11a
318
(K11a
318
)
1
Arc Sequences
6 8 1 9 11 2 10 3 5 7 4
Solving Sequence
7,10 2,8
3 11 6 1 4 5 9
c
7
c
2
c
10
c
6
c
1
c
3
c
5
c
9
c
4
, c
8
, c
11
Representation Ideals
I =
6
\
i=1
I
u
i
I
u
1
= hu 1, a + 1, b + 1i
I
u
2
= hu
4
+ u 1, u
3
+ u
2
+ b, u
3
+ u
2
+ a + 1i
I
u
3
= hu
12
2u
10
+ u
9
5u
7
+ 6u
6
+ u
5
9u
4
+ 5u
3
+ 6u
2
2u 1, 352u
11
94u
10
+ ··· + 697b + 936,
1440u
11
+ 638u
10
+ ··· + 697a + 2634i
I
u
4
= hu
18
+ u
17
+ ··· + u
2
1, 900967u
17
+ 78843u
16
+ ··· + 1982053b 1777862,
372351u
17
+ 1342734u
16
+ ··· + 1982053a 2640641i
I
u
5
= hu
20
8u
18
+ ··· + u 1, 321u
19
+ 125u
18
+ ··· + 367b + 610,
1165u
19
509u
18
+ ··· + 367a 1838i
I
u
6
= hu
60
u
59
+ ··· 109u + 17,
2.09517 × 10
101
u
59
+ 2.44801 × 10
100
u
58
+ ··· + 5.25066 × 10
101
b + 3.92526 × 10
102
,
1.15506 × 10
102
u
59
+ 7.80096 × 10
100
u
58
+ ··· + 8.92612 × 10
102
a 5.37881 × 10
103
i
There are 6 irreducible components with 115 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 1, a + 1, b + 1i
(i) Arc colorings
a
7
=
0
1
a
10
=
1
1
a
2
=
1
0
a
8
=
1
0
a
3
=
1
0
a
11
=
1
2
a
6
=
1
1
a
1
=
0
1
a
4
=
1
1
a
5
=
0
1
a
9
=
1
0
a
9
=
1
0
(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 = 1.00000
a = 1.00000
b = 1.00000
4.93480 18.0000
3
II. I
u
2
= hu
4
+ u 1, u
3
+ u
2
+ b, u
3
+ u
2
+ a + 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
u
3
u
2
1
u
3
u
2
a
2
=
1
0
a
8
=
u
3
u
2
u 1
u
2
a
3
=
u
3
+ 2
u + 1
a
11
=
u
3
u
2
1
u
3
u
2
1
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
4
=
u + 1
1
a
5
=
u
u
a
9
=
u
3
1
u
3
a
9
=
u
3
1
u
3
(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 = 1.22074
a = 0.671044
b = 0.328956
8.36260 19.9194
u = 0.248126 1.033982I
a = 0.788105 0.401358I
b = 1.78810 0.40136I
3.04135 1.96274I 6.36273 + 1.58218I
u = 0.248126 + 1.033982I
a = 0.788105 + 0.401358I
b = 1.78810 + 0.40136I
3.04135 + 1.96274I 6.36273 1.58218I
u = 0.724492
a = 1.90517
b = 0.905166
4.29983 3.35519
5
III. I
u
3
= hu
12
2u
10
+ · · · 2u 1, 352u
11
94u
10
+ · · · + 697b +
936, 1440u
11
+ 638u
10
+ · · · + 697a + 2634i
(i) Arc colorings
a
7
=
0
u
a
10
=
2.06600u
11
0.915352u
10
+ ··· + 3.52941u 3.77905
0.505022u
11
+ 0.134864u
10
+ ··· 0.529412u 1.34290
a
2
=
1
0
a
8
=
1.05022u
11
+ 0.348637u
10
+ ··· 3.29412u + 3.57102
1
a
3
=
1.05022u
11
+ 0.348637u
10
+ ··· 3.29412u + 4.57102
1
a
11
=
2.06600u
11
0.915352u
10
+ ··· + 3.52941u 3.77905
0.364419u
11
0.358680u
10
+ ··· 0.294118u 2.25825
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
4
=
0.691535u
11
+ 0.286944u
10
+ ··· 2.76471u + 3.20660
0.566714u
11
0.0774749u
10
+ ··· + 0.176471u + 0.984218
a
5
=
1.25825u
11
0.364419u
10
+ ··· + 2.94118u 2.22238
