11n
160
(K11n
160
)
1
Arc Sequences
10 5 1 8 10 3 11 5 3 4 7
Solving Sequence
5,10 3,6
7 2 1 9 8 4 11
c
5
c
6
c
2
c
1
c
9
c
8
c
4
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
9
3u
8
+ 3u
7
3u
6
u
5
+ 6u
4
3u
3
3u
2
1,
10u
8
21u
7
5u
6
+ 18u
5
54u
4
+ 73u
3
+ 28u
2
+ 28a 100u + 1,
9u
8
+ 35u
7
48u
6
+ 44u
5
13u
4
58u
3
+ 42u
2
+ 28b + 27u 10i
I
u
2
= hu
42
+ 20u
40
+ ··· + 749u 101,
1.37761 × 10
93
u
41
8.98126 × 10
92
u
40
+ ··· + 6.36373 × 10
94
b 1.48981 × 10
95
,
5.02531 × 10
95
u
41
1.23855 × 10
95
u
40
+ ··· + 6.42736 × 10
96
a + 2.36484 × 10
98
i
There are 2 irreducible components with 51 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
=
hu
9
3u
8
+· · ·3u
2
1, 10u
8
21u
7
+· · ·+28a+1, 9u
8
+35u
7
+· · ·+28b10i
(i) Arc colorings
a
5
=
0
u
a
10
=
5
14
u
8
+
3
4
u
7
+ ··· +
25
7
u
1
28
9
28
u
8
5
4
u
7
+ ···
27
28
u +
5
14
a
3
=
1
0
a
6
=
0.892857u
8
+ 2.75000u
7
+ ··· + 1.67857u + 1.28571
3
28
u
8
1
4
u
7
+ ···
9
28
u +
2
7
a
7
=
u
8
+ 3u
7
3u
6
+ 3u
5
+ u
4
6u
3
+ 3u
2
+ 2u + 1
3
28
u
8
1
4
u
7
+ ···
9
28
u +
2
7
a
2
=
1
u
2
a
1
=
5
14
u
8
+ u
7
+ ··· +
1
14
u +
45
14
3
14
u
8
1
2
u
7
+ ···
23
14
u
3
7
a
9
=
0.678571u
8
+ 2u
7
+ ··· + 4.53571u 0.392857
9
28
u
8
5
4
u
7
+ ···
27
28
u +
5
14
a
8
=
0.678571u
8
+ 2u
7
+ ··· + 4.53571u 0.392857
1
14
u
8
1
4
u
7
+ ···
2
7
u +
11
28
a
4
=
17
14
u
8
7
2
u
7
+ ···
65
14
u
3
7
1
7
u
8
+
4
7
u
6
+ ··· +
10
7
u
5
7
a
11
=
9
14
u
8
11
4
u
7
+ ··· +
4
7
u +
41
28
5
28
u
8
+ u
7
+ ···
55
28
u +
3
28
a
11
=
9
14
u
8
11
4
u
7
+ ··· +
4
7
u +
41
28
5
28
u
8
+ u
7
+ ···
55
28
u +
3
28
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.796448 0.144077I
a = 1.58027 + 0.49718I
b = 0.079781 + 0.541877I
7.57318 6.23029I 10.70312 + 5.64960I
u = 0.796448 + 0.144077I
a = 1.58027 0.49718I
b = 0.079781 0.541877I
7.57318 + 6.23029I 10.70312 5.64960I
u = 0.048121 0.465250I
a = 0.50444 1.82038I
b = 0.560397 + 0.742763I
1.99801 + 1.72753I 3.97057 2.65342I
u = 0.048121 + 0.465250I
a = 0.50444 + 1.82038I
b = 0.560397 0.742763I
1.99801 1.72753I 3.97057 + 2.65342I
u = 0.07249 1.46762I
a = 1.308116 0.248379I
b = 1.76179 0.64696I
4.53577 + 3.70953I 0.23420 7.12511I
u = 0.07249 + 1.46762I
a = 1.308116 + 0.248379I
b = 1.76179 + 0.64696I
4.53577 3.70953I 0.23420 + 7.12511I
u = 1.087785 0.549338I
a = 0.037467 + 0.285860I
b = 0.404070 0.936159I
5.07942 + 1.69947I 16.7062 3.0605I
u = 1.087785 + 0.549338I
a = 0.037467 0.285860I
b = 0.404070 + 0.936159I
5.07942 1.69947I 16.7062 + 3.0605I
u = 2.17611
a = 0.692963
b = 1.05137
0.490477 53.2282
3
II. I
u
2
= hu
42
+ 20u
40
+ · · · + 749u 101, 1.38 × 10
93
u
41
8.98 ×
10
92
u
40
