11a
294
(K11a
294
)
1
Arc Sequences
9 5 1 8 2 11 10 3 6 7 4
Solving Sequence
4,11
1
3,7
6 10 8 5 2 9
c
11
c
3
c
6
c
10
c
7
c
4
c
2
c
9
c
1
, c
5
, c
8
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= h8u
3
12u
2
+ 36u 5, b + 1, 16u
2
+ 15a + 24u 62i
I
u
2
= h8u
24
+ 28u
23
+ ··· 55u 19,
1.05794 × 10
61
u
23
3.92592 × 10
61
u
22
+ ··· + 2.40811 × 10
62
b + 1.05881 × 10
62
,
3.86381 × 10
62
u
23
+ 9.84893 × 10
62
u
22
+ ··· + 4.57541 × 10
63
a 1.56602 × 10
64
i
I
u
3
= hu
40
13u
39
+ ··· + 626914u + 73649,
4.47814 × 10
186
u
39
5.95363 × 10
187
u
38
+ ··· + 1.42011 × 10
191
b + 9.27385 × 10
191
,
5.77310 × 10
190
u
39
+ 7.72710 × 10
191
u
38
+ ··· + 2.25066 × 10
195
a 1.60098 × 10
196
i
There are 3 irreducible components with 67 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
= h8u
3
12u
2
+ 36u 5, b + 1, 16u
2
+ 15a + 24u 62i
(i) Arc colorings
a
4
=
1
0
a
11
=
16
15
u
2
8
5
u +
62
15
1
a
1
=
16
15
u
2
8
5
u +
77
15
1
a
3
=
16
15
u
2
8
5
u +
92
15
1
a
7
=
0
u
a
6
=
32
45
u
2
+
28
45
u
104
45
1
3
u +
2
3
a
10
=
16
15
u
2
8
5
u +
62
15
2
3
u
2
+
2
3
u 1
a
8
=
32
45
u
2
28
45
u +
104
45
2
9
u
2
+
1
9
u
7
18
a
5
=
8
45
u
2
22
45
u +
86
45
1
6
u
1
6
a
2
=
8
9
u
2
10
9
u +
38
9
1
6
u
5
6
a
9
=
32
45
u
2
28
45
u +
104
45
2
9
u
2
+
1
9
u
7
18
a
9
=
32
45
u
2
28
45
u +
104
45
2
9
u
2
+
1
9
u
7
18
(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 = 0.145240
a = 3.92345
b = 1.00000
0.531480 2.14246
u = 0.67738 1.96071I
a = 0.561725 + 0.303758I
b = 1.00000
4.66906 + 2.82812I 2.05377 0.32679I
u = 0.67738 + 1.96071I
a = 0.561725 0.303758I
b = 1.00000
4.66906 2.82812I 2.05377 + 0.32679I
3
II. I
u
2
= h8u
24
+ 28u
23
+ · · · 55u 19, 1.06 × 10
61
u
23
3.93 × 10
61
u
22
+
· · · + 2.41 × 10
62
b + 1.06 × 10
62
, 3.86 × 10
62
u
23
+ 9.85 × 10
62
u
22
+ · · · +
4.58 × 10
63
a 1.57 × 10
64
i
(i) Arc colorings
a
4
=
1
0
a
11
=
0.0844473u
23
0.215258u
22
+ ··· 11.0860u + 3.42269
0.0439323u
23
+ 0.163029u
22
+ ··· + 5.84793u 0.439687
a
1
=
0.128380u
23
0.378287u
22
+ ··· 16.9339u + 3.86238
0.0439323u
23
+ 0.163029u
22
+ ··· + 5.84793u 0.439687
a
3
=
0.130844u
23
+ 0.637662u
22
+ ··· 10.6042u + 8.03456
0.0935150u
23
0.367916u
22
+ ··· + 0.0561641u 1.85680
a
7
=
0
u
a
6
=
0.382464u
23
1.42112u
22
+ ··· 20.0294u 0.126278
0.139094u
23
+ 0.513972u
22
