.149226 − 1.014830I
b = 1.78901 + 1.43406I
−5.25125 + 0.68579I 5.61474 + 0.93865I
u = −0.818507 − 0.418994I
a = 0.149226 + 1.014830I
b = 1.78901 − 1.43406I
−5.25125 − 0.68579I 5.61474 − 0.93865I
u = 0.624245 + 0.671788I
a = 0.421688 + 1.150570I
b = −0.584922 − 0.354810I
5.44904 + 2.23619I 4.08223 − 3.08847I
u = 0.624245 − 0.671788I
a = 0.421688 − 1.150570I
b = −0.584922 + 0.354810I
5.44904 − 2.23619I 4.08223 + 3.08847I
u = −1.023250 + 0.383143I
a = −1.399580 + 0.049686I
b = −0.137063 − 0.842520I
−4.55029 − 3.91642I 4.57066 + 2.81955I
u = −1.023250 − 0.383143I
a = −1.399580 − 0.049686I
b = −0.137063 + 0.842520I
−4.55029 + 3.91642I 4.57066 − 2.81955I
u = −1.156040 + 0.034465I
a = 0.073453 − 0.680796I
b = −0.48025 + 1.49217I
2.03013 + 0.06329I 5.83733 + 0.25546I
u = −1.156040 − 0.034465I
a = 0.073453 + 0.680796I
b = −0.48025 − 1.49217I
2.03013 − 0.06329I 5.83733 − 0.25546I
u = 0.795313 + 0.244851I
a = 0.02386 + 1.42526I
b = 0.45732 − 1.49635I
1.16010 + 2.70821I 1.48721 − 5.36654I
u = 0.795313 − 0.244851I
a = 0.02386 − 1.42526I
b = 0.45732 + 1.49635I
1.16010 − 2.70821I 1.48721 + 5.36654I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873624 + 0.796874I
a = 0.740021 − 0.848178I
b = −0.138479 + 1.278340I
4.61816 + 0.06790I 5.73031 − 0.16143I
u = −0.873624 − 0.796874I
a = 0.740021 + 0.848178I
b = −0.138479 − 1.278340I
4.61816 − 0.06790I 5.73031 + 0.16143I
u = −0.796958
a = 1.72442
b = 0.0618987
0.572803 10.1420
u = 0.718056 + 1.055960I
a = 0.821578 − 0.291189I
b = 0.111688 − 0.747195I
−9.10651 + 0.37265I −0.282021 + 0.198994I
u = 0.718056 − 1.055960I
a = 0.821578 + 0.291189I
b = 0.111688 + 0.747195I
−9.10651 − 0.37265I −0.282021 − 0.198994I
u = 1.115300 + 0.723201I
a = −0.038982 − 0.938537I
b = −1.15595 + 1.86596I
−7.65463 + 6.05562I 2.17136 − 4.65322I
u = 1.115300 − 0.723201I
a = −0.038982 + 0.938537I
b = −1.15595 − 1.86596I
−7.65463 − 6.05562I 2.17136 + 4.65322I
u = −1.167780 + 0.765588I
a = −0.272505 + 1.070770I
b = −0.35697 − 1.64614I
5.69085 − 6.45106I 6.67961 + 5.50435I
u = −1.167780 − 0.765588I
a = −0.272505 − 1.070770I
b = −0.35697 + 1.64614I
5.69085 + 6.45106I 6.67961 − 5.50435I
u = 1.37025 + 0.39698I
a = 0.223661 − 0.786242I
b = 0.280709 + 1.271790I
8.63028 + 2.56200I 10.62309 + 0.27158I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.37025 − 0.39698I
a = 0.223661 + 0.786242I
b = 0.280709 − 1.271790I
8.63028 − 2.56200I 10.62309 − 0.27158I
u = 0.004317 + 0.547819I
a = −0.721264 + 1.206740I
b = 0.150599 + 0.025373I
−1.21990 − 1.07662I −2.59095 + 4.11373I
u = 0.004317 − 0.547819I
a = −0.721264 − 1.206740I
b = 0.150599 − 0.025373I
−1.21990 + 1.07662I −2.59095 − 4.11373I
u = −0.443842
a = −0.206304
b = −0.607008
0.892044 12.1650
u = 1.55455 + 0.15333I
a = −0.406036 + 0.700408I
b = 0.17299 − 1.70175I
