11n
177
(K11n
177
)
1
Arc Sequences
5 8 1 7 1 10 11 3 4 5 9
Solving Sequence
4,7 5,9
10 11 1 2 3 6 8
c
4
c
9
c
10
c
11
c
1
c
3
c
6
c
8
c
2
, c
5
, c
7
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
20
+ 7u
19
+ ··· + 7u + 1, 90743068u
19
115535639u
18
+ ··· + 126101637a + 926160181,
1128911936u
19
+ 7112577889u
18
+ ··· + 378304911b + 2114101036i
I
u
2
= hu
61
6u
60
+ ··· + 22u 1, 6.99835 × 10
132
u
60
3.73036 × 10
133
u
59
+ ··· + 7.67152 × 10
131
b + 1.03281 × 10
133
,
1.09862 × 10
133
u
60
+ 5.58168 × 10
133
u
59
+ ··· + 7.67152 × 10
131
a + 2.18003 × 10
133
i
There are 2 irreducible components with 81 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
20
+ 7u
19
+ · · · + 7u + 1, 9.07 × 10
7
u
19
1.16 × 10
8
u
18
+ · · · + 1.26 ×
10
8
a +9.26 ×10
8
, 1.13×10
9
u
19
+7.11× 10
9
u
18
+· · ·+ 3 .78 ×10
8
b +2.11 ×10
9
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u
2
a
9
=
0.719603u
19
+ 0.916210u
18
+ ··· 47.0765u 7.34455
2.98413u
19
18.8012u
18
+ ··· 30.1315u 5.58835
a
10
=
2.26453u
19
17.8850u
18
+ ··· 77.2080u 12.9329
2.98413u
19
18.8012u
18
+ ··· 30.1315u 5.58835
a
11
=
1.51690u
19
13.3458u
18
+ ··· 63.5738u 9.37781
3.82843u
19
24.0392u
18
+ ··· 34.2439u 6.28264
a
1
=
5.08792u
19
33.3716u
18
+ ··· 19.0922u + 3.78084
2.59919u
19
15.9162u
18
+ ··· 16.7894u 1.49831
a
2
=
3.49566u
19
21.8039u
18
+ ··· + 8.31611u + 7.52299
1.48526u
19
9.28206u
18
+ ··· 12.2437u 1.07639
a
3
=
4.90234u
19
34.2834u
18
+ ··· 110.216u 25.4823
0.787547u
19
+ 5.75304u
18
+ ··· + 4.69080u 0.480646
a
6
=
8.80294u
19
56.3928u
18
+ ··· 39.7359u + 6.01428
1.28089u
19
8.32450u
18
+ ··· 9.36213u + 0.513647
a
8
=
4.00744u
19
24.6679u
18
+ ··· + 23.6106u + 12.8190
1.78790u
19
10.4025u
18
+ ··· 4.51105u + 1.29364
a
8
=
4.00744u
19
24.6679u
18
+ ··· + 23.6106u + 12.8190
1.78790u
19
10.4025u
18
+ ··· 4.51105u + 1.29364
(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 = 1.74325 0.56061I
a = 0.559492 0.462325I
b = 0.359943 + 0.340200I
4.20835 + 3.34749I 10.38285 + 6.22702I
u = 1.74325 + 0.56061I
a = 0.559492 + 0.462325I
b = 0.359943 0.340200I
4.20835 3.34749I 10.38285 6.22702I
u = 1.25091 1.08948I
a = 0.769491 + 0.199641I
b = 0.995029 + 0.394706I
3.16335 + 4.45169I 5.12268 4.32037I
u = 1.25091 + 1.08948I
a = 0.769491 0.199641I
b = 0.995029 0.394706I
3.16335 4.45169I 5.12268 + 4.32037I
u = 1.16470 1.00953I
a = 1.039942 0.832857I
b = 1.260649 + 0.074928I
0.49537 + 4.42981I 0.62033 12.45769I
u = 1.16470 + 1.00953I
a = 1.039942 + 0.832857I
b = 1.260649 0.074928I
0.49537 4.42981I 0.62033 + 12.45769I
u = 0.788389 0.225503I
a = 2.06691 + 0.21154I
b = 1.164856 0.462424I
1.19434 + 6.17955I 7.14225 5.75160I
