11a
330
(K11a
330
)
1
Arc Sequences
10 6 1 8 9 2 11 5 3 7 4
Solving Sequence
4,8
5 9
6,11
1 3 2 7 10
c
4
c
8
c
5
c
11
c
3
c
2
c
7
c
10
c
1
, c
6
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
15
2u
14
7u
13
+ 16u
12
+ 15u
11
46u
10
3u
9
+ 54u
8
25u
7
16u
6
+ 26u
5
12u
4
6u
3
+ 7u
2
2u 1,
u
13
u
12
7u
11
+ 8u
10
+ 16u
9
22u
8
10u
7
+ 23u
6
7u
5
5u
4
+ 7u
3
3u
2
+ b u + 1,
u
14
+ 2u
13
+ ··· + a + 2i
I
u
2
= hu
59
3u
58
+ ··· 68u 47,
1.12011 × 10
74
u
58
+ 2.75629 × 10
74
u
57
+ ··· + 3.44884 × 10
73
b 1.05135 × 10
76
,
1.49619 × 10
76
u
58
+ 3.79895 × 10
76
u
57
+ ··· + 1.62096 × 10
75
a 1.57571 × 10
78
i
There are 2 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
15
2u
14
+· · ·2u1, u
13
u
12
+· · ·+b+1, u
14
+2u
13
+· · ·+a+2i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
2u
2
a
11
=
u
14
2u
13
+ ··· + 6u 2
u
13
+ u
12
+ ··· + u 1
a
1
=
u
14
u
13
+ ··· + 5u 1
u
13
+ u
12
+ ··· + u 1
a
3
=
u
8
5u
6
+ u
5
+ 7u
4
3u
3
u
2
+ 2u 1
u
13
+ u
12
+ ··· + u 1
a
2
=
u
8
u
7
5u
6
+ 5u
5
+ 7u
4
7u
3
u
2
+ 2u 2
u
14
+ 9u
12
+ ··· 2u 2
a
7
=
u
14
+ 2u
13
+ ··· 5u + 2
u
14
+ u
13
+ ··· + 3u
2
2u
a
10
=
u
5
3u
3
+ 2u
u
14
u
13
+ ··· + u
2
+ 2u
a
10
=
u
5
3u
3
+ 2u
u
14
u
13
+ ··· + u
2
+ 2u
(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 = 1.62956 0.11015I
a = 1.018688 + 0.151448I
b = 0.429910 1.194277I
14.4815 + 1.9499I 11.70621 0.15719I
u = 1.62956 + 0.11015I
a = 1.018688 0.151448I
b = 0.429910 + 1.194277I
14.4815 1.9499I 11.70621 + 0.15719I
u = 1.28962
a = 0.514199
b = 0.581197
3.36193 14.4311
u = 0.859236 0.096648I
a = 0.290049 + 0.225922I
b = 0.455127 0.900633I
1.37447 1.85175I 6.24665 0.44232I
u = 0.859236 + 0.096648I
a = 0.290049 0.225922I
b = 0.455127 + 0.900633I
1.37447 + 1.85175I 6.24665 + 0.44232I
u = 0.257945
a = 3.61884
b = 0.931093
0.131193 4.21559
u = 0.147449 0.698939I
a = 0.14152 + 2.06872I
b = 0.102496 + 1.303926I
7.44398 + 1.12715I 9.32440 0.18246I
u = 0.147449 + 0.698939I
a = 0.14152 2.06872I
b = 0.102496 1.303926I
7.44398 1.12715I 9.32440 + 0.18246I
u = 0.488833 0.456106I
a = 0.60478 + 1.47650I
b = 0.258245 0.780965I
5.17256 + 2.76956I 12.90399 4.24420I
u = 0.488833 + 0.456106I
a = 0.60478 1.47650I
b = 0.258245 + 0.780965I
5.17256 2.76956I 12.90399 + 4.24420I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.318057 0.189471I
a = 0.574725 + 0.296326I
b = 0.214298 + 0.558537I
8.33813 5.13031I 13.01330 + 4.52627I
u = 1.318057 + 0.189471I
a = 0.574725 0.296326I
b = 0.214298 0.558537I
8.33813 + 5.13031I 13.01330 4.52627I
u = 1.52270
a = 0.865968
b = 1.27999
6.18333 5.55828
u = 1.54689 0.23410I
a = 0.914905 + 0.329736I
b = 0.15368 1.44939I
12.76516 4.69419I 12.91855 + 3.93139I
u = 1.54689 + 0.23410I
a = 0.914905 0.329736I
b = 0.15368 + 1.44939I
12.76516 + 4.69419I 12.91855 3.93139I
4
II. I
u
2
=
hu
59
3u
58
+· · ·68u47, 1.12×10
74
