11a
320
(K11a
320
)
1
Arc Sequences
8 6 1 10 9 2 11 3 5 7 4
Solving Sequence
7,11 4,8
1 2 3 6 10 5 9
c
7
c
11
c
1
c
3
c
6
c
10
c
4
c
9
c
2
, c
5
, c
8
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
17
+ u
16
+ ··· u 13, 2.54539 × 10
16
u
16
4.76533 × 10
16
u
15
+ ··· + 9.40328 × 10
15
b 3.76651 × 10
17
,
1.34761 × 10
17
u
16
2.52119 × 10
17
u
15
+ ··· + 1.22243 × 10
17
a 1.52676 × 10
18
i
I
u
2
= hu
71
6u
70
+ ··· + 24u 1,
3.68700 × 10
350
u
70
+ 2.12214 × 10
351
u
69
+ ··· + 2.78551 × 10
349
b 1.22625 × 10
351
,
3.02634 × 10
351
u
70
1.76106 × 10
352
u
69
+ ··· + 2.78551 × 10
349
a + 1.63208 × 10
352
i
There are 2 irreducible components with 88 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
17
+u
16
+· · ·u 13, 2.55×10
16
u
16
4.77× 10
16
u
15
+· · ·+9.40 ×10
15
b
3.77× 10
17
, 1.35× 10
17
u
16
2.52 × 10
17
u
15
+· · · +1.22 × 10
17
a 1.53 × 10
18
i
(i) Arc colorings
a
7
=
0
u
a
11
=
1.10240u
16
+ 2.06245u
15
+ ··· + 17.8175u + 12.4896
2.70691u
16
+ 5.06774u
15
+ ··· + 49.4328u + 40.0553
a
4
=
1
0
a
8
=
2.17878u
16
+ 4.23589u
15
+ ··· + 33.9951u + 35.8270
2.40041u
16
+ 4.64754u
15
+ ··· + 39.8085u + 34.2216
a
1
=
1.60451u
16
3.00528u
15
+ ··· 31.6153u 27.5657
2.70691u
16
+ 5.06774u
15
+ ··· + 49.4328u + 40.0553
a
2
=
1.11211u
16
+ 2.24465u
15
+ ··· + 12.0330u + 15.4796
4.04030u
16
+ 7.55853u
15
+ ··· + 75.4829u + 60.9006
a
3
=
1.41794u
16
+ 2.67712u
15
+ ··· + 18.9082u + 20.1599
1.21449u
16
+ 2.35572u
15
+ ··· + 19.1222u + 17.0162
a
6
=
1.11853u
16
2.01083u
15
+ ··· 21.1497u 18.1268
1.56050u
16
+ 2.91920u
15
+ ··· + 32.4243u + 23.6895
a
10
=
1.10240u
16
+ 2.06245u
15
+ ··· + 17.8175u + 12.4896
1.80408u
16
+ 3.30427u
15
+ ··· + 34.1416u + 27.5746
a
5
=
0.575319u
16
1.07965u
15
+ ··· 0.0246223u 6.85187
1.57791u
16
+ 2.99402u
15
+ ··· + 25.4833u + 20.7455
a
9
=
1.72715u
16
+ 3.22734u
15
+ ··· + 32.2954u + 27.6515
0.607245u
16
+ 1.39372u
15
+ ··· + 0.947490u + 4.52630
a
9
=
1.72715u
16
+ 3.22734u
15
+ ··· + 32.2954u + 27.6515
0.607245u
16
+ 1.39372u
15
+ ··· + 0.947490u + 4.52630
(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 = 1.93750 0.51744I
a = 0.334424 + 0.017007I
b = 0.411986 + 1.047170I
4.11922 1.69900I 9.79770 + 2.05049I
u = 1.93750 + 0.51744I
a = 0.334424 0.017007I
b = 0.411986 1.047170I
4.11922 + 1.69900I 9.79770 2.05049I
u = 1.35413 0.51864I
a = 0.711685 0.009703I
b = 0.970340 + 0.369674I
1.58186 1.44687I 12.74306 + 0.50340I
u = 1.35413 + 0.51864I
a = 0.711685 + 0.009703I
b = 0.970340 0.369674I
1.58186 + 1.44687I 12.74306 0.50340I
u = 1.27323 0.84448I
a = 0.996309 0.145518I
b = 0.415465 1.043717I
3.82426 5.50171I 7.72486 + 9.04908I
u = 1.27323 + 0.84448I
a = 0.996309 + 0.145518I
b = 0.415465 + 1.043717I
3.82426 + 5.50171I 7.72486 9.04908I
u = 0.275981 0.338995I
a = 3.06153 + 2.06104I
b = 0.195728 + 0.611465I
1.99220 2.29835I 12.88695 + 2.30559I
u = 0.275981 + 0.338995I
