11a
30
(K11a
30
)
1
Arc Sequences
5 1 8 2 9 3 11 6 4 7 10
Solving Sequence
5,9 2,6
1 3 7 4 10 8 11
c
5
c
1
c
2
c
6
c
4
c
9
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
74
u
73
+ ··· u + 1, 4.32400 × 10
95
u
73
9.45395 × 10
96
u
72
+ ··· + 1.65961 × 10
97
b 2.98615 × 10
96
,
4.35536 × 10
96
u
73
4.61345 × 10
96
u
72
+ ··· + 1.65961 × 10
97
a 1.06770 × 10
98
i
There are 1 irreducible components with 74 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
74
u
73
+· · ·u+1, 4.32×10
95
u
73
9.45×10
96
u
72
+· · ·+1.66×10
97
b
2.99 × 10
96
, 4.36 × 10
96
u
73
4.61 × 10
96
u
72
+ · · · + 1.66 × 10
97
a 1.07 × 10
98
i
(i) Arc colorings
a
5
=
0
u
a
9
=
0.262433u
73
+ 0.277984u
72
+ ··· + 4.20161u + 6.43344
0.0260543u
73
+ 0.569649u
72
+ ··· 4.90850u + 0.179931
a
2
=
1
0
a
6
=
1.59709u
73
+ 1.16339u
72
+ ··· 39.5769u 0.0893345
1.21741u
73
+ 2.88944u
72
+ ··· 1.39171u 0.357875
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
1.85321u
73
+ 1.94769u
72
+ ··· 42.5439u + 2.50419
0.972093u
73
+ 2.19919u
72
+ ··· + 1.17531u 1.57417
a
4
=
u
u
a
10
=
0.200805u
73
+ 0.121306u
72
+ ··· + 3.35398u + 6.99258
0.489292u
73
+ 0.726327u
72
+ ··· 4.06086u 0.379215
a
8
=
0.801512u
73
0.694390u
72
+ ··· + 6.87747u 2.86929
0.390085u
73
+ 0.133844u
72
+ ··· + 1.37339u + 0.694390
a
11
=
2.04691u
73
+ 0.431599u
72
+ ··· 29.2718u + 1.94790
1.26728u
73
0.544088u
72
+ ··· 0.654202u + 0.356501
a
11
=
2.04691u
73
+ 0.431599u
72
+ ··· 29.2718u + 1.94790
1.26728u
73
0.544088u
72
+ ··· 0.654202u + 0.356501
(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 = 1.121611 0.263459I
a = 0.222523 1.038980I
b = 0.002619 + 0.200358I
6.19874 1.17606I 10.59937 + 1.67709I
u = 1.121611 + 0.263459I
a = 0.222523 + 1.038980I
b = 0.002619 0.200358I
6.19874 + 1.17606I 10.59937 1.67709I
u = 1.109803 0.659392I
a = 0.437073 0.837400I
b = 0.138113 + 0.485863I
5.77201 + 4.94079I 9.17638 7.24375I
u = 1.109803 + 0.659392I
a = 0.437073 + 0.837400I
b = 0.138113 0.485863I
5.77201 4.94079I 9.17638 + 7.24375I
u = 0.905631 0.988625I
a = 0.590751 + 0.662829I
b = 0.429428 1.031633I
4.76292 + 2.16296I 7.99562 3.01601I
u = 0.905631 + 0.988625I
a = 0.590751 0.662829I
b = 0.429428 + 1.031633I
4.76292 2.16296I 7.99562 + 3.01601I
u = 0.812545 0.520379I
a = 0.628344 + 1.058319I
b = 0.309170 0.421126I
3.70932 + 1.58303I 3.09879 2.53504I
u = 0.812545 + 0.520379I
a = 0.628344 1.058319I
b = 0.309170 + 0.421126I
3.70932 1.58303I 3.09879 + 2.53504I
u = 0.76722 1.25365I
a = 0.617182 + 0.526672I
b = 0.93702 1.13846I
3.27619 + 7.91420I 4.41049 10.44384I
u = 0.76722 + 1.25365I
a = 0.617182 0.526672I
b = 0.93702 + 1.13846I
3.27619 7.91420I 4.41049 + 10.44384I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.636273 0.871096I