u
58
+2.76×10
74
u
57
+· · ·+3.45×10
73
b
1.05× 10
76
, 1.50× 10
76
u
58
+3.80 ×10
76
u
57
+· · · +1.62 ×10
75
a 1.58× 10
78
i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
5
=
1
u
2
a
9
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
2u
2
a
11
=
9.23031u
58
23.4365u
57
+ ··· + 3493.41u + 972.086
3.24779u
58
7.99193u
57
+ ··· + 1122.55u + 304.842
a
1
=
5.98251u
58
15.4445u
57
+ ··· + 2370.86u + 667.245
3.24779u
58
7.99193u
57
+ ··· + 1122.55u + 304.842
a
3
=
2.41804u
58
6.03112u
57
+ ··· + 1112.39u + 331.970
3.35170u
58
8.54361u
57
+ ··· + 1242.14u + 331.682
a
2
=
5.18004u
58
13.0960u
57
+ ··· + 2212.35u + 639.499
2.03204u
58
5.19353u
57
+ ··· + 732.562u + 188.668
a
7
=
3.24999u
58
7.66870u
57
+ ··· + 1187.04u + 318.226
2.73447u
58
7.36256u
57
+ ··· + 1055.99u + 271.177
a
10
=
0.648359u
58
+ 1.03490u
57
+ ··· + 370.690u + 121.526
2.37556u
58
5.68960u
57
+ ··· + 673.282u + 160.207
a
10
=
0.648359u
58
+ 1.03490u
57
+ ··· + 370.690u + 121.526
2.37556u
58
5.68960u
57
+ ··· + 673.282u + 160.207
(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 = 1.63522 0.16039I
a = 0.003749 0.275010I
b = 0.23042 + 1.41743I
12.00310 + 1.72842I 11.74362 0.30714I
u = 1.63522 + 0.16039I
a = 0.003749 + 0.275010I
b = 0.23042 1.41743I
12.00310 1.72842I 11.74362 + 0.30714I
u = 1.60407 0.19460I
a = 0.938387 0.141608I
b = 0.58039 + 1.68597I
13.1880 + 8.2730I 10.57843 5.37996I
u = 1.60407 + 0.19460I
a = 0.938387 + 0.141608I
b = 0.58039 1.68597I
13.1880 8.2730I 10.57843 + 5.37996I
u = 1.58483 0.22376I
a = 0.987123 + 0.209265I
b = 0.273747 1.367094I
11.87835 + 3.53773I 8.99766 + 0.19863I
u = 1.58483 + 0.22376I
a = 0.987123 0.209265I
b = 0.273747 + 1.367094I
11.87835 3.53773I 8.99766 0.19863I
u = 1.57638 0.12949I
a = 0.436873 + 0.982897I
b = 0.186350 1.361054I
11.80620 + 7.29433I 11.73130 6.22760I
u = 1.57638 + 0.12949I
a = 0.436873 0.982897I
b = 0.186350 + 1.361054I
11.80620 7.29433I 11.73130 + 6.22760I
u = 1.56748
a = 0.881028
b = 1.73811
7.31990 14.1720
u = 1.50589
a = 0.891008
b = 0.701190
7.41921 13.8922
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.44030 0.20799I
a = 0.221441 + 0.421025I
b = 0.542037 0.003122I
7.30101 + 4.74836I 5.03007 2.51272I
u = 1.44030 + 0.20799I
a = 0.221441 0.421025I
b = 0.542037 + 0.003122I
7.30101 4.74836I 5.03007 + 2.51272I
u = 1.072726 0.002898I
a = 0.708113 0.180531I
b = 0.679774 + 0.774687I
1.97600 + 2.55273I 10.26685 5.82236I
u = 1.072726 + 0.002898I
a = 0.708113 + 0.180531I
b = 0.679774 0.774687I
1.97600 2.55273I 10.26685 + 5.82236I
u = 0.870656 0.926885I
a = 0.986934 0.667144I
b = 0.31968 1.41732I
10.3757 + 9.8566I 10.78324 6.83815I
u = 0.870656 + 0.926885I
a = 0.986934 + 0.667144I
b = 0.31968 + 1.41732I
10.3757 9.8566I 10.78324 + 6.83815I
u = 0.655609 0.435361I
a = 1.52726 0.50194I
b = 0.899285 0.164244I
5.22435 + 5.58403I 7.88408 6.48040I
