11a
354
(K11a
354
)
1
Arc Sequences
5 9 8 1 10 2 11 3 6 4 7
Solving Sequence
5,10 2,6
7 1 4 9 3 8 11
c
5
c
6
c
1
c
4
c
9
c
2
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hu
21
6u
19
+ ··· + 57u 24, 3.17705 × 10
22
u
20
7.96995 × 10
21
u
19
+ ··· + 3.34979 × 10
24
b 6.52244 × 10
23
,
3.20938 × 10
23
u
20
8.49999 × 10
22
u
19
+ ··· + 1.00494 × 10
25
a 1.55146 × 10
25
i
I
u
2
= ha
34
8a
33
+ ··· + 10a
2
+ 1, 9.85568 × 10
47
b + 1.93850 × 10
46
a
33
+ ··· 5.59203 × 10
48
a + 4.47308 × 10
47
,
3.28523 × 10
47
u + 7.81651 × 10
46
a
33
+ ··· 4.94568 × 10
47
a + 2.19460 × 10
46
i
I
u
3
= hu 1, a + 1, 2b + 1i
I
u
4
= h4b
2
+ 4b + 3, a + 1, u + 1i
There are 4 irreducible components with 58 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
21
6u
19
+· · ·+57u24, 3.18×10
22
u
20
7.97×10
21
u
19
+· · ·+3.35×10
24
b
6.52× 10
23
, 3.21 × 10
23
u
20
8.50 ×10
22
u
19
+· · · +1.00 ×10
25
a 1.55× 10
25
i
(i) Arc colorings
a
5
=
0
u
a
10
=
0.0319361u
20
+ 0.00845824u
19
+ ··· + 0.207488u + 1.54384
0.00948434u
20
+ 0.00237924u
19
+ ··· 1.42422u + 0.194712
a
2
=
1
0
a
6
=
0.0207196u
20
+ 0.0168710u
19
+ ··· 1.44302u + 0.426320
0.00414837u
20
+ 0.0108360u
19
+ ··· 0.330233u + 0.621628
a
7
=
0.0165713u
20
+ 0.00603499u
19
+ ··· 1.11278u 0.195307
0.00414837u
20
+ 0.0108360u
19
+ ··· 0.330233u + 0.621628
a
1
=
1
u
2
a
4
=
u
u
3
+ u
a
9
=
0.0737484u
20
+ 0.0279609u
19
+ ··· 0.341011u + 2.41501
0.0104442u
20
+ 0.0106526u
19
+ ··· 2.56537u + 0.422479
a
3
=
0.0597537u
20
0.0577894u
19
+ ··· 1.27604u + 0.700822
0.00806566u
20
0.00119049u
19
+ ··· + 2.24688u 0.0471451
a
8
=
0.0455642u
20
0.0246470u
19
+ ··· + 2.27332u 0.207976
0.0163507u
20
0.0301443u
19
+ ··· + 1.47731u 1.17843
a
11
=
0.0427721u
20
+ 0.0112293u
19
+ ··· + 0.592658u + 1.64340
0.000959906u
20
+ 0.00827334u
19
+ ··· 1.14116u + 0.227767
a
11
=
0.0427721u
20
+ 0.0112293u
19
+ ··· + 0.592658u + 1.64340
0.000959906u
20
+ 0.00827334u
19
+ ··· 1.14116u + 0.227767
(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 = 1.89114 0.74167I
a = 0.183263 + 0.548069I
b = 1.06062 1.27747I
8.68556 + 1.36021I 3.27021 3.85751I
u = 1.89114 + 0.74167I
a = 0.183263 0.548069I
b = 1.06062 + 1.27747I
8.68556 1.36021I 3.27021 + 3.85751I
u = 1.29660 0.72895I
a = 0.702275 + 0.582958I
b = 1.92269 0.98747I
3.28365 11.20834I 7.47113 + 8.56307I
u = 1.29660 + 0.72895I
a = 0.702275 0.582958I
b = 1.92269 + 0.98747I
3.28365 + 11.20834I 7.47113 8.56307I
u = 1.011865 0.167863I
a = 1.000236 + 0.469303I
b = 0.438354 + 0.068037I
3.50254 0.45372I 13.2351 + 10.9889I
u = 1.011865 + 0.167863I
a = 1.000236 0.469303I