+ · · · + 6.36 × 10
94
b 1.49 × 10
95
, 5.03 × 10
95
u
41
1.24 × 10
95
u
40
+
· · · + 6.43 × 10
96
a + 2.36 × 10
98
i
(i) Arc colorings
a
5
=
0
u
a
10
=
0.0781862u
41
+ 0.0192700u
40
+ ··· + 187.238u 36.7933
0.0216479u
41
+ 0.0141132u
40
+ ··· 18.1532u + 2.34110
a
3
=
1
0
a
6
=
0.0784504u
41
+ 0.0536097u
40
+ ··· + 261.218u 52.2702
0.0265474u
41
+ 0.00428021u
40
+ ··· + 57.1137u 11.0712
a
7
=
0.0519030u
41
+ 0.0493295u
40
+ ··· + 204.105u 41.1990
0.0265474u
41
+ 0.00428021u
40
+ ··· + 57.1137u 11.0712
a
2
=
1
u
2
a
1
=
0.0560057u
41
0.0200714u
40
+ ··· 172.895u + 34.9117
0.0436759u
41
0.0271300u
40
+ ··· + 14.1412u + 0.298544
a
9
=
0.0998341u
41
+ 0.00515681u
40
+ ··· + 205.391u 39.1344
0.0216479u
41
+ 0.0141132u
40
+ ··· 18.1532u + 2.34110
a
8
=
0.0998341u
41
+ 0.00515681u
40
+ ··· + 205.391u 39.1344
0.000478245u
41
0.00411528u
40
+ ··· 4.20753u + 1.82026
a
4
=
0.00531825u
41
0.0493745u
40
+ ··· 121.866u + 26.1489
0.0775758u
41
+ 0.0100320u
40
+ ··· 119.757u + 20.0369
a
11
=
0.297466u
41
+ 0.101977u
40
+ ··· 342.494u + 44.9999
0.00292049u
41
+ 0.00829692u
40
+ ··· 2.68211u 1.46488
a
11
=
0.297466u
41
+ 0.101977u
40
+ ··· 342.494u + 44.9999
0.00292049u
41
+ 0.00829692u
40
+ ··· 2.68211u 1.46488
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.64314
a = 0.754707
b = 1.06758
0.445368 132.910
u = 1.54579 0.18285I
a = 0.165051 + 0.217661I
b = 0.873097 0.018070I
5.60720 6.66981I 4.81384 + 5.61602I
u = 1.54579 + 0.18285I
a = 0.165051 0.217661I
b = 0.873097 + 0.018070I
5.60720 + 6.66981I 4.81384 5.61602I
u = 0.57790 1.71570I
a = 1.095249 0.128831I
b = 1.62757 + 0.37825I
5.50962 8.17142I 1.83275 + 6.34212I
u = 0.57790 + 1.71570I
a = 1.095249 + 0.128831I
b = 1.62757 0.37825I
5.50962 + 8.17142I 1.83275 6.34212I
u = 0.52555 1.75387I
a = 1.101026 + 0.054372I
b = 1.70254 0.60123I
0.9874 14.3018I 4.52058 + 7.23021I
u = 0.52555 + 1.75387I
a = 1.101026 0.054372I
b = 1.70254 + 0.60123I
0.9874 + 14.3018I 4.52058 7.23021I
u = 0.492771 0.001301I
a = 0.391224 1.172736I
b = 0.545886 0.397696I
0.96120 1.37637I 2.37205 + 4.71298I
u = 0.492771 + 0.001301I
a = 0.391224 + 1.172736I
b = 0.545886 + 0.397696I
0.96120 + 1.37637I 2.37205 4.71298I
u = 0.41431 2.06998I
a = 0.984324 + 0.180580I
b = 1.165815 0.238843I
0.510430 0.864801I 13.7057 6.3010I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.41431 + 2.06998I
a = 0.984324 0.180580I
b = 1.165815 + 0.238843I
0.510430 + 0.864801I 13.7057 + 6.3010I
u = 0.045927 0.526713I
a = 0.799839 + 1.113350I
b = 0.434584 + 0.300537I
0.95288 + 2.06296I 2.70729 3.81916I
u = 0.045927 + 0.526713I
a = 0.799839 1.113350I
b = 0.434584 0.300537I