a = 3.06153 2.06104I
b = 0.195728 0.611465I
1.99220 + 2.29835I 12.88695 2.30559I
u = 0.049905 0.935496I
a = 0.42852 1.42951I
b = 0.092981 + 0.715967I
0.66199 1.48033I 1.64235 0.60543I
u = 0.049905 + 0.935496I
a = 0.42852 + 1.42951I
b = 0.092981 0.715967I
0.66199 + 1.48033I 1.64235 + 0.60543I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.721233 0.108706I
a = 0.655203 0.042945I
b = 0.19891 + 1.62363I
12.20839 + 1.95505I 9.77000 2.99480I
u = 0.721233 + 0.108706I
a = 0.655203 + 0.042945I
b = 0.19891 1.62363I
12.20839 1.95505I 9.77000 + 2.99480I
u = 0.910378 0.008813I
a = 0.930457 + 0.648234I
b = 0.319700 + 1.188614I
1.54004 + 3.31007I 6.32469 4.61953I
u = 0.910378 + 0.008813I
a = 0.930457 0.648234I
b = 0.319700 1.188614I
1.54004 3.31007I 6.32469 + 4.61953I
u = 1.40944
a = 0.665375
b = 1.06426
3.16307 6.26088
u = 2.05441 1.44856I
a = 0.345289 0.011799I
b = 0.415450 0.673435I
8.23130 + 5.15613I 5.47996 8.66451I
u = 2.05441 + 1.44856I
a = 0.345289 + 0.011799I
b = 0.415450 + 0.673435I
8.23130 5.15613I 5.47996 + 8.66451I
4
II. I
u
2
= hu
71
6u
70
+ · · · + 24u 1, 3.69 × 10
350
u
70
+ 2.12 × 10
351
u
69
+
· · · + 2.79 × 10
349
b 1.23 × 10
351
, 3.03 × 10
351
u
70
1.76 × 10
352
u
69
+ · · · +
2.79 × 10
349
a + 1.63 × 10
352
i
(i) Arc colorings
a
7
=
0
u
a
11
=
108.646u
70
+ 632.221u
69
+ ··· + 11060.8u 585.919
13.2364u
70
76.1852u
69
+ ··· 990.385u + 44.0223
a
4
=
1
0
a
8
=
7.10200u
70
+ 33.5913u
69
+ ··· 2269.41u + 179.129
4.79436u
70
+ 28.6025u
69
+ ··· + 680.994u 35.8610
a
1
=
121.882u
70
+ 708.406u
69
+ ··· + 12051.2u 629.941
13.2364u
70
76.1852u
69
+ ··· 990.385u + 44.0223
a
2
=
22.3823u
70
124.957u
69
+ ··· 144.336u 33.4188
1.31848u
70
+ 7.10992u
69
+ ··· 31.4262u + 1.58258
a
3
=
43.8334u
70
+ 256.801u
69
+ ··· + 4589.98u 221.168
7.97243u
70
46.4294u
69
+ ··· 780.909u + 41.4975
a
6
=
92.8933u
70
+ 542.293u
69
+ ··· + 10180.2u 572.424
25.7336u
70
149.484u
69
+ ··· 2498.41u + 129.906
a
10
=
108.646u
70
+ 632.221u
69
+ ··· + 11060.8u 585.919
16.7594u
70
96.6981u
69
+ ··· 1353.46u + 63.6774
a
5
=
26.8403u
70
159.333u
69
+ ··· 3459.49u + 174.569
7.47410u
70
+ 43.9640u
69
+ ··· + 874.279u 48.0005
a
9
=
113.477u
70
655.791u
69
+ ··· 9783.37u + 494.108
18.5245u
70
+ 106.765u
69
+ ··· + 1500.19u 73.2771
a
9
=
113.477u
70
655.791u
69
+ ··· 9783.37u + 494.108
18.5245u
70
+ 106.765u
69
+ ··· + 1500.19u 73.2771
(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 = 1.87826 0.29444I
a = 0.489204 + 0.167135I
b = 1.40638 0.36204I
2.53123 1.88371I 3.98008 + 4.04657I
u = 1.87826 + 0.29444I
a = 0.489204 0.167135I
b = 1.40638 + 0.36204I
2.53123 + 1.88371I 3.98008 4.04657I
u = 1.83683 0.72776I
a = 0.412058 + 0.068946I
b = 0.046777 + 1.050157I
4.71218 + 0.33668I 4.92868 + 1.00383I
u = 1.83683 + 0.72776I
a = 0.412058 0.068946I
b = 0.046777 1.050157I
4.71218 0.33668I 4.92868 1.00383I
u = 1.66200 0.78283I