+ ··· + 6.43440u + 0.0886571
a
10
=
0.0844473u
23
0.215258u
22
+ ··· 11.0860u + 3.42269
0.0761201u
23
+ 0.280276u
22
+ ··· + 6.19948u 0.248955
a
8
=
0.382464u
23
+ 1.42112u
22
+ ··· + 20.0294u + 0.126278
0.0966189u
23
0.360821u
22
+ ··· 2.95890u + 0.107267
a
5
=
0.365909u
23
1.35783u
22
+ ··· 18.6240u + 0.104188
0.127545u
23
+ 0.472822u
22
+ ··· + 5.65726u + 0.596862
a
2
=
0.164856u
23
0.601423u
22
+ ··· 6.51753u + 3.87247
0.0770245u
23
+ 0.316896u
22
+ ··· + 1.78226u 0.777065
a
9
=
0.189951u
23
0.634417u
22
+ ··· 12.5559u 0.150964
0.147898u
23
+ 0.532508u
22
+ ··· + 6.49808u + 0.699449
a
9
=
0.189951u
23
0.634417u
22
+ ··· 12.5559u 0.150964
0.147898u
23
+ 0.532508u
22
+ ··· + 6.49808u + 0.699449
(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 = 1.08345 2.22165I
a = 0.423759 0.325330I
b = 1.347431 + 0.188650I
4.17750 3.32302I 7.49326 + 7.01534I
u = 1.08345 + 2.22165I
a = 0.423759 + 0.325330I
b = 1.347431 0.188650I
4.17750 + 3.32302I 7.49326 7.01534I
u = 0.95301 2.80249I
a = 0.487188 + 0.034000I
b = 0.55509 1.37302I
4.2704 + 16.0735I 4.86533 8.67439I
u = 0.95301 + 2.80249I
a = 0.487188 0.034000I
b = 0.55509 + 1.37302I
4.2704 16.0735I 4.86533 + 8.67439I
u = 0.672132 1.021388I
a = 0.532627 0.501555I
b = 0.49469 1.37599I
9.3482 + 11.6156I 9.04984 7.14425I
u = 0.672132 + 1.021388I
a = 0.532627 + 0.501555I
b = 0.49469 + 1.37599I
9.3482 11.6156I 9.04984 + 7.14425I
u = 0.67062 1.40074I
a = 0.944539 0.128693I
b = 0.207861 + 1.159743I
2.26090 + 6.77325I 8.15326 8.68487I
u = 0.67062 + 1.40074I
a = 0.944539 + 0.128693I
b = 0.207861 1.159743I
2.26090 6.77325I 8.15326 + 8.68487I
u = 0.323179 0.600704I
a = 1.06518 + 1.12737I
b = 0.047276 + 1.186362I
7.49230 + 1.49785I 16.5794 3.5131I
u = 0.323179 + 0.600704I
a = 1.06518 1.12737I
b = 0.047276 1.186362I
7.49230 1.49785I 16.5794 + 3.5131I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.240357 0.464460I
a = 0.147711 0.695555I
b = 0.662890 0.292141I
1.22051 0.86188I 4.63925 + 4.32694I
u = 0.240357 + 0.464460I
a = 0.147711 + 0.695555I
b = 0.662890 + 0.292141I
1.22051 + 0.86188I 4.63925 4.32694I
u = 0.199601 1.034128I
a = 1.210010 + 0.409226I
b = 0.263704 0.229700I
3.41691 2.41506I 4.35202 + 1.54076I
u = 0.199601 + 1.034128I
a = 1.210010 0.409226I
b = 0.263704 + 0.229700I
3.41691 + 2.41506I 4.35202 1.54076I