0.566714u
11
+ 0.0774749u
10
+ ··· 0.176471u 0.984218
a
9
=
1
0
a
9
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.36109 0.59989I
a = 0.583021 0.456173I
b = 1.49269 + 1.63300I
5.59278 14.0000
u = 1.36109 + 0.59989I
a = 0.583021 + 0.456173I
b = 1.49269 1.63300I
5.59278 14.0000
u = 0.849985 0.107756I
a = 0.15190 1.75032I
b = 0.189428 + 1.216412I
2.30291 14.0000
u = 0.849985 + 0.107756I
a = 0.15190 + 1.75032I
b = 0.189428 1.216412I
2.30291 14.0000
u = 0.319710
a = 3.19668
b = 1.29129
5.59278 14.0000
u = 0.128305 1.331903I
a = 0.588280 0.308870I
b = 1.75750 0.34178I
2.30291 14.0000
u = 0.128305 + 1.331903I
a = 0.588280 + 0.308870I
b = 1.75750 + 0.34178I
2.30291 14.0000
u = 0.580134
a = 0.411989
b = 1.75669
5.59278 14.0000
u = 0.721680 0.842764I
a = 0.313126 + 1.043711I
b = 0.710863 0.183182I
2.30291 14.0000
u = 0.721680 + 0.842764I
a = 0.313126 1.043711I
b = 0.710863 + 0.183182I
2.30291 14.0000
7
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.13635
a = 1.17388
b = 0.102214
5.59278 14.0000
u = 1.32540
a = 0.729484
b = 0.336556
5.59278 14.0000
8
IV.
I
u
4
= hu
18
+ u
17
+ · · · + u
2
1, 9.01 × 10
5
u
17
+ 7.88 × 10
4
u
16
+ · · · + 1.98 ×
10
6
b 1.78 ×10
6
, 3.72× 10
5
u
17
+1.34× 10
6
u
16
+· · ·+ 1.98 ×10
6
a 2.64 ×10
6
i
(i) Arc colorings
a
7
=
0
u
a
10
=
0.187861u
17
0.677446u
16
+ ··· + 5.62561u + 1.33228
0.454563u
17
0.0397785u
16
+ ··· + 2.06932u + 0.896980
a
2
=
1
0
a
8
=
0.0670699u
17
+ 0.526535u
16
+ ··· + 0.818316u + 1.86468
0.451948u
17
+ 0.218673u
16
+ ··· + 0.601597u + 0.0859684
a
3
=
0.343733u
17
+ 0.573494u
16
+ ··· 3.43113u + 2.30647
0.572497u
17
+ 0.268771u
16
+ ··· 2.24851u + 0.799368
a
11
=
0.187861u
17
0.677446u
16
+ ··· + 5.62561u + 1.33228
0.171077u
17
0.320336u
16
+ ··· + 1.88146u + 0.407395
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
4
=
0.418192u
17
+ 0.463227u
16
+ ··· 1.60927u + 1.83513
0.00845336u
17
+ 0.364603u
16
+ ··· 1.75892u + 0.515882
a
5
=
0.426645u
17
0.0986240u
16
+ ··· 0.149649u 1.31924
0.757695u
17
0.460834u
16
+ ··· + 1.61964u 1.27985
a
9
=
0.515882u
17
0.507429u
16
+ ··· + 6.94486u + 1.75892
0.763966u
17
+ 0.0147246u
16
+ ··· + 3.34917u + 0.139285
a
9
=
0.515882u
17
0.507429u
16
+ ··· + 6.94486u + 1.75892
0.763966u
17
+ 0.0147246u
16
+ ··· + 3.34917u + 0.139285
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.244326 0.432653I
a = 0.640426 + 0.669927I
b = 1.89549 0.14793I
0.46162 9.59091I 11.3598 + 8.6982I
u = 1.244326 + 0.432653I
a = 0.640426 0.669927I
b = 1.89549 + 0.14793I
0.46162 + 9.59091I 11.3598 8.6982I
u = 1.219634 0.122646I
a = 0.419802 0.772436I
b = 1.84111 + 1.75570I
4.77876 5.57099I 14.6445 + 6.8943I