a = 0.727411 0.045166I
b = 0.48232 1.33424I
3.81421 11.00460I 7.38999 + 8.31477I
u = 1.66200 + 0.78283I
a = 0.727411 + 0.045166I
b = 0.48232 + 1.33424I
3.81421 + 11.00460I 7.38999 8.31477I
u = 1.49272 1.55271I
a = 0.622204 0.207211I
b = 0.65349 + 1.41571I
6.32046 9.15200I 6.83141 + 6.17062I
u = 1.49272 + 1.55271I
a = 0.622204 + 0.207211I
b = 0.65349 1.41571I
6.32046 + 9.15200I 6.83141 6.17062I
u = 1.47320 1.08978I
a = 0.436321 + 0.007789I
b = 0.582442 1.060303I
4.88583 2.21298I 2.50915 + 5.81033I
u = 1.47320 + 1.08978I
a = 0.436321 0.007789I
b = 0.582442 + 1.060303I
4.88583 + 2.21298I 2.50915 5.81033I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.404152 0.037588I
a = 0.822306 0.265281I
b = 0.942608 + 0.017959I
0.32112 5.84881I 11.37632 + 6.97318I
u = 1.404152 + 0.037588I
a = 0.822306 + 0.265281I
b = 0.942608 0.017959I
0.32112 + 5.84881I 11.37632 6.97318I
u = 1.27629 0.95407I
a = 0.922878 0.019202I
b = 0.336740 0.978403I
3.89503 4.72871I 6.49145 0.75096I
u = 1.27629 + 0.95407I
a = 0.922878 + 0.019202I
b = 0.336740 + 0.978403I
3.89503 + 4.72871I 6.49145 + 0.75096I
u = 1.256662 0.049784I
a = 0.562183 0.269974I
b = 0.447415 1.183117I
0.95702 + 2.39465I 10.82367 + 0.51455I
u = 1.256662 + 0.049784I
a = 0.562183 + 0.269974I
b = 0.447415 + 1.183117I
0.95702 2.39465I 10.82367 0.51455I
u = 1.026671 0.285886I
a = 1.098792 + 0.542622I
b = 0.353533 + 1.029636I
0.74759 4.36932I 10.78802 + 8.88400I
u = 1.026671 + 0.285886I
a = 1.098792 0.542622I
b = 0.353533 1.029636I
0.74759 + 4.36932I 10.78802 8.88400I
u = 0.776979 0.514381I
a = 0.932226 + 0.124001I
b = 0.255272 + 0.548146I
2.89013 1.78350I 4.97596 + 3.66282I
u = 0.776979 + 0.514381I
a = 0.932226 0.124001I
b = 0.255272 0.548146I
2.89013 + 1.78350I 4.97596 3.66282I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.721769 0.948826I
a = 0.641886 0.690818I
b = 0.574723 + 0.330407I
1.79167 1.75090I 12.48087 + 4.54784I
u = 0.721769 + 0.948826I
a = 0.641886 + 0.690818I
b = 0.574723 0.330407I
1.79167 + 1.75090I 12.48087 4.54784I
u = 0.662430 0.113589I
a = 1.72314 0.11590I
b = 0.423933 + 0.883947I
3.17690 1.80430I 5.86416 + 1.21596I
u = 0.662430 + 0.113589I
a = 1.72314 + 0.11590I
b = 0.423933 0.883947I
3.17690 + 1.80430I 5.86416 1.21596I
u = 0.481471 0.244222I
a = 0.916278 0.582012I
b = 0.232384 1.034918I
2.02658 + 2.02846I 7.89654 4.38897I
u = 0.481471 + 0.244222I
a = 0.916278 + 0.582012I
b = 0.232384 + 1.034918I
2.02658 2.02846I 7.89654 + 4.38897I
u = 0.481129 0.013049I
a = 0.18944 1.44707I
b = 0.571182 + 0.076246I
2.82580 + 1.80720I 7.38072 3.47906I
u = 0.481129 + 0.013049I
a = 0.18944 + 1.44707I
b = 0.571182 0.076246I
2.82580 1.80720I 7.38072 + 3.47906I
u = 0.336035 1.369513I
a = 0.502854 + 1.117800I
b = 0.047825 1.017727I
3.38826 2.90800I 6.31710 + 3.12646I
u = 0.336035 + 1.369513I
a = 0.502854 1.117800I
b = 0.047825 + 1.017727I