u = 0.788389 + 0.225503I
a = 2.06691 0.21154I
b = 1.164856 + 0.462424I
1.19434 6.17955I 7.14225 + 5.75160I
u = 0.707689 0.412567I
a = 1.76404 + 0.27870I
b = 1.072191 0.043440I
3.01685 + 1.94709I 2.17570 3.84431I
u = 0.707689 + 0.412567I
a = 1.76404 0.27870I
b = 1.072191 + 0.043440I
3.01685 1.94709I 2.17570 + 3.84431I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.356427 0.624501I
a = 0.393756 + 0.181030I
b = 0.95816 1.39951I
1.79922 + 1.91581I 10.61370 5.31696I
u = 0.356427 + 0.624501I
a = 0.393756 0.181030I
b = 0.95816 + 1.39951I
1.79922 1.91581I 10.61370 + 5.31696I
u = 0.219224 0.286923I
a = 3.91926 + 2.85715I
b = 0.347284 + 0.981370I
5.99125 + 4.45821I 9.91425 3.94197I
u = 0.219224 + 0.286923I
a = 3.91926 2.85715I
b = 0.347284 0.981370I
5.99125 4.45821I 9.91425 + 3.94197I
u = 0.717599 0.163144I
a = 0.83846 1.60432I
b = 0.027021 0.443269I
4.39215 0.76384I 1.31293 + 11.96948I
u = 0.717599 + 0.163144I
a = 0.83846 + 1.60432I
b = 0.027021 + 0.443269I
4.39215 + 0.76384I 1.31293 11.96948I
u = 0.754373 1.110109I
a = 0.347493 + 0.199274I
b = 0.504871 + 0.746622I
4.41710 6.04390I 11.7885 + 8.3222I
u = 0.754373 + 1.110109I
a = 0.347493 0.199274I
b = 0.504871 0.746622I
4.41710 + 6.04390I 11.7885 8.3222I
u = 1.04212
a = 0.696466
b = 1.09048
1.39500 7.03289
u = 1.47513
a = 3.72204
b = 2.26462
7.13067 24.6897
4
II. I
u
2
= hu
61
6u
60
+ · · · + 22u 1, 7.00 × 10
132
u
60
3.73 × 10
133
u
59
+
· · · + 7.67 × 10
131
b + 1.03 × 10
133
, 1.10 × 10
133
u
60
+ 5.58 × 10
133
u
59
+ · · · +
7.67 × 10
131
a + 2.18 × 10
133
i
(i) Arc colorings
a
4
=
1
0
a
7
=
0
u
a
5
=
1
u
2
a
9
=
14.3208u
60
72.7585u
59
+ ··· 206.500u 28.4172
9.12251u
60
+ 48.6261u
59
+ ··· + 255.177u 13.4629
a
10
=
5.19828u
60
24.1323u
59
+ ··· + 48.6770u 41.8802
9.12251u
60
+ 48.6261u
59
+ ··· + 255.177u 13.4629
a
11
=
8.52693u
60
42.2903u
59
+ ··· 56.4373u 35.4746
9.81786u
60
+ 52.7933u
59
+ ··· + 291.755u 15.2769
a
1
=
18.4544u
60
+ 102.527u
59
+ ··· + 767.838u 85.5388
1.70495u
60
10.5911u
59
+ ··· 122.814u + 4.69515
a
2
=
16.2066u
60
+ 91.1518u
59
+ ··· + 728.723u 82.0347
0.141591u
60
1.02642u
59
+ ··· 78.6144u + 2.58393
a
3
=
6.21910u
60
+ 36.8107u
59
+ ··· + 409.616u 90.7939
1.82316u
60
9.71183u
59
+ ··· 56.7906u + 0.467394
a
6
=
32.7048u
60
176.974u
59
+ ··· 1174.08u + 136.318
1.84026u
60
+ 9.79497u
59
+ ··· + 51.9233u + 0.0365336
a
8
=
20.7759u
60
113.720u
59
+ ··· 810.749u + 113.254
6.06601u
60
+ 32.7803u
59
+ ··· + 197.445u 7.16283
a
8
=
20.7759u
60
113.720u
59
+ ··· 810.749u + 113.254
6.06601u
60
+ 32.7803u
59
+ ··· + 197.445u 7.16283
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.79250 0.51553I
a = 0.552573 0.571506I
b = 0.326709 + 0.579680I