b = 0.438354 0.068037I
3.50254 + 0.45372I 13.2351 10.9889I
u = 0.508583 0.245922I
a = 0.909451 + 0.214481I
b = 0.143050 0.951971I
3.45120 1.15767I 7.19855 + 5.90528I
u = 0.508583 + 0.245922I
a = 0.909451 0.214481I
b = 0.143050 + 0.951971I
3.45120 + 1.15767I 7.19855 5.90528I
u = 0.33964 1.52106I
a = 0.713910 0.273536I
b = 2.04135 + 0.24573I
6.35701 + 3.86289I 1.42698 7.24526I
u = 0.33964 + 1.52106I
a = 0.713910 + 0.273536I
b = 2.04135 0.24573I
6.35701 3.86289I 1.42698 + 7.24526I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.173107 1.254654I
a = 1.042481 + 0.445032I
b = 1.86666 0.07408I
14.7040 8.5355I 2.42060 + 4.78360I
u = 0.173107 + 1.254654I
a = 1.042481 0.445032I
b = 1.86666 + 0.07408I
14.7040 + 8.5355I 2.42060 4.78360I
u = 0.261262
a = 1.09926
b = 0.244086
0.522581 19.0061
u = 0.868563 0.334615I
a = 1.33171 0.86981I
b = 0.517795 0.272207I
2.63271 + 1.46369I 5.79825 4.59200I
u = 0.868563 + 0.334615I
a = 1.33171 + 0.86981I
b = 0.517795 + 0.272207I
2.63271 1.46369I 5.79825 + 4.59200I
u = 1.259744 0.049663I
a = 0.406479 0.439226I
b = 0.416658 + 0.276484I
2.36275 1.38248I 10.93113 + 5.35701I
u = 1.259744 + 0.049663I
a = 0.406479 + 0.439226I
b = 0.416658 0.276484I
2.36275 + 1.38248I 10.93113 5.35701I
u = 1.27655 0.93600I
a = 0.576083 0.464647I
b = 1.75285 + 1.05604I
2.01539 + 5.30911I 6.93058 7.06093I
u = 1.27655 + 0.93600I
a = 0.576083 + 0.464647I
b = 1.75285 1.05604I
2.01539 5.30911I 6.93058 + 7.06093I
u = 1.33922 0.65997I
a = 0.761610 0.669960I
b = 2.05975 + 0.86477I
11.0553 + 15.1817I 5.60482 7.58890I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.33922 + 0.65997I
a = 0.761610 + 0.669960I
b = 2.05975 0.86477I
11.0553 15.1817I 5.60482 + 7.58890I
4
II.
I
u
2
= ha
34
8a
33
+ · · · + 10a
2
+ 1, 9.86 × 10
47
b + 1.94 × 10
46
a
33
+ · · · 5.59 ×
10
48
a+4.47×10
47
, 3.29×10
47
u+7.82×10
46
a
33
+· · ·4.95×10
47
a+2.19×10
46
i
(i) Arc colorings
a
5
=
0
0.237929a
33
+ 1.94713a
32
+ ··· + 1.50543a 0.0668022
a
10
=
a
0.0196689a
33
+ 0.0974257a
32
+ ··· + 5.67392a 0.453858
a
2
=
1
0
a
6
=
0.0667139a
33
+ 0.479514a
32
+ ··· 0.237929a + 0.0436956
0.241897a
33
+ 1.98337a
32
+ ··· + 0.529253a 0.125721
a
7
=
0.175183a
33
1.50386a
32
+ ··· 0.767182a + 0.169416
0.241897a
33
+ 1.98337a
32
+ ··· + 0.529253a 0.125721
a
1
=
1
0.0920163a
33
0.638938a
32
+ ··· 2.29957a 1.22105
a
4
=
0.237929a
33
+ 1.94713a
32
+ ··· + 1.50543a 0.0668022
0.368323a
33
2.83782a
32
+ ··· + 3.18457a 0.502218
a
9
=
0.000854678a
33
0.00426749a
32
+ ··· + 1.09719a + 0.0126396
0.0545479a
33
0.503620a
32
+ ··· + 4.56973a 0.473309
a
3
=
0.0747168a
33
+ 0.576003a
32