u = 0.127345
a = 5.15582
b = 1.29551
0.112715 17.2961
u = 0.01988 2.52445I
a = 0.524877 0.044897I
b = 0.912691 0.587846I
5.99931 2.29383I 3.48033 + 0.30083I
u = 0.01988 + 2.52445I
a = 0.524877 + 0.044897I
b = 0.912691 + 0.587846I
5.99931 + 2.29383I 3.48033 0.30083I
u = 0.319821
a = 1.55353
b = 0.161437
0.853473 12.2559
u = 0.377294 0.111308I
a = 0.50306 2.85399I
b = 0.411983 + 1.346681I
6.85359 6.74871I 7.12828 + 3.44529I
u = 0.377294 + 0.111308I
a = 0.50306 + 2.85399I
b = 0.411983 1.346681I
6.85359 + 6.74871I 7.12828 3.44529I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.462655 0.549485I
a = 1.57538 0.03156I
b = 0.138302 + 1.193198I
5.61526 4.36903I 11.9512 + 7.5869I
u = 0.462655 + 0.549485I
a = 1.57538 + 0.03156I
b = 0.138302 1.193198I
5.61526 + 4.36903I 11.9512 7.5869I
u = 1.47604 1.42382I
a = 0.554507 0.495537I
b = 0.381421 + 1.074635I
2.48001 6.89114I 2.89593 + 8.03535I
u = 1.47604 + 1.42382I
a = 0.554507 + 0.495537I
b = 0.381421 1.074635I
2.48001 + 6.89114I 2.89593 8.03535I
7
III. I
u
3
= hu
40
13u
39
+ · · · + 626914u + 73649, 4.48 × 10
186
u
39
5.95 ×
10
187
u
38
+ · · · + 1.42 × 10
191
b + 9.27 × 10
191
, 5.77 × 10
190
u
39
+ 7.73 ×
10
191
u
38
+ · · · + 2.25 × 10
195
a 1.60 × 10
196
i
(i) Arc colorings
a
4
=
1
0
a
11
=
0.0000256507u
39
0.000343326u
38
+ ··· + 34.0655u + 7.11336
0.0000315338u
39
+ 0.000419238u
38
+ ··· 40.1918u 6.53038
a
1
=
0.0000571845u
39
0.000762563u
38
+ ··· + 74.2574u + 13.6437
0.0000315338u
39
+ 0.000419238u
38
+ ··· 40.1918u 6.53038
a
3
=
0.0000170175u
39
+ 0.000220286u
38
+ ··· 37.5410u 8.04810
1.27554 × 10
6
u
39
0.0000137952u
38
+ ··· + 6.69717u + 1.07317
a
7
=
0
u
a
6
=
0.0000352108u
39
+ 0.000467252u
38
+ ··· 43.6343u 6.93531
1.84570 × 10
6
u
39
0.0000245519u
38
+ ··· + 2.89392u + 1.15938
a
10
=
0.0000256507u
39
0.000343326u
38
+ ··· + 34.0655u + 7.11336
0.0000264642u
39
+ 0.000351338u
38
+ ··· 35.8951u 5.80368
a
8
=
0.0000352108u
39
0.000467252u
38
+ ··· + 43.6343u + 6.93531
2.21794 × 10
7
u
39
+ 3.30131 × 10
6
u
38
+ ··· + 2.47624u 0.458807
a
5
=
0.0000375864u
39
0.000497048u
38
+ ··· + 52.2809u + 9.24705
1.89048 × 10
6
u
39
+ 0.0000257009u
38
+ ··· + 2.28051u 0.189431
a
2
=
9.68547 × 10
7
u
39
0.0000154929u
38
+ ··· 4.28672u 1.14591
0.0000134399u
39
+ 0.000179530u
38
+ ··· 14.5462u 1.68185
a
9