4.00502 + 3.50717I 14.2677 12.3216I
u = 1.79250 + 0.51553I
a = 0.552573 + 0.571506I
b = 0.326709 0.579680I
4.00502 3.50717I 14.2677 + 12.3216I
u = 1.27973 1.06767I
a = 0.831962 + 0.163731I
b = 0.955356 + 0.410479I
3.77024 + 4.53103I 8.22458 6.69536I
u = 1.27973 + 1.06767I
a = 0.831962 0.163731I
b = 0.955356 0.410479I
3.77024 4.53103I 8.22458 + 6.69536I
u = 1.162973 0.773277I
a = 1.341960 + 0.150884I
b = 0.601403 0.990246I
3.01562 + 7.11329I 6.04272 5.67554I
u = 1.162973 + 0.773277I
a = 1.341960 0.150884I
b = 0.601403 + 0.990246I
3.01562 7.11329I 6.04272 + 5.67554I
u = 1.06198 1.02689I
a = 1.069110 0.634165I
b = 1.350591 0.237746I
0.20782 + 3.93388I 7.66338 + 0.06770I
u = 1.06198 + 1.02689I
a = 1.069110 + 0.634165I
b = 1.350591 + 0.237746I
0.20782 3.93388I 7.66338 0.06770I
u = 0.964628 0.709303I
a = 1.010534 0.312692I
b = 1.121706 0.172128I
0.28694 + 2.95538I 2.97672 3.80080I
u = 0.964628 + 0.709303I
a = 1.010534 + 0.312692I
b = 1.121706 + 0.172128I
0.28694 2.95538I 2.97672 + 3.80080I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.917787 0.165107I
a = 0.379101 1.262778I
b = 0.0981432 + 0.1002442I
1.88623 + 2.18277I 1.04287 4.49672I
u = 0.917787 + 0.165107I
a = 0.379101 + 1.262778I
b = 0.0981432 0.1002442I
1.88623 2.18277I 1.04287 + 4.49672I
u = 0.913197 0.485728I
a = 1.212196 0.288201I
b = 0.558966 + 0.006287I
2.15550 + 2.60300I 3.71097 4.89250I
u = 0.913197 + 0.485728I
a = 1.212196 + 0.288201I
b = 0.558966 0.006287I
2.15550 2.60300I 3.71097 + 4.89250I
u = 0.738595 0.236148I
a = 0.832894 + 0.053513I
b = 0.87846 1.74873I
4.62267 + 5.03624I 1.21514 6.28743I
u = 0.738595 + 0.236148I
a = 0.832894 0.053513I
b = 0.87846 + 1.74873I
4.62267 5.03624I 1.21514 + 6.28743I
u = 0.621665 0.901773I
a = 0.0688202 0.0979216I
b = 0.096125 + 1.177072I
4.69632 0.83070I 7.50096 + 0.09771I
u = 0.621665 + 0.901773I
a = 0.0688202 + 0.0979216I
b = 0.096125 1.177072I
4.69632 + 0.83070I 7.50096 0.09771I
u = 0.555444 0.142845I
a = 2.26625 + 5.05458I
b = 0.254393 0.501810I
5.39490 + 4.53513I 4.41246 6.52317I
u = 0.555444 + 0.142845I
a = 2.26625 5.05458I
b = 0.254393 + 0.501810I
5.39490 4.53513I 4.41246 + 6.52317I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.522533 0.730901I
a = 0.144357 0.171554I
b = 0.432120 0.823592I
0.17125 + 1.80764I 1.37492 3.40193I
u = 0.522533 + 0.730901I
a = 0.144357 + 0.171554I
b = 0.432120 + 0.823592I
0.17125 1.80764I 1.37492 + 3.40193I
u = 0.414111 0.938629I
a = 0.1178343 + 0.0321293I
b = 0.534913 + 0.792872I
2.45305 + 5.61811I 4.16455 7.21914I
u = 0.414111 + 0.938629I
a = 0.1178343 0.0321293I
b = 0.534913 0.792872I
2.45305 5.61811I 4.16455 + 7.21914I
u = 0.320157 0.193639I