u = 1.219634 + 0.122646I
a = 0.419802 + 0.772436I
b = 1.84111 1.75570I
4.77876 + 5.57099I 14.6445 6.8943I
u = 1.155402 0.382844I
a = 0.805383 + 0.853229I
b = 0.0599737 + 0.0141160I
8.49225 3.12657I 16.5106 + 4.5687I
u = 1.155402 + 0.382844I
a = 0.805383 0.853229I
b = 0.0599737 0.0141160I
8.49225 + 3.12657I 16.5106 4.5687I
u = 0.52847 1.35181I
a = 0.499034 0.492920I
b = 1.82277 + 0.03177I
2.78527 + 3.16569I 11.24611 7.60453I
u = 0.52847 + 1.35181I
a = 0.499034 + 0.492920I
b = 1.82277 0.03177I
2.78527 3.16569I 11.24611 + 7.60453I
u = 0.333926
a = 0.716134
b = 0.234092
0.538352 18.5399
u = 0.148267 0.251923I
a = 2.14317 2.34534I
b = 1.168914 0.407268I
1.73441 2.46344I 11.30045 + 4.80762I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.148267 + 0.251923I
a = 2.14317 + 2.34534I
b = 1.168914 + 0.407268I
1.73441 + 2.46344I 11.30045 4.80762I
u = 0.503027 0.934053I
a = 0.870982 + 0.607288I
b = 1.24828 0.81372I
5.93090 + 0.43570I 2.98328 1.68118I
u = 0.503027 + 0.934053I
a = 0.870982 0.607288I
b = 1.24828 + 0.81372I
5.93090 0.43570I 2.98328 + 1.68118I
u = 0.969317
a = 1.11851
b = 1.01033
4.93604 18.1165
u = 1.306394 0.030156I
a = 0.225308 + 0.468162I
b = 0.390793 + 0.857611I
7.41832 1.14356I 14.7481 + 6.1062I
u = 1.306394 + 0.030156I
a = 0.225308 0.468162I
b = 0.390793 0.857611I
7.41832 + 1.14356I 14.7481 6.1062I
u = 1.37244 0.65413I
a = 0.787491 0.532626I
b = 1.80080 + 1.22375I
3.9350 + 17.2773I 12.8790 9.3490I
u = 1.37244 + 0.65413I
a = 0.787491 + 0.532626I
b = 1.80080 1.22375I
3.9350 17.2773I 12.8790 + 9.3490I
11
V. I
u
5
= hu
20
8u
18
+ · · · + u 1, 321u
19
+ 125u
18
+ · · · + 367b +
610, 1165u
19
509u
18
+ · · · + 367a 1838i
(i) Arc colorings
a
7
=
0
u
a
10
=
3.17439u
19
+ 1.38692u
18
+ ··· + 3.88283u + 5.00817
0.874659u
19
0.340599u
18
+ ··· + 3.49046u 1.66213
a
2
=
1
0
a
8
=
0.972752u
19
+ 0.752044u
18
+ ··· + 7.23706u + 6.02997
0.681199u
19
0.198910u
18
+ ··· 1.07357u 0.250681
a
3
=
1.25068u
19
0.681199u
18
+ ··· + 0.980926u + 0.675749
0.00544959u
19
0.449591u
18
+ ··· 1.15259u 0.594005
a
11
=
3.17439u
19
+ 1.38692u
18
+ ··· + 3.88283u + 5.00817
1.79564u
19
0.359673u
18
+ ··· + 5.27793u 0.275204
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
4
=
0.656676u
19
0.675749u
18
+ ··· + 1.61308u + 1.42234
1.02452u
19
0.523161u
18
+ ··· 2.68665u 0.673025
a
5
=
2.61035u
19
1.35422u
18
+ ··· 8.08992u 5.52861
1.32425u
19
+ 0.749319u
18
+ ··· 4.07902u + 1.65668
a
9
=
4.12534u
19
+ 1.34060u
18
+ ··· + 10.5095u + 8.66213
0.994550u
19
+ 0.449591u
18
+ ··· 0.847411u + 0.594005
a
9
=
4.12534u
19
+ 1.34060u
18
+ ··· + 10.5095u + 8.66213
0.994550u
19
+ 0.449591u
18
+ ··· 0.847411u + 0.594005