=
0.0000481625u
39
0.000642220u
38
+ ··· + 62.4536u + 10.3506
0.0000278171u
39
+ 0.000370641u
38
+ ··· 34.3838u 5.98284
a
9
=
0.0000481625u
39
0.000642220u
38
+ ··· + 62.4536u + 10.3506
0.0000278171u
39
+ 0.000370641u
38
+ ··· 34.3838u 5.98284
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.66081 1.21289I
a = 0.411363 0.544801I
b = 0.495392 + 0.955288I
4.68486 + 2.84648I 1.60998 2.97861I
u = 1.66081 + 1.21289I
a = 0.411363 + 0.544801I
b = 0.495392 0.955288I
4.68486 2.84648I 1.60998 + 2.97861I
u = 0.81339 2.73407I
a = 0.456132 + 0.015900I
b = 0.67909 1.31567I
4.94645 + 3.96853I 7.89349 3.79787I
u = 0.81339 + 2.73407I
a = 0.456132 0.015900I
b = 0.67909 + 1.31567I
4.94645 3.96853I 7.89349 + 3.79787I
u = 0.760382 0.894228I
a = 1.040612 0.554329I
b = 0.392505 + 0.067994I
1.14075 + 4.43308I 0.68370 2.52728I
u = 0.760382 + 0.894228I
a = 1.040612 + 0.554329I
b = 0.392505 0.067994I
1.14075 4.43308I 0.68370 + 2.52728I
u = 0.504541 0.250436I
a = 1.28117 + 1.48403I
b = 0.31766 1.39547I
2.02098 2.13456I 4.50898 + 2.16962I
u = 0.504541 + 0.250436I
a = 1.28117 1.48403I
b = 0.31766 + 1.39547I
2.02098 + 2.13456I 4.50898 2.16962I
u = 0.483471 0.543967I
a = 0.471578 + 0.853615I
b = 0.162072 0.252940I
3.61438 0.81573I 5.67172 + 1.07888I
u = 0.483471 + 0.543967I
a = 0.471578 0.853615I
b = 0.162072 + 0.252940I
3.61438 + 0.81573I 5.67172 1.07888I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.358112 0.792226I
a = 0.365910 0.809477I
b = 0.56866 1.40361I
8.84775 12.4403
u = 0.358112 + 0.792226I
a = 0.365910 + 0.809477I
b = 0.56866 + 1.40361I
8.84775 12.4403
u = 0.326834 0.046393I
a = 0.88678 1.90377I
b = 0.195325 + 1.163084I
1.62333 + 2.35832I 2.35225 4.49783I
u = 0.326834 + 0.046393I
a = 0.88678 + 1.90377I
b = 0.195325 1.163084I
1.62333 2.35832I 2.35225 + 4.49783I
u = 0.152118 0.263221I
a = 1.70861 1.94967I
b = 1.084143 0.080482I
4.77271 + 6.07240I 7.45285 5.87540I
u = 0.152118 + 0.263221I
a = 1.70861 + 1.94967I
b = 1.084143 + 0.080482I
4.77271 6.07240I 7.45285 + 5.87540I
u = 0.11121 2.05637I
a = 0.681235 0.025942I
b = 0.676901 0.349305I
4.68486 2.84648I 1.60998 + 2.97861I
u = 0.11121 + 2.05637I
a = 0.681235 + 0.025942I
b = 0.676901 + 0.349305I
4.68486 + 2.84648I 1.60998 2.97861I
u = 0.491223 1.031985I
a = 0.411720 0.553165I
b = 0.49433 1.41099I