a = 0.030056 + 0.299044I
b = 0.910875 + 0.038382I
0.979140 + 0.794104I 4.88709 + 0.51596I
u = 0.636273 + 0.871096I
a = 0.030056 0.299044I
b = 0.910875 0.038382I
0.979140 0.794104I 4.88709 0.51596I
u = 0.613032 1.148643I
a = 0.694678 0.534302I
b = 1.05655 + 1.43473I
1.81406 + 3.75257I 0.74412 4.43411I
u = 0.613032 + 1.148643I
a = 0.694678 + 0.534302I
b = 1.05655 1.43473I
1.81406 3.75257I 0.74412 + 4.43411I
u = 0.611740 0.677389I
a = 0.192765 0.428569I
b = 0.979625 0.589896I
1.44361 + 4.12461I 1.60848 8.74026I
u = 0.611740 + 0.677389I
a = 0.192765 + 0.428569I
b = 0.979625 + 0.589896I
1.44361 4.12461I 1.60848 + 8.74026I
u = 0.549545 1.067760I
a = 0.098301 + 0.313585I
b = 0.908011 0.651294I
0.22924 + 5.70067I 3.12131 5.75856I
u = 0.549545 + 1.067760I
a = 0.098301 0.313585I
b = 0.908011 + 0.651294I
0.22924 5.70067I 3.12131 + 5.75856I
u = 0.488379 0.853979I
a = 0.938103 + 0.514390I
b = 8.04702 0.06024I
1.62217 0.05885I 14.9771 62.8852I
u = 0.488379 + 0.853979I
a = 0.938103 0.514390I
b = 8.04702 + 0.06024I
1.62217 + 0.05885I 14.9771 + 62.8852I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.473139 0.843516I
a = 0.798846 0.503636I
b = 5.47585 1.27838I
1.60692 + 3.97998I 10.4876 34.2104I
u = 0.473139 + 0.843516I
a = 0.798846 + 0.503636I
b = 5.47585 + 1.27838I
1.60692 3.97998I 10.4876 + 34.2104I
u = 0.448860 1.081111I
a = 0.762825 0.513583I
b = 1.57068 + 1.47211I
1.70570 + 3.66146I 3.73929 3.91918I
u = 0.448860 + 1.081111I
a = 0.762825 + 0.513583I
b = 1.57068 1.47211I
1.70570 3.66146I 3.73929 + 3.91918I
u = 0.427892 1.048719I
a = 0.168193 0.308901I
b = 0.636805 + 0.850694I
1.13505 + 1.41023I 4.53209 0.05631I
u = 0.427892 + 1.048719I
a = 0.168193 + 0.308901I
b = 0.636805 0.850694I
1.13505 1.41023I 4.53209 + 0.05631I
u = 0.395146 0.549899I
a = 0.881591 0.288726I
b = 0.25079 1.50544I
1.52579 1.41180I 0.43215 + 2.14680I
u = 0.395146 + 0.549899I
a = 0.881591 + 0.288726I
b = 0.25079 + 1.50544I
1.52579 + 1.41180I 0.43215 2.14680I
u = 0.372530 0.824350I
a = 0.385723 0.096201I
b = 0.040074 + 0.883619I
0.30697 + 1.55903I 1.96359 5.08447I
u = 0.372530 + 0.824350I
a = 0.385723 + 0.096201I
b = 0.040074 0.883619I
0.30697 1.55903I 1.96359 + 5.08447I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.331910 0.162106I
a = 0.15182 1.49705I
b = 0.567616 0.789428I
1.59490 1.49760I 1.53502 + 0.67981I
u = 0.331910 + 0.162106I
a = 0.15182 + 1.49705I
b = 0.567616 + 0.789428I
1.59490 + 1.49760I 1.53502 0.67981I
u = 0.076509 1.358079I
a = 0.813568 0.334633I
b = 1.22164 + 0.97777I
1.83044 + 8.58305I 1.84029 8.84239I
u = 0.076509 + 1.358079I
a = 0.813568 + 0.334633I
b = 1.22164 0.97777I