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.361797 0.242619I
a = 0.095947 + 0.513760I
b = 0.583410 + 0.595260I
7.12244 10.1534
u = 1.361797 + 0.242619I
a = 0.095947 0.513760I
b = 0.583410 0.595260I
7.12244 10.1534
u = 1.006884 0.379394I
a = 0.695728 0.774823I
b = 1.52282 + 1.87081I
5.60500 3.07077I 11.10306 + 5.53745I
u = 1.006884 + 0.379394I
a = 0.695728 + 0.774823I
b = 1.52282 1.87081I
5.60500 + 3.07077I 11.10306 5.53745I
u = 1.005264 0.622930I
a = 0.912993 + 0.311512I
b = 1.51476 0.38432I
2.31904 5.08447I 9.51292 + 2.92589I
u = 1.005264 + 0.622930I
a = 0.912993 0.311512I
b = 1.51476 + 0.38432I
2.31904 + 5.08447I 9.51292 2.92589I
u = 0.721984
a = 1.16680
b = 1.90416
6.32941 27.2567
u = 0.543411 0.587321I
a = 0.71857 1.38681I
b = 0.468357 + 0.086560I
3.51176 5.53076
u = 0.543411 + 0.587321I
a = 0.71857 + 1.38681I
b = 0.468357 0.086560I
3.51176 5.53076
u = 0.307724 0.858449I
a = 0.976897 0.701129I
b = 0.883988 0.244304I
3.58542 5.93598
13
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.307724 + 0.858449I
a = 0.976897 + 0.701129I
b = 0.883988 + 0.244304I
3.58542 5.93598
u = 0.502690 0.120984I
a = 0.92430 + 2.61389I
b = 0.212461 0.073115I
2.31904 + 5.08447I 9.51292 2.92589I
u = 0.502690 + 0.120984I
a = 0.92430 2.61389I
b = 0.212461 + 0.073115I
2.31904 5.08447I 9.51292 + 2.92589I
u = 0.641197 0.460705I
a = 0.741778 0.455522I
b = 2.40890 + 1.17537I
1.76138 + 5.90098I 8.4456 11.9708I
u = 0.641197 + 0.460705I
a = 0.741778 + 0.455522I
b = 2.40890 1.17537I
1.76138 5.90098I 8.4456 + 11.9708I
u = 1.22178
a = 1.10145
b = 0.252409
6.32941 27.2567
u = 1.322278 0.225447I
a = 0.547307 + 0.865735I
b = 1.23645 1.11406I
1.76138 + 5.90098I 8.4456 11.9708I
u = 1.322278 + 0.225447I
a = 0.547307 0.865735I
b = 1.23645 + 1.11406I
1.76138 5.90098I 8.4456 + 11.9708I
u = 1.50902 0.12166I
a = 0.061893 + 0.356567I
b = 1.029644 + 0.198033I
5.60500 3.07077I 11.10306 + 5.53745I
u = 1.50902 + 0.12166I
a = 0.061893 0.356567I
b = 1.029644 0.198033I
5.60500 + 3.07077I 11.10306 5.53745I
14
VI. I
u
6
= hu
60
u
59
+ · · · 109u + 17, 2.10 × 10
101
u
59
+ 2.45 × 10
100
u
58
+
· · · + 5.25 × 10
101
b + 3.93 × 10
102
, 1.16 × 10
102
u
59
+ 7.80 × 10
100
u
58
+ · · · +
8.93 × 10
102
a 5.38 × 10
103
i
(i) Arc colorings
a
7
=
0
u
a
10
=
0.129402u
59
0.00873947u
58
+ ··· 2.44980u + 6.02592
0.399029u
59
0.0466229u
58
+ ··· + 30.8128u 7.47574
a
2
=
1
0
a
8
=
0.00364583u
59
0.0279086u
58
+ ··· 5.70623u 2.88673
0.0256342u
59
+ 0.00484519u
58
+ ··· 2.79686u + 1.81796
a
3
=
0.119475u
59
0.0252683u
58
+ ··· 16.4829u 0.102673
0.0734909u
59
0.00608760u
58
+ ··· + 2.13578u + 0.830190
a
11
=
0.129402u
59
0.00873947u
58
+ ··· 2.44980u + 6.02592
0.258596u
59