u = 0.655609 + 0.435361I
a = 1.52726 + 0.50194I
b = 0.899285 + 0.164244I
5.22435 5.58403I 7.88408 + 6.48040I
u = 0.647619 0.225990I
a = 1.90147 0.85004I
b = 0.42877 1.41249I
9.17648 0.45587I 13.79187 0.50236I
u = 0.647619 + 0.225990I
a = 1.90147 + 0.85004I
b = 0.42877 + 1.41249I
9.17648 + 0.45587I 13.79187 + 0.50236I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.507724 1.289266I
a = 0.303043 + 0.951975I
b = 0.042705 + 1.359629I
9.00112 2.68298I 13.37182 + 3.04466I
u = 0.507724 + 1.289266I
a = 0.303043 0.951975I
b = 0.042705 1.359629I
9.00112 + 2.68298I 13.37182 3.04466I
u = 0.486013 0.140699I
a = 0.526562 0.989442I
b = 0.351844 + 0.983970I
0.77762 + 2.37468I 0.58026 5.71266I
u = 0.486013 + 0.140699I
a = 0.526562 + 0.989442I
b = 0.351844 0.983970I
0.77762 2.37468I 0.58026 + 5.71266I
u = 0.485094 0.213274I
a = 3.30156 + 0.35475I
b = 0.001691 + 1.297034I
8.58837 + 2.03485I 15.0115 3.6514I
u = 0.485094 + 0.213274I
a = 3.30156 0.35475I
b = 0.001691 1.297034I
8.58837 2.03485I 15.0115 + 3.6514I
u = 0.462881 0.565944I
a = 0.55152 + 1.59437I
b = 0.0819864 + 0.0135157I
4.44971 2.14107I 5.59927 1.54259I
u = 0.462881 + 0.565944I
a = 0.55152 1.59437I
b = 0.0819864 0.0135157I
4.44971 + 2.14107I 5.59927 + 1.54259I
u = 0.020007 0.394814I
a = 0.649909 1.080939I
b = 0.564266 0.401283I
0.96759 1.06374I 3.58491 + 4.50505I
u = 0.020007 + 0.394814I
a = 0.649909 + 1.080939I
b = 0.564266 + 0.401283I
0.96759 + 1.06374I 3.58491 4.50505I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.415938 0.579248I
a = 0.846887 0.499107I
b = 0.574644 0.026281I
1.35011 1.88524I 3.00166 + 3.83760I
u = 0.415938 + 0.579248I
a = 0.846887 + 0.499107I
b = 0.574644 + 0.026281I
1.35011 + 1.88524I 3.00166 3.83760I
u = 0.452712
a = 1.61649
b = 0.0591731
0.981228 11.9021
u = 0.453128
a = 2.33221
b = 1.18104
0.221271 19.3562
u = 0.481157 0.783711I
a = 0.87764 + 1.18816I
b = 0.033355 + 1.312053I
4.90675 + 0.17949I 6.45758 + 0.24351I
u = 0.481157 + 0.783711I
a = 0.87764 1.18816I
b = 0.033355 1.312053I
4.90675 0.17949I 6.45758 0.24351I
u = 0.547371 0.629034I
a = 0.275474 0.246041I
b = 0.362689 1.069455I
4.32344 + 1.31427I 8.87224 + 0.47673I
u = 0.547371 + 0.629034I
a = 0.275474 + 0.246041I
b = 0.362689 + 1.069455I
4.32344 1.31427I 8.87224 0.47673I
u = 0.566889 0.487295I
a = 1.27041 0.78556I
b = 0.293328 + 1.120327I
4.51202 5.11815I 8.89658 + 7.24819I
u = 0.566889 + 0.487295I
a = 1.27041 + 0.78556I
b = 0.293328 1.120327I
4.51202 + 5.11815I 8.89658 7.24819I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.663884 0.670936I
a = 1.15868 0.88811I
b = 0.33009 1.44308I
5.56188 5.09196I 7.87626 + 5.74174I
u = 0.663884 + 0.670936I
a = 1.15868 + 0.88811I
b = 0.33009 + 1.44308I
5.56188 + 5.09196I 7.87626 5.74174I
u = 0.912889 0.065447I
a = 0.654408 0.408442I
b = 0.109027 + 0.587707I
1.58471 0.10901I 7.61205 + 0.31750I