0.95288 2.06296I 2.70729 + 3.81916I
u = 0.018310 0.894802I
a = 0.645532 0.373937I
b = 0.02747 1.48614I
4.81718 + 6.58441I 5.59437 5.87348I
u = 0.018310 + 0.894802I
a = 0.645532 + 0.373937I
b = 0.02747 + 1.48614I
4.81718 6.58441I 5.59437 + 5.87348I
u = 0.01981 1.75119I
a = 0.999628 0.228933I
b = 1.58501 + 0.02240I
7.93236 + 2.29439I 1.44420 0.77498I
u = 0.01981 + 1.75119I
a = 0.999628 + 0.228933I
b = 1.58501 0.02240I
7.93236 2.29439I 1.44420 + 0.77498I
u = 0.07435 1.78893I
a = 0.938825 + 0.216455I
b = 1.83715 + 0.14822I
5.41237 + 6.59053I 2.62123 6.46618I
u = 0.07435 + 1.78893I
a = 0.938825 0.216455I
b = 1.83715 0.14822I
5.41237 6.59053I 2.62123 + 6.46618I
u = 0.08366 1.50753I
a = 1.270158 0.266824I
b = 1.48604 0.87974I
3.06015 + 4.00976I 4.45214 4.88488I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.08366 + 1.50753I
a = 1.270158 + 0.266824I
b = 1.48604 + 0.87974I
3.06015 4.00976I 4.45214 + 4.88488I
u = 0.086589 0.706593I
a = 0.0935123 + 0.0986752I
b = 0.276525 + 1.147408I
1.12929 + 2.58933I 0.40470 5.03166I
u = 0.086589 + 0.706593I
a = 0.0935123 0.0986752I
b = 0.276525 1.147408I
1.12929 2.58933I 0.40470 + 5.03166I
u = 0.14313 1.50275I
a = 1.278823 0.003892I
b = 1.83391 + 0.52303I
4.55674 + 2.88338I 1.15978 + 1.33841I
u = 0.14313 + 1.50275I
a = 1.278823 + 0.003892I
b = 1.83391 0.52303I
4.55674 2.88338I 1.15978 1.33841I
u = 0.26966 1.44580I
a = 1.162277 0.264169I
b = 1.76880 + 0.29663I
4.33527 + 2.92425I 1.15497 2.08183I
u = 0.26966 + 1.44580I
a = 1.162277 + 0.264169I
b = 1.76880 0.29663I
4.33527 2.92425I 1.15497 + 2.08183I
u = 0.301319 1.190513I
a = 1.25885 + 0.85918I
b = 1.70529 + 0.20752I
3.08658 1.51461I 1.61949 + 2.96401I
u = 0.301319 + 1.190513I
a = 1.25885 0.85918I
b = 1.70529 0.20752I
3.08658 + 1.51461I 1.61949 2.96401I
u = 0.301486 0.307655I
a = 2.44416 3.19617I
b = 0.560869 0.365926I
6.74843 5.64741I 3.18941 + 1.63716I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.301486 + 0.307655I
a = 2.44416 + 3.19617I
b = 0.560869 + 0.365926I
6.74843 + 5.64741I 3.18941 1.63716I
u = 0.403159 0.306921I
a = 0.13087 + 1.45597I
b = 0.556105 1.209910I
4.10677 + 1.00823I 6.95415 + 0.51830I
u = 0.403159 + 0.306921I
a = 0.13087 1.45597I
b = 0.556105 + 1.209910I
4.10677 1.00823I 6.95415 0.51830I
u = 0.474707 0.528975I
a = 0.486188 1.148845I
b = 0.909102 + 0.548313I
3.52003 + 2.03312I 8.42216 3.37678I
u = 0.474707 + 0.528975I
a = 0.486188 + 1.148845I
b = 0.909102 0.548313I
3.52003 2.03312I 8.42216 + 3.37678I
u = 0.53365 1.65271I
a = 0.735794 + 0.194295I
b = 1.55859 0.49514I
0.24491 + 5.34601I 6.61771 6.40608I
u = 0.53365 + 1.65271I
a = 0.735794 0.194295I
b = 1.55859 + 0.49514I