0.0743158u
58
+ ··· + 17.9552u 5.12734
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
4
=
0.134484u
59
0.0249922u
58
+ ··· 20.5517u 0.473246
0.194125u
59
+ 0.00761251u
58
+ ··· 6.11851u + 2.39761
a
5
=
0.0274541u
59
+ 0.0469954u
58
+ ··· + 0.202747u + 5.11716
0.429618u
59
0.0280978u
58
+ ··· 49.3590u + 7.67462
a
9
=
0.362039u
59
+ 0.0499478u
58
+ ··· 35.7935u + 6.08364
0.326932u
59
0.0216627u
58
+ ··· 24.3303u + 4.32207
a
9
=
0.362039u
59
+ 0.0499478u
58
+ ··· 35.7935u + 6.08364
0.326932u
59
0.0216627u
58
+ ··· 24.3303u + 4.32207
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
15
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.64506 0.30278I
a = 0.224340 + 0.448622I
b = 0.188420 0.502074I
6.56195 + 4.20028I 14.6505 7.5466I
u = 1.64506 + 0.30278I
a = 0.224340 0.448622I
b = 0.188420 + 0.502074I
6.56195 4.20028I 14.6505 + 7.5466I
u = 1.50639 0.03128I
a = 0.222595 + 0.473641I
b = 0.484555 + 0.566618I
5.82415 2.23290I 14.1085 2.1221I
u = 1.50639 + 0.03128I
a = 0.222595 0.473641I
b = 0.484555 0.566618I
5.82415 + 2.23290I 14.1085 + 2.1221I
u = 1.33093 0.72650I
a = 0.734941 + 0.513147I
b = 1.67915 1.35639I
0.13405 10.50230I 10.61660 + 7.72054I
u = 1.33093 + 0.72650I
a = 0.734941 0.513147I
b = 1.67915 + 1.35639I
0.13405 + 10.50230I 10.61660 7.72054I
u = 1.290139 0.372995I
a = 0.658283 0.351462I
b = 0.0637226 + 0.1194615I
3.15719 4.84917I 13.58414 + 3.73183I
u = 1.290139 + 0.372995I
a = 0.658283 + 0.351462I
b = 0.0637226 0.1194615I
3.15719 + 4.84917I 13.58414 3.73183I
u = 1.269273 0.579030I
a = 0.898123 0.557931I
b = 1.59647 + 1.06798I
6.51599 10.49728I 15.4762 + 6.5662I
u = 1.269273 + 0.579030I
a = 0.898123 + 0.557931I
b = 1.59647 1.06798I
6.51599 + 10.49728I 15.4762 6.5662I
16
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.058312 0.321731I
a = 0.512357 0.691342I
b = 1.236433 + 0.287428I
0.48113 1.41291I 11.50731 + 0.65666I
u = 1.058312 + 0.321731I
a = 0.512357 + 0.691342I
b = 1.236433 0.287428I
0.48113 + 1.41291I 11.50731 0.65666I
u = 0.952526 0.271233I
a = 0.855614 + 0.735538I
b = 0.748695 + 0.391789I
1.57409 1.75671I 11.26354 + 2.48942I
u = 0.952526 + 0.271233I
a = 0.855614 0.735538I
b = 0.748695 0.391789I
1.57409 + 1.75671I 11.26354 2.48942I
u = 0.884656 0.446724I
a = 0.452605 0.287924I
b = 1.33546 0.52354I
2.06368 5.36613I 15.7641 + 4.3359I
u = 0.884656 + 0.446724I
a = 0.452605 + 0.287924I
b = 1.33546 + 0.52354I
2.06368 + 5.36613I 15.7641 4.3359I
u = 0.868439 0.693479I
a = 0.432874 0.997544I
b = 1.085149 + 0.303522I
1.57409 1.75671I 11.26354 + 2.48942I
u = 0.868439 + 0.693479I
a = 0.432874 + 0.997544I
b = 1.085149 0.303522I
1.57409 + 1.75671I 11.26354 2.48942I