a = 1.47360 + 1.08863I
b = 1.30170 + 1.34174I
1.23241 + 1.81263I 4.83572 3.41464I
u = 0.320157 + 0.193639I
a = 1.47360 1.08863I
b = 1.30170 1.34174I
1.23241 1.81263I 4.83572 + 3.41464I
u = 0.0549213
a = 35.8349
b = 1.17575
8.81824 11.0144
u = 0.397713 0.895040I
a = 0.47437 + 1.47017I
b = 0.941582 + 0.717587I
8.02679 3.97936I 9.71153 + 5.92772I
u = 0.397713 + 0.895040I
a = 0.47437 1.47017I
b = 0.941582 0.717587I
8.02679 + 3.97936I 9.71153 5.92772I
u = 0.446774 0.299657I
a = 1.233864 + 0.263450I
b = 0.619078 0.455052I
1.310999 + 0.288972I 7.97577 1.37388I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.446774 + 0.299657I
a = 1.233864 0.263450I
b = 0.619078 + 0.455052I
1.310999 0.288972I 7.97577 + 1.37388I
u = 0.597452 0.128326I
a = 2.48113 0.24157I
b = 1.163418 + 0.183697I
2.67011 1.18908I 2.36924 2.70122I
u = 0.597452 + 0.128326I
a = 2.48113 + 0.24157I
b = 1.163418 0.183697I
2.67011 + 1.18908I 2.36924 + 2.70122I
u = 0.613736 0.239101I
a = 2.52425 + 0.04849I
b = 1.231987 0.461080I
0.79598 6.19961I 13.0645 + 6.4291I
u = 0.613736 + 0.239101I
a = 2.52425 0.04849I
b = 1.231987 + 0.461080I
0.79598 + 6.19961I 13.0645 6.4291I
u = 0.657807 0.856967I
a = 0.643301 1.062158I
b = 1.23123 + 1.82016I
9.08401 5.81465I 8.75436 + 5.87621I
u = 0.657807 + 0.856967I
a = 0.643301 + 1.062158I
b = 1.23123 1.82016I
9.08401 + 5.81465I 8.75436 5.87621I
u = 0.684118 0.083322I
a = 1.23986 1.63279I
b = 0.443324 0.492133I
4.49837 0.35042I 4.30932 5.56885I
u = 0.684118 + 0.083322I
a = 1.23986 + 1.63279I
b = 0.443324 + 0.492133I
4.49837 + 0.35042I 4.30932 + 5.56885I
u = 0.73271 1.22086I
a = 0.070280 + 1.186808I
b = 0.62002 1.71714I
4.00110 + 1.61857I 9.32212 5.29590I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.73271 + 1.22086I
a = 0.070280 1.186808I
b = 0.62002 + 1.71714I
4.00110 1.61857I 9.32212 + 5.29590I
u = 0.740215 0.784625I
a = 0.659445 + 0.163645I
b = 0.503386 0.896416I
9.14900 + 1.39395I 7.66547 0.07252I
u = 0.740215 + 0.784625I
a = 0.659445 0.163645I
b = 0.503386 + 0.896416I
9.14900 1.39395I 7.66547 + 0.07252I
u = 0.758542 0.836328I
a = 0.886679 0.576803I
b = 0.749984 0.861069I
3.79837 4.86090I 6.23298 + 3.29979I
u = 0.758542 + 0.836328I
a = 0.886679 + 0.576803I
b = 0.749984 + 0.861069I
3.79837 + 4.86090I 6.23298 3.29979I
u = 0.870157
a = 0.569651
b = 0.981523
1.86682 10.5557
u = 0.89363 1.22465I
a = 0.193674 0.792804I
b = 0.87409 + 1.16058I
9.28034 + 8.26953I 6.49557 5.58835I
u = 0.89363 + 1.22465I
a = 0.193674 + 0.792804I
b = 0.87409 1.16058I
9.28034 8.26953I 6.49557 + 5.58835I
u = 0.947645 0.793400I
a = 0.980234 + 0.176631I
b = 0.67780 + 1.29191I
8.65446 7.29554I 6.66688 + 5.38635I
u = 0.947645 + 0.793400I