3.98744 + 3.00009I 5.48464 − 3.04608I
u = 1.55455 − 0.15333I
a = −0.406036 − 0.700408I
b = 0.17299 + 1.70175I
3.98744 − 3.00009I 5.48464 + 3.04608I
u = −1.48154 + 0.82940I
a = −0.017919 − 0.925838I
b = 0.78170 + 1.80867I
−1.77013 − 11.72040I 4.67233 + 5.69667I
u = −1.48154 − 0.82940I
a = −0.017919 + 0.925838I
b = 0.78170 − 1.80867I
−1.77013 + 11.72040I 4.67233 − 5.69667I
u = −0.54089 + 1.67235I
a = −0.545917 + 0.023732I
b = −0.117829 − 0.641723I
−5.21310 + 3.06517I 5.76591 − 3.12781I
u = −0.54089 − 1.67235I
a = −0.545917 − 0.023732I
b = −0.117829 + 0.641723I
−5.21310 − 3.06517I 5.76591 + 3.12781I
7
II. I
u
2
= hu
6
− u
5
− u
2
+ b + 2u, −u
8
+ 2u
7
− 3u
5
+ 2u
4
− u
3
+ u
2
+ a + 2u −
3, u
9
− 2u
8
− u
7
+ 4u
6
− u
5
− u
3
− 3u
2
+ 3u + 1i
(i) Arc colorings
a
7
=
1
0
a
11
=
0
u
a
4
=
u
8
− 2u
7
+ 3u
5
− 2u
4
+ u
3
− u
2
− 2u + 3
−u
6
+ u
5
+ u
2
− 2u
a
8
=
1
−u
2
a
5
=
2u
8
− 3u
7
− 2u
6
+ 5u
5
− 2u
4
+ 2u
3
− 5u + 3
−u
8
+ u
7
+ 2u
6
− u
5
− 2u
4
− u
3
+ u
2
+ 2u + 1
a
1
=
u
8
− 2u
7
+ 3u
5
− 2u
4
+ u
3
− u
2
− u + 3
−u
6
+ u
5
+ u
4
− u
3
− u
a
2
=
u
8
− 2u
7
− u
6
+ 4u
5
− u
4
− u
2
− 2u + 3
−u
6
+ u
5
+ u
4
− u
3
− u
a
6
=
−u
7
+ u
6
+ 2u
5
− 2u
4
− u
3
+ 2
u
5
− u
4
− u
3
+ u
2
a
10
=
−u
u
a
3
=
u
8
− 2u
7
− u
6
+ 4u
5
− u
4
− u
2
− 3u + 3
−u
4
+ u
3
+ u
2
− u
a
9
=
u
7
− u
6
− 2u
5
+ 2u
4
+ u
3
+ u
2
− u − 3
−u
8
+ u
7
+ 2u
6
− 2u
5
− u
4
+ 2u
a
9
=
u
7
− u
6
− 2u
5
+ 2u
4
+ u
3
+ u
2
− u − 3
−u
8
+ u
7
+ 2u
6
− 2u
5
− u
4
+ 2u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
8
+ u
7
+ 2u
6
− 4u
5
+ u
2
+ 4u + 1
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 5u
7
+ 9u
5
+ u
4
+ 8u
3
+ u
2
+ 3u + 1
c
2
u
9
+ 10u
8
+ 43u
7
+ 106u
6
+ 167u
5
+ 173u
4
+ 116u
3
+ 45u
2
+ 7u − 1
c
3
u
9
− u
8
− u
7
− u
6
+ 3u
4
+ 3u
3
+ 4u
2
+ 2u + 1
c
4
, c
5
u
9
− u
8
− 5u
7
+ 5u
6
+ 8u
5
− 8u
4
− 4u
3
+ 3u
2
+ u + 1
c
6
u
9
+ 5u
7
+ 9u
5
− u
4
+ 8u
3
− u
2
+ 3u − 1
c
7
u
9
− 2u
8
− u
7
+ 4u
6
− u
5
− u
3
− 3u
2
+ 3u + 1
c
8
u
9
+ u
8
− 5u
7
− 5u
6
+ 8u
5
+ 8u
4
− 4u
3
− 3u
2
+ u − 1
c
9
u
9
− 3u
8
+ 3u
7
− 5u
6
+ 6u
5
+ 6u
3
− 3u
2
− 3u − 1
c
10
u
9
+ 2u
8
− u
7
− 4u
6
− u
5
− u
3
+ 3u
2
+ 3u − 1
c
11
u
9
− 2u
8
+ 4u
7
− 3u
6
+ 3u
5
− u
3
+ u
2
− u − 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
9
+ 10y
8
+ 43y
7
+ 106y
6
+ 167y
5
+ 173y
4
+ 116y
3
+ 45y
2
+ 7y −1
c
2
y
9
− 14y
8
+ ··· + 139y −1
c
3
y
9
− 3y
8
− y
7
+ 11y
6
+ 12y
5
− 3y
4
− 13y
3
− 10y
2
− 4y −1
c
4
, c
5
, c
8
y
9
− 11y
8
+ 51y
7
− 129y
6
+ 192y
5
− 166y
4
+ 70y
3
− y
2
− 5y −1
c
7
, c
10
y
9
− 6y
8
+ 15y
7
− 16y
6
− 3y
5
+ 24y
4
− 13y
3
− 15y
2
+ 15y −1
c
9
y
9
− 3y
8
− 9y
7
+ 23y
6
+ 48y
5
+ 18y
4
− 10y
3
− 45y
2
+ 3y −1
c
11
y
9
+ 4y
8
+ 10y
7
+ 13y
6
+ 3y
5
− 12y
4
− 11y
3
+ y
2