u = 0.723442 0.483773I
a = 1.26637 + 0.65103I
b = 1.54780 0.60966I
1.99201 3.02567I 9.17011 + 1.57690I
u = 0.723442 + 0.483773I
a = 1.26637 0.65103I
b = 1.54780 + 0.60966I
1.99201 + 3.02567I 9.17011 1.57690I
17
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.673649 0.289156I
a = 0.009006 0.367834I
b = 1.89179 0.62354I
2.10401 5.43294I 16.4599 + 1.4390I
u = 0.673649 + 0.289156I
a = 0.009006 + 0.367834I
b = 1.89179 + 0.62354I
2.10401 + 5.43294I 16.4599 1.4390I
u = 0.335964 0.575378I
a = 0.425849 1.053158I
b = 0.067861 0.169301I
0.48113 + 1.41291I 11.50731 0.65666I
u = 0.335964 + 0.575378I
a = 0.425849 + 1.053158I
b = 0.067861 + 0.169301I
0.48113 1.41291I 11.50731 + 0.65666I
u = 0.205467 0.686465I
a = 1.55584 0.94030I
b = 1.130941 + 0.576276I
3.74729 + 5.28000I 5.18091 3.40493I
u = 0.205467 + 0.686465I
a = 1.55584 + 0.94030I
b = 1.130941 0.576276I
3.74729 5.28000I 5.18091 + 3.40493I
u = 0.173863 0.983906I
a = 0.981842 + 0.751380I
b = 1.311420 + 0.372273I
3.15719 + 4.84917I 13.58414 3.73183I
u = 0.173863 + 0.983906I
a = 0.981842 0.751380I
b = 1.311420 0.372273I
3.15719 4.84917I 13.58414 + 3.73183I
u = 0.172475 0.855408I
a = 0.225124 + 0.766556I
b = 1.330860 + 0.026355I
2.27554 5.83321I 13.60048 + 3.60394I
u = 0.172475 + 0.855408I
a = 0.225124 0.766556I
b = 1.330860 0.026355I
2.27554 + 5.83321I 13.60048 3.60394I
18
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.099098 0.640186I
a = 1.74206 0.06299I
b = 1.155946 0.237960I
2.17471 2.01374I 7.73585 + 3.91188I
u = 0.099098 + 0.640186I
a = 1.74206 + 0.06299I
b = 1.155946 + 0.237960I
2.17471 + 2.01374I 7.73585 3.91188I
u = 0.135724
a = 5.00269
b = 1.38185
5.55198 15.3382
u = 0.185453 1.290280I
a = 0.770163 + 0.538543I
b = 1.72480 + 0.18152I
0.13405 10.50230I 10.61660 + 7.72054I
u = 0.185453 + 1.290280I
a = 0.770163 0.538543I
b = 1.72480 0.18152I
0.13405 + 10.50230I 10.61660 7.72054I
u = 0.639831 0.484680I
a = 0.122902 + 0.545450I
b = 0.542628 0.147669I
2.17471 + 2.01374I 7.73585 3.91188I
u = 0.639831 + 0.484680I
a = 0.122902 0.545450I
b = 0.542628 + 0.147669I
2.17471 2.01374I 7.73585 + 3.91188I
u = 0.681546 0.443831I
a = 0.93897 1.06221I
b = 1.066642 0.320787I
1.99201 3.02567I 9.17011 + 1.57690I
u = 0.681546 + 0.443831I
a = 0.93897 + 1.06221I
b = 1.066642 + 0.320787I
1.99201 + 3.02567I 9.17011 1.57690I
u = 0.903459 0.213520I
a = 0.46861 + 1.67890I
b = 0.395277 1.092846I
1.72325 + 5.82388I 14.0227 8.3964I
19
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.903459 + 0.213520I
a = 0.46861 1.67890I
b = 0.395277 + 1.092846I
1.72325 5.82388I 14.0227 + 8.3964I
u = 0.913487 0.729355I
a = 1.044556 0.156978I
b = 1.63654 + 0.47332I
1.72325 + 5.82388I 14.0227 8.3964I
