11n
160
(K11n
160
)
A knot diagram
1
Linearized knot diagam
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
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.61154 × 10
116
u
41
+ 7.44138 × 10
116
u
40
+ ··· + 2.20130 × 10
118
b + 2.20567 × 10
118
,
2.76575 × 10
118
u
41
8.73496 × 10
118
u
40
+ ··· + 2.42143 × 10
119
a + 9.10967 × 10
119
,
u
42
3u
41
+ ··· 184u 11i
I
u
2
= h31u
8
+ 26u
7
+ 50u
6
+ 165u
5
26u
4
204u
3
34u
2
+ 47b + 86u + 75,
34u
8
+ 27u
7
+ 23u
6
+ 184u
5
74u
4
342u
3
+ 131u
2
+ 47a + 158u 83,
u
9
+ 2u
8
+ 2u
7
+ 7u
6
+ 5u
5
10u
4
6u
3
+ 6u
2
+ 3u + 1i
* 2 irreducible components of dim
C
= 0, with total 51 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−2.61 × 10
116
u
41
+ 7.44 × 10
116
u
40
+ · · · + 2.20 × 10
118
b + 2.21 ×
10
118
, 2.77 × 10
118
u
41
8.73 × 10
118
u
40
+ · · · + 2.42 × 10
119
a + 9.11 ×
10
119
, u
42
3u
41
+ · · · 184u 11i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
0.114220u
41
+ 0.360736u
40
+ ··· + 116.228u 3.76211
0.0118637u
41
0.0338046u
40
+ ··· 14.7028u 1.00199
a
6
=
1
u
2
a
7
=
0.0851467u
41
+ 0.256373u
40
+ ··· + 160.031u + 16.8852
0.0100801u
41
+ 0.0314357u
40
+ ··· + 4.32560u 0.298656
a
2
=
0.102356u
41
+ 0.326932u
40
+ ··· + 101.525u 4.76410
0.0118637u
41
0.0338046u
40
+ ··· 14.7028u 1.00199
a
1
=
0.102356u
41
+ 0.326932u
40
+ ··· + 101.525u 4.76410
0.00934866u
41
0.0266415u
40
+ ··· 12.1739u 0.783495
a
9
=
0.183123u
41
0.552897u
40
+ ··· 292.420u 21.2506
0.00244803u
41
+ 0.00733234u
40
+ ··· + 2.14687u + 0.897796
a
8
=
0.180675u
41
0.545564u
40
+ ··· 290.273u 20.3528
0.00244803u
41
+ 0.00733234u
40
+ ··· + 2.14687u + 0.897796
a
4
=
0.157339u
41
+ 0.476272u
40
+ ··· + 234.882u + 15.0129
0.00294723u
41
0.0113162u
40
+ ··· 3.44539u 0.785309
a
11
=
0.149328u
41
+ 0.463397u
40
+ ··· + 205.737u + 5.85422
0.00974472u
41
0.0271814u
40
+ ··· 13.4504u 1.21086
a
11
=
0.149328u
41
+ 0.463397u
40
+ ··· + 205.737u + 5.85422
0.00974472u
41
0.0271814u
40
+ ··· 13.4504u 1.21086
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0.0407139u
41
+ 0.122846u
40
+ ··· + 94.2507u + 5.40926
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
42
+ 2u
41
+ ··· 124u 4
c
2
u
42
+ 20u
40
+ ··· 749u 101
c
3
u
42
6u
41
+ ··· 8u + 1
c
4
, c
8
u
42
+ 2u
41
+ ··· + 556u + 116
c
5
u
42
3u
41
+ ··· 184u 11
c
6
u
42
+ u
40
+ ··· + 106u 97
c
7
, c
11
u
42
4u
41
+ ··· 47u 13
c
9
u
42
u
41
+ ··· + 112u 23
c
10
u
42
+ 2u
41
+ ··· + 128u + 29
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
42
72y
41
+ ··· 5760y + 16
c
2
y
42
+ 40y
41
+ ··· + 72673y + 10201
c
3
y
42
+ 4y
41
+ ··· 30y + 1
c
4
, c
8
y
42
24y
41
+ ··· 45120y + 13456
c
5
y
42
+ 51y
41
+ ··· + 5722y + 121
c
6
y
42
+ 2y
41
+ ··· + 164916y + 9409
c
7
, c
11
y
42
+ 26y
41