a = 0.980234 0.176631I
b = 0.67780 1.29191I
8.65446 + 7.29554I 6.66688 5.38635I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.96516 1.14793I
a = 0.358213 0.334904I
b = 0.435129 0.465442I
3.79970 5.99586I 1.93389 + 7.19294I
u = 0.96516 + 1.14793I
a = 0.358213 + 0.334904I
b = 0.435129 + 0.465442I
3.79970 + 5.99586I 1.93389 7.19294I
u = 1.06742
a = 0.962281
b = 1.59779
4.17679 1.24526
u = 1.128936 0.818009I
a = 0.412888 + 0.064929I
b = 0.019530 + 0.514482I
2.50680 1.31837I 1.83401 + 3.58189I
u = 1.128936 + 0.818009I
a = 0.412888 0.064929I
b = 0.019530 0.514482I
2.50680 + 1.31837I 1.83401 3.58189I
u = 1.13951 0.97223I
a = 1.58015 0.02291I
b = 1.29432 1.24376I
8.3594 16.0917I 5.10700 + 7.91248I
u = 1.13951 + 0.97223I
a = 1.58015 + 0.02291I
b = 1.29432 + 1.24376I
8.3594 + 16.0917I 5.10700 7.91248I
u = 1.15944 0.95015I
a = 1.72217 0.35123I
b = 1.23928 + 1.37839I
2.68997 9.29142I 3.41999 + 7.85642I
u = 1.15944 + 0.95015I
a = 1.72217 + 0.35123I
b = 1.23928 1.37839I
2.68997 + 9.29142I 3.41999 7.85642I
u = 1.40565 0.45452I
a = 3.34491 + 0.35737I
b = 2.02754 0.83166I
6.95721 + 0.21792I 6.3147 16.1801I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.40565 + 0.45452I
a = 3.34491 0.35737I
b = 2.02754 + 0.83166I
6.95721 0.21792I 6.3147 + 16.1801I
11
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
20
u
19
+ ··· 2u + 1)(u
61
+ 2u
60
+ ··· 25u + 1)
c
2
(u
20
10u
18
+ ··· 3u + 1)(u
61
+ u
60
+ ··· + 1440u + 211)
c
3
(u
20
+ 7u
19
+ ··· 4u 1)(u
61
+ 4u
60
+ ··· 957u 121)
c
4
(u
20
+ 7u
19
+ ··· + 7u + 1)(u
61
+ 6u
60
+ ··· + 22u + 1)
c
5
(u
20
+ u
19
+ ··· + 2u + 1)(u
61
+ 2u
60
+ ··· 25u + 1)
c
6
(u
20
u
19
+ ··· + u + 1)(u
61
+ 4u
60
+ ··· + 6790u 2531)
c
7
(u
20
+ 2u
17
+ ··· 11u 1)(u
61
+ u
60
+ ··· 9850u 2333)
c
8
(u
20
10u
18
+ ··· + 3u + 1)(u
61
+ u
60
+ ··· + 1440u + 211)
c
9
(u
20
u
19
+ ··· 2u 1)(u
61
+ 2u
60
+ ··· + 529u + 41)
c
10
(u
20
u
19
+ ··· + 5u
2
+ 1)(u
61
10u
59
+ ··· 62973u 14123)
c
11
(u
20
11u
19
+ ··· u 1)(u
61
+ 4u
60
+ ··· + 6u 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
20
5y
19
+ ··· + 14y + 1)(y
61
54y
60
+ ··· + 111y 1)
c
2
, c
8
(y
20
20y
19
+ ··· 23y + 1)(y
61
57y
60
+ ··· + 631204y 44521)
c
3
(y
20
7y
19
+ ··· + 14y + 1)(y
61
28y
60
+ ··· + 684255y 14641)
c
4
(y
20
11y
19
+ ··· 3y + 1)(y
61
16y
60
+ ··· + 364y 1)
c
6
(y
20
+ 11y
19
+ ··· 9y + 1)
(y
61
14y
60
+ ··· + 234688910y 6405961)
c
7
(y
20
30y
18
+ ··· 15y + 1)
(y
61
+ 23y
60
+ ··· + 27116488y 5442889)
c
9
(y
20
11y
19
+ ··· + 6y + 1)(y
61
+ 52y
59
+ ··· 12653y 1681)
c
10
(y
20
+ 9y
19
+ ··· + 10y + 1)
(y
61
20y
60
+ ··· + 4161767199y 199459129)
c
11
(y
20
11y
19
+ ··· 39y + 1)(y
61
8y
60
+ ··· + 12y 1)
13