1.83044 8.58305I 1.84029 + 8.84239I
u = 0.002331 1.262767I
a = 0.871152 + 0.342368I
b = 1.20966 0.89105I
3.04551 + 3.42311I 4.75978 3.23100I
u = 0.002331 + 1.262767I
a = 0.871152 0.342368I
b = 1.20966 + 0.89105I
3.04551 3.42311I 4.75978 + 3.23100I
u = 0.044485 0.183329I
a = 6.06256 0.92178I
b = 0.221183 + 0.916092I
1.47076 + 2.21494I 0.98118 4.30242I
u = 0.044485 + 0.183329I
a = 6.06256 + 0.92178I
b = 0.221183 0.916092I
1.47076 2.21494I 0.98118 + 4.30242I
u = 0.088093 1.145906I
a = 0.159324 0.672962I
b = 0.32644 + 1.66783I
4.54644 + 4.33882I 6.72843 3.56231I
u = 0.088093 + 1.145906I
a = 0.159324 + 0.672962I
b = 0.32644 1.66783I
4.54644 4.33882I 6.72843 + 3.56231I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.155697 0.809103I
a = 1.104598 + 0.560997I
b = 1.036572 0.481405I
1.13641 + 1.44571I 6.07290 4.28126I
u = 0.155697 + 0.809103I
a = 1.104598 0.560997I
b = 1.036572 + 0.481405I
1.13641 1.44571I 6.07290 + 4.28126I
u = 0.196875 1.092949I
a = 0.130987 + 0.790036I
b = 0.21874 1.72634I
5.52578 1.17971I 8.59982 + 2.15292I
u = 0.196875 + 1.092949I
a = 0.130987 0.790036I
b = 0.21874 + 1.72634I
5.52578 + 1.17971I 8.59982 2.15292I
u = 0.510315 0.716522I
a = 1.64068 0.79700I
b = 0.442165 + 0.797520I
1.85423 + 1.80714I 3.40155 8.09072I
u = 0.510315 + 0.716522I
a = 1.64068 + 0.79700I
b = 0.442165 0.797520I
1.85423 1.80714I 3.40155 + 8.09072I
u = 0.558020 1.039771I
a = 0.371930 + 0.928956I
b = 0.11445 1.79925I
3.26838 5.57628I 5.30278 + 6.93314I
u = 0.558020 + 1.039771I
a = 0.371930 0.928956I
b = 0.11445 + 1.79925I
3.26838 + 5.57628I 5.30278 6.93314I
u = 0.564206 0.338491I
a = 1.220332 + 0.384292I
b = 0.144799 0.374435I
1.47671 + 1.08782I 3.50377 1.91086I
u = 0.564206 + 0.338491I
a = 1.220332 0.384292I
b = 0.144799 + 0.374435I
1.47671 1.08782I 3.50377 + 1.91086I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.570967 0.950116I
a = 0.91441 + 1.18652I
b = 0.92763 2.05370I
1.08144 6.25961I 0.32390 + 13.01064I
u = 0.570967 + 0.950116I
a = 0.91441 1.18652I
b = 0.92763 + 2.05370I
1.08144 + 6.25961I 0.32390 13.01064I
u = 0.585176 0.803100I
a = 0.60243 1.46525I
b = 0.75264 + 1.92459I
3.48567 + 0.24626I 11.31963 1.81493I
u = 0.585176 + 0.803100I
a = 0.60243 + 1.46525I
b = 0.75264 1.92459I
3.48567 0.24626I 11.31963 + 1.81493I
u = 0.589516 0.882245I
a = 1.56789 + 0.34750I
b = 0.860787 0.039906I
3.23570 4.91684I 9.8919 + 10.1988I
u = 0.589516 + 0.882245I
a = 1.56789 0.34750I
b = 0.860787 + 0.039906I
3.23570 + 4.91684I 9.8919 10.1988I
u = 0.611725 0.837729I
a = 0.875570 0.894468I
b = 0.34146 + 1.40169I
3.80887 2.41257I 10.33536 + 3.40648I
u = 0.611725 + 0.837729I
a = 0.875570 + 0.894468I
b = 0.34146 1.40169I
3.80887 + 2.41257I 10.33536 3.40648I