+ ··· 805y + 169
c
9
y
42
45y
41
+ ··· 1274y + 529
c
10
y
42
12y
41
+ ··· 22358y + 841
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.838508 + 0.288184I
a = 1.170650 + 0.251577I
b = 0.474707 + 0.528975I
3.52003 + 2.03312I 8.42216 3.37678I
u = 0.838508 0.288184I
a = 1.170650 0.251577I
b = 0.474707 0.528975I
3.52003 2.03312I 8.42216 + 3.37678I
u = 1.192800 + 0.009739I
a = 0.0763919 + 0.0920066I
b = 0.593548 + 0.597226I
1.94227 0.55855I 3.25163 2.41810I
u = 1.192800 0.009739I
a = 0.0763919 0.0920066I
b = 0.593548 0.597226I
1.94227 + 0.55855I 3.25163 + 2.41810I
u = 0.394106 + 0.627152I
a = 1.78252 0.23343I
b = 0.403159 0.306921I
4.10677 1.00823I 6.95415 0.51830I
u = 0.394106 0.627152I
a = 1.78252 + 0.23343I
b = 0.403159 + 0.306921I
4.10677 + 1.00823I 6.95415 + 0.51830I
u = 0.549682 + 0.472418I
a = 0.724998 + 0.076343I
b = 0.045927 + 0.526713I
0.95288 + 2.06296I 2.70729 3.81916I
u = 0.549682 0.472418I
a = 0.724998 0.076343I
b = 0.045927 0.526713I
0.95288 2.06296I 2.70729 + 3.81916I
u = 0.071542 + 1.319740I
a = 0.310251 + 1.197800I
b = 0.53365 1.65271I
0.24491 5.34601I 6.61771 + 6.40608I
u = 0.071542 1.319740I
a = 0.310251 1.197800I
b = 0.53365 + 1.65271I
0.24491 + 5.34601I 6.61771 6.40608I
5
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.322779 + 0.584470I
a = 1.96834 1.04003I
b = 0.018310 + 0.894802I
4.81718 + 6.58441I 5.59437 5.87348I
u = 0.322779 0.584470I
a = 1.96834 + 1.04003I
b = 0.018310 0.894802I
4.81718 6.58441I 5.59437 + 5.87348I
u = 0.194310 + 0.577382I
a = 0.904526 0.641045I
b = 0.492771 0.001301I
0.96120 + 1.37637I 2.37205 4.71298I
u = 0.194310 0.577382I
a = 0.904526 + 0.641045I
b = 0.492771 + 0.001301I
0.96120 1.37637I 2.37205 + 4.71298I
u = 0.207450 + 0.501375I
a = 1.094850 0.376955I
b = 1.257640 + 0.545229I
4.48395 + 1.62517I 2.04474 0.35828I
u = 0.207450 0.501375I
a = 1.094850 + 0.376955I
b = 1.257640 0.545229I
4.48395 1.62517I 2.04474 + 0.35828I
u = 0.294933 + 0.306279I
a = 1.39370 + 1.50859I
b = 1.54579 + 0.18285I
5.60720 6.66981I 4.81384 + 5.61602I
u = 0.294933 0.306279I
a = 1.39370 1.50859I
b = 1.54579 0.18285I
5.60720 + 6.66981I 4.81384 5.61602I
u = 0.368795
a = 0.896001
b = 0.725613
1.10908 10.5890
u = 0.45702 + 1.66340I
a = 0.199299 1.049700I
b = 0.07435 + 1.78893I
5.41237 + 6.59053I 0
6
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.45702 1.66340I
a = 0.199299 + 1.049700I
b = 0.07435 1.78893I
5.41237 6.59053I 0
u = 1.72020 + 0.21164I
a = 0.346970 0.170035I
b = 0.301486 + 0.307655I
6.74843 5.64741I 0
u = 1.72020 0.21164I
a = 0.346970 + 0.170035I
b = 0.301486 0.307655I
6.74843 + 5.64741I 0
u = 0.06851 + 1.75165I
a = 0.208522 1.001630I
b = 0.26966 + 1.44580I
4.33527 + 2.92425I 0
u = 0.06851 1.75165I
a = 0.208522 + 1.001630I
b = 0.26966 1.44580I