u = 0.912889 + 0.065447I
a = 0.654408 + 0.408442I
b = 0.109027 0.587707I
1.58471 + 0.10901I 7.61205 0.31750I
u = 1.31990
a = 0.0472574
b = 0.674808
2.77979 0.437701
u = 1.55236 0.02522I
a = 0.133426 + 0.715380I
b = 0.19113 1.40151I
7.75920 2.91351I 7.55652 + 2.72251I
u = 1.55236 + 0.02522I
a = 0.133426 0.715380I
b = 0.19113 + 1.40151I
7.75920 + 2.91351I 7.55652 2.72251I
u = 1.56343 0.06205I
a = 1.285728 + 0.513846I
b = 0.270263 1.324284I
15.6947 3.0236I 16.1010 + 3.0701I
u = 1.56343 + 0.06205I
a = 1.285728 0.513846I
b = 0.270263 + 1.324284I
15.6947 + 3.0236I 16.1010 3.0701I
u = 1.59540 0.14328I
a = 0.915820 0.268097I
b = 0.698680 0.076811I
11.68026 0.45414I 9.94382 0.23365I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.59540 + 0.14328I
a = 0.915820 + 0.268097I
b = 0.698680 + 0.076811I
11.68026 + 0.45414I 9.94382 + 0.23365I
u = 1.60361 0.11834I
a = 0.911699 0.052547I
b = 1.42194 + 0.25243I
12.9698 7.5955I 10.73650 + 4.72646I
u = 1.60361 + 0.11834I
a = 0.911699 + 0.052547I
b = 1.42194 0.25243I
12.9698 + 7.5955I 10.73650 4.72646I
u = 1.60729 0.06441I
a = 0.887442 0.078089I
b = 0.81025 + 1.62623I
17.0188 0.6284I 13.76003 0.45669I
u = 1.60729 + 0.06441I
a = 0.887442 + 0.078089I
b = 0.81025 1.62623I
17.0188 + 0.6284I 13.76003 + 0.45669I
u = 1.68149 0.27693I
a = 1.006943 0.127051I
b = 0.53294 + 1.57371I
18.8364 14.4187I 11.67577 + 6.36175I
u = 1.68149 + 0.27693I
a = 1.006943 + 0.127051I
b = 0.53294 1.57371I
18.8364 + 14.4187I 11.67577 6.36175I
u = 1.78123 0.42255I
a = 0.759705 0.078407I
b = 0.27686 1.40310I
16.5334 4.0342I 14.4430 + 2.7231I
u = 1.78123 + 0.42255I
a = 0.759705 + 0.078407I
b = 0.27686 + 1.40310I
16.5334 + 4.0342I 14.4430 2.7231I
11
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
15
3u
14
+ ··· + 5u 1)(u
59
+ 8u
58
+ ··· + 7075u + 1561)
c
2
(u
15
+ u
14
+ ··· u 1)(u
59
+ 2u
58
+ ··· u + 1)
c
3
(u
15
+ 2u
14
+ ··· + 2u + 1)(u
59
+ 3u
58
+ ··· 44u 1)
c
4
, c
5
(u
15
2u
14
+ ··· 2u 1)(u
59
+ 3u
58
+ ··· 68u + 47)
c
6
(u
15
u
14
+ ··· u + 1)(u
59
+ 2u
58
+ ··· u + 1)
c
7
(u
15
3u
14
+ ··· + 3u + 1)(u
59
30u
57
+ ··· + 331u + 19)
c
8
(u
15
+ 2u
14
+ ··· 2u + 1)(u
59
+ 3u
58
+ ··· 68u + 47)
c
9
(u
15
u
14
+ ··· 7u 1)(u
59
+ 2u
58
+ ··· + 2319u 2117)
c
10
(u
15
+ 3u
14
+ ··· + 3u 1)(u
59
30u
57
+ ··· + 331u + 19)
c
11
(u
15
2u
14
+ ··· + 2u 1)(u
59
+ 3u
58
+ ··· 44u 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
15
5y
14
+ ··· + 13y 1)
(y
59
28y
58
+ ··· + 51101495y 2436721)
c
2
, c
6
(y
15
+ 11y
14
+ ··· 23y 1)(y
59
+ 48y
58
+ ··· + 143y 1)
c
3
, c
11
(y
15
+ 10y
14
+ ··· 6y 1)(y
59
+ 51y
58
+ ··· + 564y 1)
c
4
, c
5
, c
8
(y
15
18y
14
+ ··· + 18y 1)(y
59
69y
58
+ ··· + 52564y 2209)
c
7
, c
10
(y
15
17y
14
+ ··· + 17y 1)(y
59
60y
58
+ ··· + 84595y 361)
c
9
(y
15
5y
14
+ ··· + 57y 1)
(y
59
32y
58
+ ··· + 164317887y 4481689)
13