+ 3y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.168914 + 0.950661I
a = 0.049336 − 0.609720I
b = −0.784185 − 0.982357I
−6.63247 + 1.79022I 1.84978 − 1.07531I
u = −0.168914 − 0.950661I
a = 0.049336 + 0.609720I
b = −0.784185 + 0.982357I
−6.63247 − 1.79022I 1.84978 + 1.07531I
u = −1.145600 + 0.103496I
a = 0.414158 − 0.863364I
b = −0.20585 + 1.62467I
1.93998 + 1.74600I 4.48812 − 2.12055I
u = −1.145600 − 0.103496I
a = 0.414158 + 0.863364I
b = −0.20585 − 1.62467I
1.93998 − 1.74600I 4.48812 + 2.12055I
u = 1.161230 + 0.594201I
a = −0.279042 − 0.783472I
b = 0.68024 + 1.36518I
6.80275 + 0.69172I 8.39096 + 0.05325I
u = 1.161230 − 0.594201I
a = −0.279042 + 0.783472I
b = 0.68024 − 1.36518I
6.80275 − 0.69172I 8.39096 − 0.05325I
u = 1.287590 + 0.340306I
a = −0.400111 + 1.033390I
b = 0.005983 − 1.355130I
7.89851 + 3.55465I 6.26919 − 4.19762I
u = 1.287590 − 0.340306I
a = −0.400111 − 1.033390I
b = 0.005983 + 1.355130I
7.89851 − 3.55465I 6.26919 + 4.19762I
u = −0.268618
a = 3.43132
b = 0.607619
−0.278310 0.00389950
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
9
+ 5u
7
+ ··· + 3u + 1)(u
30
+ u
29
+ ··· − 10u + 1)
c
2
(u
9
+ 10u
8
+ 43u
7
+ 106u
6
+ 167u
5
+ 173u
4
+ 116u
3
+ 45u
2
+ 7u − 1)
· (u
30
+ 37u
29
+ ··· + 78u + 1)
c
3
(u
9
− u
8
− u
7
− u
6
+ 3u
4
+ 3u
3
+ 4u
2
+ 2u + 1)
· (u
30
+ 2u
29
+ ··· + 423u − 121)
c
4
, c
5
(u
9
− u
8
− 5u
7
+ 5u
6
+ 8u
5
− 8u
4
− 4u
3
+ 3u
2
+ u + 1)
· (u
30
− 2u
29
+ ··· + 10u − 11)
c
6
(u
9
+ 5u
7
+ ··· + 3u − 1)(u
30
+ u
29
+ ··· − 10u + 1)
c
7
(u
9
− 2u
8
− u
7
+ 4u
6
− u
5
− u
3
− 3u
2
+ 3u + 1)
· (u
30
− 3u
29
+ ··· − 120u + 29)
c
8
(u
9
+ u
8
− 5u
7
− 5u
6
+ 8u
5
+ 8u
4
− 4u
3
− 3u
2
+ u − 1)
· (u
30
− 2u
29
+ ··· + 10u − 11)
c
9
(u
9
− 3u
8
+ 3u
7
− 5u
6
+ 6u
5
+ 6u
3
− 3u
2
− 3u − 1)
· (u
30
− 4u
29
+ ··· + 1012u − 61)
c
10
(u
9
+ 2u
8
− u
7
− 4u
6
− u
5
− u
3
+ 3u
2
+ 3u − 1)
· (u
30
− 3u
29
+ ··· − 120u + 29)
c
11
(u
9
− 2u
8
+ 4u
7
− 3u
6
+ 3u
5
− u
3
+ u
2
− u − 1)
· (u
30
− 3u
29
+ ··· + 80u − 7)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
(y
9
+ 10y
8
+ 43y
7
+ 106y
6
+ 167y
5
+ 173y
4
+ 116y
3
+ 45y
2
+ 7y −1)
· (y
30
+ 37y
29
+ ··· + 78y + 1)
c
2
(y
9
− 14y
8
+ ··· + 139y −1)(y
30
− 79y
29
+ ··· + 2922y + 1)
c
3
(y
9
− 3y
8
− y
7
+ 11y
6
+ 12y
5
− 3y
4
− 13y
3
− 10y
2
− 4y −1)
· (y
30
− 36y
29
+ ··· − 406651y + 14641)
c
4
, c
5
, c
8
(y
9
− 11y
8
+ 51y
7
− 129y
6
+ 192y
5
− 166y
4
+ 70y
3
− y
2
− 5y −1)
· (y
30
− 28y
29
+ ··· − 122y + 121)
c
7
, c
10
(y
9
− 6y
8
+ 15y
7
− 16y
6
− 3y
5
+ 24y
4
− 13y
3
− 15y
2
+ 15y −1)
· (y
30
− 15y
29
+ ··· − 7034y + 841)
c
9
(y
9
− 3y
8
− 9y
7
+ 23y
6
+ 48y
5
+ 18y
4
− 10y
3
− 45y
2
+ 3y −1)
· (y
30
− 40y
29
+ ··· − 182466y + 3721)
c
11
(y
9
+ 4y
8
+ 10y
7
+ 13y
6
+ 3y
5
− 12y
4
− 11y
3
+ y
2
+ 3y −1)
· (y
30
+ 15y
29
+ ··· − 5378y + 49)
13