u = 0.913487 + 0.729355I
a = 1.044556 + 0.156978I
b = 1.63654 0.47332I
1.72325 5.82388I 14.0227 + 8.3964I
u = 0.918123 0.113673I
a = 0.601424 1.067971I
b = 1.44898 + 1.93632I
5.82415 + 2.23290I 14.1085 + 2.1221I
u = 0.918123 + 0.113673I
a = 0.601424 + 1.067971I
b = 1.44898 1.93632I
5.82415 2.23290I 14.1085 2.1221I
u = 1.036457 0.711450I
a = 0.803296 0.436745I
b = 1.57495 + 1.58012I
6.56195 + 4.20028I 14.6505 7.5466I
u = 1.036457 + 0.711450I
a = 0.803296 + 0.436745I
b = 1.57495 1.58012I
6.56195 4.20028I 14.6505 + 7.5466I
u = 1.157510 0.625695I
a = 0.624950 0.510871I
b = 1.71232 + 0.31893I
3.74729 + 5.28000I 5.18091 3.40493I
u = 1.157510 + 0.625695I
a = 0.624950 + 0.510871I
b = 1.71232 0.31893I
3.74729 5.28000I 5.18091 + 3.40493I
u = 1.26027
a = 0.859670
b = 0.171940
5.55198 15.3382
20
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.260713 0.276157I
a = 0.646516 + 0.779710I
b = 1.241936 0.621190I
2.06368 + 5.36613I 15.7641 4.3359I
u = 1.260713 + 0.276157I
a = 0.646516 0.779710I
b = 1.241936 + 0.621190I
2.06368 5.36613I 15.7641 + 4.3359I
u = 1.291757 0.455145I
a = 0.709922 + 0.595279I
b = 0.0254576 + 0.0551669I
6.51599 + 10.49728I 15.4762 6.5662I
u = 1.291757 + 0.455145I
a = 0.709922 0.595279I
b = 0.0254576 0.0551669I
6.51599 10.49728I 15.4762 + 6.5662I
u = 1.292282 0.285538I
a = 0.627804 + 0.797229I
b = 1.37034 0.93634I
2.10401 + 5.43294I 16.4599 1.4390I
u = 1.292282 + 0.285538I
a = 0.627804 0.797229I
b = 1.37034 + 0.93634I
2.10401 5.43294I 16.4599 + 1.4390I
u = 1.306826 0.465197I
a = 0.715297 + 0.676328I
b = 1.35807 1.20554I
2.27554 + 5.83321I 13.60048 3.60394I
u = 1.306826 + 0.465197I
a = 0.715297 0.676328I
b = 1.35807 + 1.20554I
2.27554 5.83321I 13.60048 + 3.60394I
u = 1.40424 0.40913I
a = 0.205658 + 0.470345I
b = 0.613673 0.115221I
7.98335 19.3802
u = 1.40424 + 0.40913I
a = 0.205658 0.470345I
b = 0.613673 + 0.115221I
7.98335 19.3802
21
VII. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u + 1)(u
4
+ u 1)
(u
12
2u
10
u
9
+ 5u
7
+ 6u
6
u
5
9u
4
5u
3
+ 6u
2
+ 2u 1)
(u
18
u
17
+ ··· + u
2
1)(u
20
8u
18
+ ··· + u 1)
(u
60
+ u
59
+ ··· + 109u + 17)
c
2
u(u 1)
12
(u
4
2u
2
+ u + 1)
(u
10
5u
8
+ 8u
6
+ 4u
5
6u
4
3u
3
+ 3u
2
1)
2
(u
18
+ u
17
+ ··· + 50u + 4)
(36 + 170u + 395u
2
+ 600u
3
+ 716u
4
+ 825u
5
+ 924u
6
+ 673u
7
199u
8
1261u
9
1595u
10
842u
11
+ 291u
12
+ 844u
13
+ 540u
14
253u
15
825u
16
487u
17
+ 481u
18
+ 801u
19
+ 42u
20
624u
21
351u
22
+ 197u
23
+ 250u
24
+ 14u
25
77u
26
28u
27
+ 7u
28
+ 6u
29
+ u
30
)
2
c
3
, c
10
(u 1)(u
4
+ u
3
1)(u
12
+ 2u
10
+ ··· + 4u + 1)
(u
18
+ 2u
17
+ ··· 3u + 1)(u
20
+ 3u
19
+ ··· 8u
2
1)
(u
60
+ 2u
59
+ ··· 2u 1)
c
4
(u + 1)(u
4
+ u 1)