u = 0.625155 1.073364I
a = 0.410883 0.817940I
b = 0.04353 + 1.78016I
1.05098 11.53105I 1.83642 + 9.20826I
u = 0.625155 + 1.073364I
a = 0.410883 + 0.817940I
b = 0.04353 1.78016I
1.05098 + 11.53105I 1.83642 9.20826I
8
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.673568 1.112396I
a = 0.715460 + 0.904800I
b = 1.08948 2.19861I
1.50429 11.48101I 1.18871 + 6.59783I
u = 0.673568 + 1.112396I
a = 0.715460 0.904800I
b = 1.08948 + 2.19861I
1.50429 + 11.48101I 1.18871 6.59783I
u = 0.706951 1.138362I
a = 0.674279 0.879423I
b = 1.14666 + 2.21749I
3.5208 17.3478I 1.07995 + 10.16949I
u = 0.706951 + 1.138362I
a = 0.674279 + 0.879423I
b = 1.14666 2.21749I
3.5208 + 17.3478I 1.07995 10.16949I
u = 0.710205 1.019159I
a = 0.666032 1.023387I
b = 1.09114 + 2.06332I
8.07842 8.92677I 5.13032 + 6.83901I
u = 0.710205 + 1.019159I
a = 0.666032 + 1.023387I
b = 1.09114 2.06332I
8.07842 + 8.92677I 5.13032 6.83901I
u = 0.755320 0.469376I
a = 1.005175 0.403721I
b = 0.071149 + 0.645113I
0.70694 + 6.29193I 0.55857 5.25705I
u = 0.755320 + 0.469376I
a = 1.005175 + 0.403721I
b = 0.071149 0.645113I
0.70694 6.29193I 0.55857 + 5.25705I
u = 0.838266 0.662306I
a = 1.140685 + 0.784534I
b = 0.041929 0.162630I
9.17547 + 3.15433I 7.10171 1.44147I
u = 0.838266 + 0.662306I
a = 1.140685 0.784534I
b = 0.041929 + 0.162630I
9.17547 3.15433I 7.10171 + 1.44147I
9
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.888102 0.494344I
a = 1.017387 0.975910I
b = 0.295779 + 0.300052I
3.37758 + 5.71754I 1.13248 2.59386I
u = 0.888102 + 0.494344I
a = 1.017387 + 0.975910I
b = 0.295779 0.300052I
3.37758 5.71754I 1.13248 + 2.59386I
u = 0.971458 0.512667I
a = 0.934005 + 0.914018I
b = 0.367441 0.193909I
5.45791 + 11.23757I 3.45535 6.48717I
u = 0.971458 + 0.512667I
a = 0.934005 0.914018I
b = 0.367441 + 0.193909I
5.45791 11.23757I 3.45535 + 6.48717I
10
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
(u
74
+ u
73
+ ··· + u + 1)
c
2
(u
74
+ 29u
73
+ ··· + 57u + 1)
c
3
(u
74
+ u
73
+ ··· + 11u + 1)
c
5
(u
74
+ 5u
73
+ ··· + 3u + 1)
c
6
(u
74
+ 5u
73
+ ··· + 355u + 199)
c
7
(u
74
+ 5u
73
+ ··· + 3u + 1)
c
8
(u
74
+ 5u
73
+ ··· + 3u + 1)
c
9
(u
74
+ 15u
73
+ ··· 10283u + 547)
c
10
(u
74
+ 5u
73
+ ··· + 3u + 1)
c
11
(u
74
+ 31u
73
+ ··· 5u + 1)
11
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
74
+ 29y
73
+ ··· + 57y + 1)
c
2
(y
74
+ 33y
73
+ ··· 859y + 1)
c
3
(y
74
+ 5y
73
+ ··· + 33y + 1)
c
5
(y
74
+ 53y
73
+ ··· + 5y + 1)
c
6
(y
74
63y
73
+ ··· + 1039717y + 39601)
c
7
(y
74
31y
73
+ ··· + 5y + 1)
c
8
(y
74
+ 53y
73
+ ··· + 5y + 1)
c
9
(y
74
+ 105y
73
+ ··· 37429635y + 299209)
c
10
(y
74
31y
73
+ ··· + 5y + 1)
c
11
(y
74
+ 25y
73
+ ··· + 5y + 1)
12