4.33527 2.92425I 0
u = 0.42070 + 1.74601I
a = 0.218861 + 0.855059I
b = 0.01981 1.75119I
7.93236 2.29439I 0
u = 0.42070 1.74601I
a = 0.218861 0.855059I
b = 0.01981 + 1.75119I
7.93236 + 2.29439I 0
u = 0.64354 + 1.75757I
a = 0.209152 + 0.893674I
b = 0.301319 1.190510I
3.08658 + 1.51461I 0
u = 0.64354 1.75757I
a = 0.209152 0.893674I
b = 0.301319 + 1.190510I
3.08658 1.51461I 0
u = 0.0616260 + 0.0746193I
a = 10.96120 + 5.34669I
b = 0.086589 0.706593I
1.12929 2.58933I 0.40470 + 5.03166I
7
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.0616260 0.0746193I
a = 10.96120 5.34669I
b = 0.086589 + 0.706593I
1.12929 + 2.58933I 0.40470 5.03166I
u = 0.17719 + 1.92230I
a = 0.182597 0.970850I
b = 0.14313 + 1.50275I
4.55674 + 2.88338I 0
u = 0.17719 1.92230I
a = 0.182597 + 0.970850I
b = 0.14313 1.50275I
4.55674 2.88338I 0
u = 0.50851 + 1.89248I
a = 0.236773 + 0.848855I
b = 0.08366 1.50753I
3.06015 4.00976I 0
u = 0.50851 1.89248I
a = 0.236773 0.848855I
b = 0.08366 + 1.50753I
3.06015 + 4.00976I 0
u = 1.99479
a = 0.535185
b = 2.64314
0.445368 0
u = 0.41191 + 1.95357I
a = 0.017188 + 0.836754I
b = 0.57790 1.71570I
5.50962 + 8.17142I 0
u = 0.41191 1.95357I
a = 0.017188 0.836754I
b = 0.57790 + 1.71570I
5.50962 8.17142I 0
u = 0.48329 + 1.95963I
a = 0.087238 0.890319I
b = 0.52555 + 1.75387I
0.9874 14.3018I 0
u = 0.48329 1.95963I
a = 0.087238 + 0.890319I
b = 0.52555 1.75387I
0.9874 + 14.3018I 0
8
Solutions to I
u
1
1(vol +
1CS) Cusp shape
u = 0.03402 + 2.11235I
a = 0.104154 0.553583I
b = 0.41431 + 2.06998I
0.510430 0.864801I 0
u = 0.03402 2.11235I
a = 0.104154 + 0.553583I
b = 0.41431 2.06998I
0.510430 + 0.864801I 0
9
II. I
u
2
=
h31u
8
+26u
7
+· · ·+47b+75, 34u
8
+27u
7
+· · ·+47a83, u
9
+2u
8
+· · ·+3u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
0.723404u
8
0.574468u
7
+ ··· 3.36170u + 1.76596
0.659574u
8
0.553191u
7
+ ··· 1.82979u 1.59574
a
6
=
1
u
2
a
7
=
0.148936u
8
0.382979u
7
+ ··· + 0.425532u 1.48936
0.872340u
8
+ 0.957447u
7
+ ··· + 2.93617u + 1.72340
a
2
=
1.38298u
8
1.12766u
7
+ ··· 5.19149u + 0.170213
0.659574u
8
0.553191u
7
+ ··· 1.82979u 1.59574
a
1
=
1.38298u
8
1.12766u
7
+ ··· 5.19149u + 0.170213
2.72340u
8
1.57447u
7
+ ··· 5.36170u 3.23404
a
9
=
0.936170u
8
1.97872u
7
+ ··· 8.46809u 1.36170
0.595745u
8
+ 0.531915u
7
+ ··· + 4.29787u 0.0425532
a
8
=
0.340426u
8
1.44681u
7
+ ··· 4.17021u 1.40426
0.595745u
8
+ 0.531915u
7
+ ··· + 4.29787u 0.0425532
a
4
=
0.765957u
8
1.25532u
7
+ ··· 4.38298u 2.65957
0.723404u
8
+ 1.57447u
7
+ ··· + 6.36170u + 1.23404
a
11
=
1.14894u
8
+ 1.38298u
7
+ ··· + 3.57447u + 2.48936
0.425532u
8
0.191489u
7
+ ··· 2.78723u 0.744681
a
11
=
1.14894u
8
+ 1.38298u
7
+ ··· + 3.57447u + 2.48936
0.425532u
8
0.191489u
7
+ ··· 2.78723u 0.744681