0.24491 5.34601I 6.61771 + 6.40608I
u = 0.593548 0.597226I
a = 1.00680 + 0.99663I
b = 0.090224 0.110489I
1.94227 0.55855I 3.25163 2.41810I
u = 0.593548 + 0.597226I
a = 1.00680 0.99663I
b = 0.090224 + 0.110489I
1.94227 + 0.55855I 3.25163 + 2.41810I
u = 0.725613
a = 0.508253
b = 0.330441
1.10908 10.5894
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.257641 0.545229I
a = 0.006635 0.395787I
b = 0.416122 + 0.470730I
4.48395 + 1.62517I 2.04474 0.35828I
u = 1.257641 + 0.545229I
a = 0.006635 + 0.395787I
b = 0.416122 0.470730I
4.48395 1.62517I 2.04474 + 0.35828I
8
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
9
5u
8
+ 3u
7
3u
5
+ 3u
4
+ 6u
3
6u
2
+ 4u 4)
(u
42
+ 2u
41
+ ··· 124u 4)
c
2
(u
9
3u
8
+ 3u
7
3u
6
u
5
+ 6u
4
3u
3
3u
2
1)
(u
42
+ 20u
40
+ ··· + 749u 101)
c
3
(u
9
+ 5u
8
+ 13u
7
+ 18u
6
+ 18u
5
+ 14u
4
+ 13u
3
+ 10u
2
+ 7u + 1)
(u
42
+ 6u
41
+ ··· + 8u + 1)
c
4
(u
9
+ 3u
8
+ u
7
8u
6
11u
5
+ 3u
4
+ 14u
3
+ 6u
2
4u 4)
(u
42
+ 2u
41
+ ··· + 556u + 116)
c
5
(u
9
+ 2u
8
+ 2u
7
+ 7u
6
+ 5u
5
10u
4
6u
3
+ 6u
2
+ 3u + 1)
(u
42
+ 3u
41
+ ··· + 184u 11)
c
6
(u
9
3u
8
+ 2u
7
+ 9u
6
3u
5
6u
4
+ 8u
3
+ 11u
2
+ 5u + 1)
(u
42
+ u
40
+ ··· 106u 97)
c
7
(u
9
+ u
8
+ 2u
7
+ 6u
6
+ 9u
4
3u
3
+ 4u
2
2u + 1)
(u
42
+ 4u
41
+ ··· + 47u 13)
c
8
(u
9
3u
8
+ u
7
+ 8u
6
11u
5
3u
4
+ 14u
3
6u
2
4u + 4)
(u
42
+ 2u
41
+ ··· + 556u + 116)
c
9
(u
9
2u
8
+ u
6
+ u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ u + 1)
(u
42
+ u
41
+ ··· 112u 23)
c
10
(u
9
+ u
8
u
7
+ 2u
6
+ 10u
5
+ 3u
4
3u
3
+ 4u
2
+ 5u + 1)
(u
42
+ 2u
41
+ ··· + 128u + 29)
c
11
(u
9
u
8
+ 2u
7
6u
6
9u
4
3u
3
4u
2
2u 1)
(u
42
+ 4u
41
+ ··· + 47u 13)
9
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
9
19y
8
+ 3y
7
+ 24y
6
7y
5
61y
4
+ 48y
3
+ 36y
2
32y 16)
(y
42
72y
41
+ ··· 5760y + 16)
c
2
(y
9
3y
8
11y
7
+ 15y
6
+ y
5
54y
4
+ 39y
3
+ 3y
2
6y 1)
(y
42
+ 40y
41
+ ··· + 72673y + 10201)
c
3
(y
9
+ y
8
+ 25y
7
+ 30y
6
+ 72y
5
+ 84y
4
+ 105y
3
+ 54y
2
+ 29y 1)
(y
42
+ 4y
41
+ ··· 30y + 1)
c
4
(y
9
7y
8
+ ··· + 64y 16)(y
42
24y
41
+ ··· 45120y + 13456)
c
5
(y
9
14y
7
y
6
+ 123y
5
236y
4
+ 172y
3
52y
2
3y 1)
(y
42
+ 51y
41
+ ··· + 5722y + 121)
c
6
(y
9
5y
8
+ 52y
7
113y
6
+ 225y
5
256y
4
+ 148y
3
29y
2
+ 3y 1)
(y
42
+ 2y
41
+ ··· + 164916y + 9409)
c
7
, c
11
(y
9
+ 3y
8
8y
7
60y
6
132y
5
139y
4
75y
3
22y
2
4y 1)
(y
42
+ 26y
41
+ ··· 805y + 169)
c
8
(y
9
7y
8
+ ··· + 64y 16)(y
42
24y
41
+ ··· 45120y + 13456)
c
9
(y
9
4y
8
+ 6y
7
+ 11y
6
+ 15y
5
4y
4
12y
3
16y
2
7y 1)
(y
42
45y
41
+ ··· 1274y + 529)
c
10
(y
9
3y
8
+ 17y
7
36y
6
+ 96y
5
97y
4
+ 81y
3
52y
2
+ 17y 1)
(y
42
12y
41
+ ··· 22358y + 841)
10