4.77271 6.07240I 7.45285 + 5.87540I
u = 0.491223 + 1.031985I
a = 0.411720 + 0.553165I
b = 0.49433 + 1.41099I
4.77271 + 6.07240I 7.45285 5.87540I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.52676 2.30995I
a = 0.584117 0.005247I
b = 0.177275 + 1.088718I
1.14075 4.43308I 0.68370 + 2.52728I
u = 0.52676 + 2.30995I
a = 0.584117 + 0.005247I
b = 0.177275 1.088718I
1.14075 + 4.43308I 0.68370 2.52728I
u = 0.64691 2.22991I
a = 0.522172 0.298669I
b = 1.159931 + 0.023595I
0.00745 + 10.05773I 2.70834 7.26612I
u = 0.64691 + 2.22991I
a = 0.522172 + 0.298669I
b = 1.159931 0.023595I
0.00745 10.05773I 2.70834 + 7.26612I
u = 0.781853 1.114078I
a = 0.386131 + 0.350456I
b = 0.049861 + 1.112720I
3.61438 0.81573I 5.67172 + 1.07888I
u = 0.781853 + 1.114078I
a = 0.386131 0.350456I
b = 0.049861 1.112720I
3.61438 + 0.81573I 5.67172 1.07888I
u = 0.80861 1.35056I
a = 0.493329 0.498801I
b = 0.918130 + 0.259874I
2.02098 2.13456I 4.50898 + 2.16962I
u = 0.80861 + 1.35056I
a = 0.493329 + 0.498801I
b = 0.918130 0.259874I
2.02098 + 2.13456I 4.50898 2.16962I
u = 0.844096 0.403459I
a = 0.500104 0.546840I
b = 0.502025 + 0.160176I
1.62333 2.35832I 2.35225 + 4.49783I
u = 0.844096 + 0.403459I
a = 0.500104 + 0.546840I
b = 0.502025 0.160176I
1.62333 + 2.35832I 2.35225 4.49783I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.91555 2.78902I
a = 0.474288 + 0.038017I
b = 0.59445 1.40555I
0.00745 10.05773I 2.70834 + 7.26612I
u = 0.91555 + 2.78902I
a = 0.474288 0.038017I
b = 0.59445 + 1.40555I
0.00745 + 10.05773I 2.70834 7.26612I
u = 1.091614 0.029291I
a = 0.268886 1.161496I
b = 0.46464 + 1.49110I
4.94645 + 3.96853I 7.89349 3.79787I
u = 1.091614 + 0.029291I
a = 0.268886 + 1.161496I
b = 0.46464 1.49110I
4.94645 3.96853I 7.89349 + 3.79787I
u = 1.57442 1.04400I
a = 0.158299 + 0.104969I
b = 0.123906 1.022770I
3.97005 10.7621
u = 1.57442 + 1.04400I
a = 0.158299 0.104969I
b = 0.123906 + 1.022770I
3.97005 10.7621
u = 1.70169 2.85703I
a = 0.289725 + 0.242054I
b = 0.199750 0.784968I
0.52569 + 2.16136I 0.73748 3.31855I
u = 1.70169 + 2.85703I
a = 0.289725 0.242054I
b = 0.199750 + 0.784968I
0.52569 2.16136I 0.73748 + 3.31855I
u = 2.06573 0.42182I
a = 0.025375 + 0.594923I
b = 0.053071 + 1.161370I
0.52569 + 2.16136I 0.73748 3.31855I
u = 2.06573 + 0.42182I
a = 0.025375 0.594923I
b = 0.053071 1.161370I