3.38826 + 2.90800I 6.31710 3.12646I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.161474 0.163151I
a = 2.77166 4.01423I
b = 0.26701 + 1.39737I
9.45981 2.99993I 4.76599 + 2.26484I
u = 0.161474 + 0.163151I
a = 2.77166 + 4.01423I
b = 0.26701 1.39737I
9.45981 + 2.99993I 4.76599 2.26484I
u = 0.041613 0.414187I
a = 0.86523 + 1.47648I
b = 0.01709 + 1.56834I
12.64149 1.23886I 3.38681 3.69965I
u = 0.041613 + 0.414187I
a = 0.86523 1.47648I
b = 0.01709 1.56834I
12.64149 + 1.23886I 3.38681 + 3.69965I
u = 0.134709 0.050040I
a = 7.96365 1.68439I
b = 0.048283 1.137297I
3.52458 + 2.13444I 4.20513 2.42058I
u = 0.134709 + 0.050040I
a = 7.96365 + 1.68439I
b = 0.048283 + 1.137297I
3.52458 2.13444I 4.20513 + 2.42058I
u = 0.202918 0.041557I
a = 1.27146 6.79330I
b = 0.384607 + 1.314117I
13.6021 + 8.3409I 3.37591 5.15237I
u = 0.202918 + 0.041557I
a = 1.27146 + 6.79330I
b = 0.384607 1.314117I
13.6021 8.3409I 3.37591 + 5.15237I
u = 0.209301 0.158624I
a = 4.77385 2.07921I
b = 0.046582 + 0.497650I
1.18329 + 1.57972I 17.0653 2.5439I
u = 0.209301 + 0.158624I
a = 4.77385 + 2.07921I
b = 0.046582 0.497650I
1.18329 1.57972I 17.0653 + 2.5439I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.260359
a = 1.06557
b = 0.250330
0.556749 17.9339
u = 0.436666 0.404450I
a = 0.107500 1.258579I
b = 0.40026 + 1.67882I
12.92887 2.39291I 1.55712 + 6.17823I
u = 0.436666 + 0.404450I
a = 0.107500 + 1.258579I
b = 0.40026 1.67882I
12.92887 + 2.39291I 1.55712 6.17823I
u = 0.564291 0.107816I
a = 0.22025 + 1.82644I
b = 0.327594 + 1.168438I
6.37762 + 5.16098I 4.20251 5.41563I
u = 0.564291 + 0.107816I
a = 0.22025 1.82644I
b = 0.327594 1.168438I
6.37762 5.16098I 4.20251 + 5.41563I
u = 0.734800 0.015138I
a = 1.69262 0.29840I
b = 0.350880 0.384879I
1.10877 1.58604I 13.47873 + 2.62387I
u = 0.734800 + 0.015138I
a = 1.69262 + 0.29840I
b = 0.350880 + 0.384879I
1.10877 + 1.58604I 13.47873 2.62387I
u = 0.848361 0.245593I
a = 1.43042 0.47626I
b = 0.754094 + 0.580048I
4.98219 + 1.09775I 7.30065 0.27985I
u = 0.848361 + 0.245593I
a = 1.43042 + 0.47626I
b = 0.754094 0.580048I
4.98219 1.09775I 7.30065 + 0.27985I
u = 1.116619 0.464702I
a = 0.914135 + 0.045709I
b = 0.200339 + 0.907089I
0.352598 + 1.166031I 12.57469 0.43325I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.116619 + 0.464702I
a = 0.914135 0.045709I
b = 0.200339 0.907089I
0.352598 1.166031I 12.57469 + 0.43325I
u = 1.382582 0.062925I
a = 0.689282 0.388147I
b = 0.271650 1.343534I
3.76513 4.21784I 5.15577 + 5.17023I
u = 1.382582 + 0.062925I
a = 0.689282 + 0.388147I
b = 0.271650 + 1.343534I
3.76513 + 4.21784I 5.15577 5.17023I
u = 1.38575 1.92380I
a = 0.438504 + 0.246988I
b = 0.134492 1.169684I
10.90654 + 5.21367I 3.26699 4.32050I
u = 1.38575 + 1.92380I
a = 0.438504 0.246988I
b = 0.134492 + 1.169684I
10.90654 5.21367I 3.26699 + 4.32050I
u = 1.48866 0.73350I
a = 0.832590 0.326544I
b = 0.569298 0.933529I
6.02225 + 6.08511I 6.08140 6.64271I