(ii) Obstruction class = 1
(iii) Cusp Shapes
=
854
47
u
8
+
457
47
u
7
+
962
47
u
6
+
4406
47
u
5
2337
47
u
4
5726
47
u
3
+
2743
47
u
2
+
1931
47
u
61
47
10
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
5u
8
+ 3u
7
3u
5
+ 3u
4
+ 6u
3
6u
2
+ 4u 4
c
2
u
9
3u
8
+ 3u
7
3u
6
u
5
+ 6u
4
3u
3
3u
2
1
c
3
u
9
+ 5u
8
+ 13u
7
+ 18u
6
+ 18u
5
+ 14u
4
+ 13u
3
+ 10u
2
+ 7u + 1
c
4
u
9
+ 3u
8
+ u
7
8u
6
11u
5
+ 3u
4
+ 14u
3
+ 6u
2
4u 4
c
5
u
9
+ 2u
8
+ 2u
7
+ 7u
6
+ 5u
5
10u
4
6u
3
+ 6u
2
+ 3u + 1
c
6
u
9
3u
8
+ 2u
7
+ 9u
6
3u
5
6u
4
+ 8u
3
+ 11u
2
+ 5u + 1
c
7
u
9
+ u
8
+ 2u
7
+ 6u
6
+ 9u
4
3u
3
+ 4u
2
2u + 1
c
8
u
9
3u
8
+ u
7
+ 8u
6
11u
5
3u
4
+ 14u
3
6u
2
4u + 4
c
9
u
9
2u
8
+ u
6
+ u
5
+ 2u
4
+ 2u
3
+ 4u
2
+ u + 1
c
10
u
9
+ u
8
u
7
+ 2u
6
+ 10u
5
+ 3u
4
3u
3
+ 4u
2
+ 5u + 1
c
11
u
9
u
8
+ 2u
7
6u
6
9u
4
3u
3
4u
2
2u 1
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
9
19y
8
+ 3y
7
+ 24y
6
7y
5
61y
4
+ 48y
3
+ 36y
2
32y 16
c
2
y
9
3y
8
11y
7
+ 15y
6
+ y
5
54y
4
+ 39y
3
+ 3y
2
6y 1
c
3
y
9
+ y
8
+ 25y
7
+ 30y
6
+ 72y
5
+ 84y
4
+ 105y
3
+ 54y
2
+ 29y 1
c
4
, c
8
y
9
7y
8
+ ··· + 64y 16
c
5
y
9
14y
7
y
6
+ 123y
5
236y
4
+ 172y
3
52y
2
3y 1
c
6
y
9
5y
8
+ 52y
7
113y
6
+ 225y
5
256y
4
+ 148y
3
29y
2
+ 3y 1
c
7
, c
11
y
9
+ 3y
8
8y
7
60y
6
132y
5
139y
4
75y
3
22y
2
4y 1
c
9
y
9
4y
8
+ 6y
7
+ 11y
6
+ 15y
5
4y
4
12y
3
16y
2
7y 1
c
10
y
9
3y
8
+ 17y
7
36y
6
+ 96y
5
97y
4
+ 81y
3
52y
2
+ 17y 1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
1(vol +
1CS) Cusp shape
u = 0.822660 + 0.322290I
a = 0.897214 + 0.551383I
b = 0.048121 + 0.465250I
1.99801 + 1.72753I 3.97057 2.65342I
u = 0.822660 0.322290I
a = 0.897214 0.551383I
b = 0.048121 0.465250I
1.99801 1.72753I 3.97057 + 2.65342I
u = 1.330240 + 0.168300I
a = 0.008304 0.408404I
b = 0.796448 + 0.144077I
7.57318 6.23029I 10.70312 + 5.64960I
u = 1.330240 0.168300I
a = 0.008304 + 0.408404I
b = 0.796448 0.144077I
7.57318 + 6.23029I 10.70312 5.64960I
u = 1.50796
a = 0.697213
b = 2.17611
0.490477 53.2280
u = 0.197789 + 0.290372I
a = 2.84968 0.54952I
b = 1.087790 0.549338I
5.07942 1.69947I 16.7062 + 3.0605I
u = 0.197789 0.290372I
a = 2.84968 + 0.54952I
b = 1.087790 + 0.549338I
5.07942 + 1.69947I 16.7062 3.0605I
u = 0.45935 + 1.90181I
a = 0.110015 + 0.952948I
b = 0.07249 1.46762I
4.53577 3.70953I 0.23420 + 7.12511I
u = 0.45935 1.90181I
a = 0.110015 0.952948I
b = 0.07249 + 1.46762I
4.53577 + 3.70953I 0.23420 7.12511I
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
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)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
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
, c
8
(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
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)
15