0.52569 2.16136I 0.73748 + 3.31855I
12
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(8u
3
+ 4u
2
1)(8u
24
+ 12u
23
+ ··· + u + 1)
(u
40
+ 3u
39
+ ··· + 60100u + 13049)
c
2
, c
11
(u 1)
3
(u
24
3u
23
+ ··· 6u 1)(u
40
+ 7u
39
+ ··· + 2u + 1)
c
3
(u + 1)
3
(u
24
3u
23
+ ··· 6u 1)(u
40
+ 7u
39
+ ··· + 2u + 1)
c
4
(8u
3
4u
2
+ 1)(8u
24
+ 12u
23
+ ··· + u + 1)
(u
40
+ 3u
39
+ ··· + 60100u + 13049)
c
5
(u + 1)
3
(u
24
3u
23
+ ··· 6u 1)(u
40
+ 7u
39
+ ··· + 2u + 1)
c
6
, c
7
(u
3
+ u
2
+ 2u + 1)
(1 + 2u + u
2
+ u
3
+ 9u
4
4u
5
2u
6
10u
7
25u
8
+ 2u
9
3u
10
+ 31u
11
+ 48u
12
+ 42u
13
+ 60u
14
+ 26u
15
+ 33u
16
+ 8u
17
+ 9u
18
+ u
19
+ u
20
)
2
(u
24
+ 10u
22
+ ··· 15u 4)
c
8
u
3
(1 + 3u
2
5u
3
3u
4
+ 10u
5
+ 2u
6
18u
7
+ u
8
+ 24u
9
7u
10
23u
11
+ 10u
12
+ 18u
13
10u
14
10u
15
+ 7u
16
+ 4u
17
3u
18
u
19
+ u
20
)
2
(u
24
+ 3u
23
+ ··· + 224u + 128)
c
9
(u
3
+ u
2
1)
(1 4u 5u
2
9u
3
11u
4
+ 30u
5
+ 36u
6
72u
7
65u
8
+ 82u
9
+ 57u
10
47u
11
16u
12
+ 8u
13
12u
14
+ 6u
15
+ 13u
16
4u
17
5u
18
+ u
19
+ u
20
)
2
(u
24
6u
22
+ ··· + 1079u 676)
c
10
(u
3
u
2
+ 2u 1)
(1 + 2u + u
2
+ u
3
+ 9u
4
4u
5
2u
6
10u
7
25u
8
+ 2u
9
3u
10
+ 31u
11
+ 48u
12
+ 42u
13
+ 60u
14
+ 26u
15
+ 33u
16
+ 8u
17
+ 9u
18
+ u
19
+ u
20
)
2
(u
24
+ 10u
22
+ ··· 15u 4)
13
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(64y
3
16y
2
+ 8y 1)(64y
24
656y
23
+ ··· 7y + 1)
(y
40
21y
39
+ ··· 1779930398y + 170276399)
c
2
, c
5
(y 1)
3
(y
24
+ 13y
23
+ ··· 38y + 1)(y
40
+ 27y
39
+ ··· + 40y
2
+ 1)
c
3
(y 1)
3
(y
24
+ 13y
23
+ ··· 38y + 1)(y
40
+ 27y
39
+ ··· + 40y
2
+ 1)
c
4
(64y
3
16y
2
+ 8y 1)(64y
24
656y
23
+ ··· 7y + 1)
(y
40
21y
39
+ ··· 1779930400y + 170276401)
c
6
, c
7
, c
10
(y
3
+ 3y
2
+ 2y 1)
(1 6y 21y
2
+ 37y
3
+ 175y
4
84y
5
756y
6
292y
7
+ 1655y
8
+ 1954y
9
1117y
10
3803y
11
2264y
12
+ 1720y
13
+ 3980y
14
+ 3408y
15
+ 1765y
16
+ 598y
17
+ 131y
18
+ 17y
19
+ y
20
)
2
(y
24
+ 20y
23
+ ··· 97y + 16)
c
8
y
3
(1 6y + 15y
2
47y
3
+ 119y
4
272y
5
+ 536y
6
908y
7
+ 1343y
8
1730y
9
+ 1959y
10
1951y
11
+ 1708y
12
1312y
13
+ 876y
14
504y
15
+ 245y
16
98y
17
+ 31y
18
7y
19
+ y
20
)
2
(y
24
7y
23
+ ··· 226304y + 16384)
c
9
(y
3
y
2
+ 2y 1)(y
24
12y
23
+ ··· 1380561y + 456976)
(y
40
22y
39
+ ··· 12y + 1)
c
11
(y 1)
3
(y
24
+ 13y
23
+ ··· 38y + 1)(y
40
+ 27y
39
+ ··· + 40y
2
+ 1)
14