u = 1.48866 + 0.73350I
a = 0.832590 + 0.326544I
b = 0.569298 + 0.933529I
6.02225 6.08511I 6.08140 + 6.64271I
u = 1.50072 0.23040I
a = 0.614008 + 0.190684I
b = 1.123154 0.278639I
3.38978 0.40278I 14.0514 + 11.4562I
u = 1.50072 + 0.23040I
a = 0.614008 0.190684I
b = 1.123154 + 0.278639I
3.38978 + 0.40278I 14.0514 11.4562I
u = 1.50417 0.85291I
a = 0.686831 + 0.045183I
b = 0.558176 1.269411I
0.06369 + 6.26228I 11.79118 7.00180I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.50417 + 0.85291I
a = 0.686831 0.045183I
b = 0.558176 + 1.269411I
0.06369 6.26228I 11.79118 + 7.00180I
u = 1.58505 1.81436I
a = 0.462315 0.187547I
b = 0.71970 + 1.29915I
11.25787 + 1.96679I 4.27388 2.24305I
u = 1.58505 + 1.81436I
a = 0.462315 + 0.187547I
b = 0.71970 1.29915I
11.25787 1.96679I 4.27388 + 2.24305I
u = 1.60783 1.35334I
a = 0.706118 0.094623I
b = 0.62072 + 1.39610I
11.1774 + 15.7364I 5.51063 7.83456I
u = 1.60783 + 1.35334I
a = 0.706118 + 0.094623I
b = 0.62072 1.39610I
11.1774 15.7364I 5.51063 + 7.83456I
u = 1.67455 0.12962I
a = 0.305904 + 0.337426I
b = 0.842416 0.377347I
8.76103 4.23637I 5.72805 + 1.97421I
u = 1.67455 + 0.12962I
a = 0.305904 0.337426I
b = 0.842416 + 0.377347I
8.76103 + 4.23637I 5.72805 1.97421I
u = 1.67717 0.45803I
a = 0.679124 + 0.169672I
b = 1.289833 0.094787I
7.03255 + 9.09735I 7.56149 6.40769I
u = 1.67717 + 0.45803I
a = 0.679124 0.169672I
b = 1.289833 + 0.094787I
7.03255 9.09735I 7.56149 + 6.40769I
u = 1.78535 1.04479I
a = 0.201803 0.073817I
b = 0.117612 + 0.490736I
8.37213 + 4.43001I 3.16531 + 0.91454I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.78535 + 1.04479I
a = 0.201803 + 0.073817I
b = 0.117612 0.490736I
8.37213 4.43001I 3.16531 0.91454I
12
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
17
+ 4u
14
+ ··· 2u + 1)(u
71
+ u
70
+ ··· 253u 121)
c
2
(u
17
+ u
16
+ ··· u 1)(u
71
+ 2u
70
+ ··· + 212u + 103)
c
3
(u
17
+ 3u
16
+ ··· + 3u + 1)(u
71
+ 4u
70
+ ··· 82u 19)
c
4
, c
5
(u
17
+ 10u
15
+ ··· + 4u 1)(u
71
+ u
70
+ ··· 9u + 11)
c
6
(u
17
u
16
+ ··· u + 1)(u
71
+ 2u
70
+ ··· + 212u + 103)
c
7
(u
17
+ 3u
16
+ ··· 3u 1)(u
71
18u
69
+ ··· + 28u 19)
c
8
(u
17
+ 2u
15
+ ··· + 8u 1)(u
71
+ u
70
+ ··· + 75261u + 69721)
c
9
(u
17
+ 10u
15
+ ··· + 4u + 1)(u
71
+ u
70
+ ··· 9u + 11)
c
10
(u
17
3u
16
+ ··· 3u + 1)(u
71
18u
69
+ ··· + 28u 19)
c
11
(u
17
3u
16
+ ··· + 3u 1)(u
71
+ 4u
70
+ ··· 82u 19)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
17
8y
15
+ ··· + 14y 1)(y
71
+ 13y
70
+ ··· 110473y 14641)
c
2
, c
6
(y
17
+ 11y
16
+ ··· 9y 1)(y
71
+ 52y
70
+ ··· 123976y 10609)
c
3
, c
11
(y
17
+ 11y
16
+ ··· 11y 1)(y
71
+ 48y
70
+ ··· 4562y 361)
c
4
, c
5
, c
9
(y
17
+ 20y
16
+ ··· + 6y 1)(y
71
+ 77y
70
+ ··· + 103y 121)
c
7
, c
10
(y
17
13y
16
+ ··· + 17y 1)(y
71
36y
70
+ ··· + 9258y 361)
c
8
(y
17
+ 4y
16
+ ··· + 64y 1)
(y
71
+ 37y
70
+ ··· 78658032583y 4861017841)
14