(u
12
2u
10
u
9
+ 5u
7
+ 6u
6
u
5
9u
4
5u
3
+ 6u
2
+ 2u 1)
(u
18
u
17
+ ··· + u
2
1)(u
20
8u
18
+ ··· + u 1)
(u
60
+ u
59
+ ··· + 109u + 17)
c
5
u
4
(u 1)(1 5u
2
+ 2u
3
+ u
6
)
2
(u
18
+ 6u
17
+ ··· 416u 64)
(u
20
+ 8u
14
52u
12
138u
10
+ 104u
8
+ 527u
6
+ 296u
4
356u
2
319)
(u
60
4u
59
+ ··· 4u + 1)
c
6
(u + 1)(u
4
u 1)
(u
12
2u
10
u
9
+ 5u
7
+ 6u
6
u
5
9u
4
5u
3
+ 6u
2
+ 2u 1)
(u
18
u
17
+ ··· + u
2
1)(u
20
8u
18
+ ··· u 1)
(u
60
+ u
59
+ ··· + 109u + 17)
c
7
, c
11
(u 1)(u
4
u
3
1)(u
12
+ 2u
10
+ ··· + 4u + 1)
(u
18
+ 2u
17
+ ··· 3u + 1)(u
20
3u
19
+ ··· 8u
2
1)
(u
60
+ 2u
59
+ ··· 2u 1)
c
8
u(u 1)
12
(u
4
2u
2
u + 1)
(u
10
5u
8
+ 8u
6
4u
5
6u
4
+ 3u
3
+ 3u
2
1)
2
(u
18
+ u
17
+ ··· + 50u + 4)(u
60
+ 12u
59
+ ··· + 12240u + 1296)
c
9
(u + 1)(u
4
u 1)
(u
12
2u
10
u
9
+ 5u
7
+ 6u
6
u
5
9u
4
5u
3
+ 6u
2
+ 2u 1)
(u
18
u
17
+ ··· + u
2
1)(u
20
8u
18
+ ··· u 1)
(u
60
+ u
59
+ ··· + 109u + 17)
22
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y 1)(y
4
2y
2
y + 1)(y
12
4y
11
+ ··· 16y + 1)
(y
18
11y
17
+ ··· 2y + 1)(y
20
16y
19
+ ··· 13y + 1)
(y
60
41y
59
+ ··· 18409y + 289)
c
2
y(y 1)
12
(y
4
4y
3
+ 6y
2
5y + 1)
(1 6y + 21y
2
61y
3
+ 118y
4
144y
5
+ 130y
6
92y
7
+ 41y
8
10y
9
+ y
10
)
2
(y
18
13y
17
+ ··· 1100y + 16)
(1296 460y + 3577y
2
8332y
3
+ 9468y
4
8367y
5
+ 1.87 × 10
4
y
6
3.19 × 10
4
y
7
+ 3.58 × 10
4
y
8
5.15 × 10
4
y
9
+ 9.77 × 10
4
y
10
1.56 × 10
5
y
11
+ 1.79 × 10
5
y
12
1.35 × 10
5
y
13
+ 4.40 × 10
4
y
14
+ 2.85 × 10
4
y
15
1.91 × 10
4
y
16
8.88 × 10
4
y
17
+ 2.50 × 10
5
y
18
3.83 × 10
5
y
19
+ 4.25 × 10
5
y
20
3.69 × 10
5
y
21
+ 2.59 × 10
5
y
22
1.48 × 10
5
y
23
+ 6.80 × 10
4
y
24
2.50 × 10
4
y
25
+ 7147y
26
1530y
27
+ 231y
28
22y
29
+ y
30
)
2
c
3
, c
7
, c
10
(y 1)(y
4
y
3
2y
2
+ 1)(y
12
+ 4y
11
+ ··· 16y + 1)
(y
18
+ 8y
17
+ ··· 9y + 1)(y
20
+ 13y
19
+ ··· + 16y + 1)
(y
60
+ 32y
59
+ ··· + 20y + 1)
c
4
(y 1)(y
4
2y
2
y + 1)(y
12
4y
11
+ ··· 16y + 1)
(y
18
11y
17
+ ··· 2y + 1)(y
20
16y
19
+ ··· 13y + 1)
(y
60
41y
59
+ ··· 18409y + 289)
c
5
y
4
(y 1)(y
6
10y
4
2y
3
+ 25y
2
10y + 1)
2
(319 356y + 296y
2
+ 527y
3
+ 104y
4
138y
5
52y
6
+ 8y
7
+ y
10
)
2
(y
18
+ 56y
16
+ ··· 37888y + 4096)(y
60
4y
59
+ ··· 168y + 1)
c
8
y(y 1)
12
(y
4
4y
3
+ 6y
2
5y + 1)
(1 6y + 21y
2
61y
3
+ 118y
4
144y
5
+ 130y
6
92y
7
+ 41y
8
10y
9
+ y
10
)
2
(y
18
13y
17
+ ··· 1100y + 16)
(y
60
44y
59
+ ··· 1192320y + 1679616)
c
9
(y 1)(y
4
2y
2
y + 1)(y
12
4y
11
+ ··· 16y + 1)
(y
18
11y
17
+ ··· 2y + 1)(y
20
16y
19
+ ··· 13y + 1)
(y
60
41y
59
+ ··· 18409y + 289)
c
11
(y 1)(y
4
y
3
2y
2
+ 1)(y
12
+ 4y
11
+ ··· 16y + 1)
(y
18
+ 8y
17
+ ··· 9y + 1)(y
20
+ 13y
19
+ ··· + 16y + 1)
(y
60
+ 32y
59
+ ··· + 20y + 1)
23