+ ··· 0.416712a + 0.964843
0.124589a
33
+ 1.04808a
32
+ ··· + 0.958443a 1.24210
a
8
=
0.0847759a
33
0.768052a
32
+ ··· + 4.31533a 0.354474
0.154409a
33
+ 1.19623a
32
+ ··· 6.62301a + 0.877120
a
11
=
0.207060a
33
1.55071a
32
+ ··· 5.55365a + 1.31441
0.0809767a
33
+ 0.655734a
32
+ ··· + 3.10946a 1.63830
a
11
=
0.207060a
33
1.55071a
32
+ ··· 5.55365a + 1.31441
0.0809767a
33
+ 0.655734a
32
+ ··· + 3.10946a 1.63830
(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 = 1.162589 + 0.537552I
a = 0.931900 0.817568I
b = 1.66165 + 0.69149I
6.70220 8.83664I 7.62632 + 5.87120I
u = 1.162589 0.537552I
a = 0.931900 + 0.817568I
b = 1.66165 0.69149I
6.70220 + 8.83664I 7.62632 5.87120I
u = 1.156823 0.481476I
a = 0.767470 0.748840I
b = 1.58383 + 0.75982I
0.35577 6.09306I 11.29297 + 6.87425I
u = 1.156823 + 0.481476I
a = 0.767470 + 0.748840I
b = 1.58383 0.75982I
0.35577 + 6.09306I 11.29297 6.87425I
u = 0.774885 + 0.615952I
a = 0.63711 1.50479I
b = 0.743314 + 0.296871I
12.06087 2.39923I 3.13400 + 3.27109I
u = 0.774885 0.615952I
a = 0.63711 + 1.50479I
b = 0.743314 0.296871I
12.06087 + 2.39923I 3.13400 3.27109I
u = 1.151921 + 0.412149I
a = 0.517960 0.702479I
b = 1.49546 + 0.73449I
0.85249 2.05778I 13.01930 + 0.37816I
u = 1.151921 0.412149I
a = 0.517960 + 0.702479I
b = 1.49546 0.73449I
0.85249 + 2.05778I 13.01930 0.37816I
u = 0.758174 0.422247I
a = 0.46261 1.43772I
b = 0.511570 + 0.892770I
4.41315 1.83062I 4.40697 + 5.22267I
u = 0.758174 + 0.422247I
a = 0.46261 + 1.43772I
b = 0.511570 0.892770I
4.41315 + 1.83062I 4.40697 5.22267I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.172060 0.309872I
a = 0.172224 0.867890I
b = 1.75297 + 0.14157I
5.15765 + 0.50801I 9.57451 + 0.23246I
u = 1.172060 + 0.309872I
a = 0.172224 + 0.867890I
b = 1.75297 0.14157I
5.15765 0.50801I 9.57451 0.23246I
u = 0.112463 0.679715I
a = 0.152161 0.652918I
b = 0.587037 0.124459I
2.59185 + 1.70542I 8.10923 4.02096I
u = 0.112463 + 0.679715I
a = 0.152161 + 0.652918I
b = 0.587037 + 0.124459I
2.59185 1.70542I 8.10923 + 4.02096I
u = 1.172060 + 0.309872I
a = 0.105479 0.141513I
b = 0.44315 1.53433I
5.15765 0.50801I 9.57451 0.23246I
u = 1.172060 0.309872I
a = 0.105479 + 0.141513I
b = 0.44315 + 1.53433I
5.15765 + 0.50801I 9.57451 + 0.23246I
u = 0.231761 + 0.782357I
a = 0.016370 1.228241I
b = 0.428341 0.336597I
9.44087 + 3.91820I 4.40216 2.39256I
u = 0.231761 0.782357I
a = 0.016370 + 1.228241I
b = 0.428341 + 0.336597I
9.44087 3.91820I 4.40216 + 2.39256I
u = 0.756727
a = 0.213682 1.372330I
b = 2.05361 + 1.83882I
2.28510 14.8691
u = 0.756727
a = 0.213682 + 1.372330I
b = 2.05361 1.83882I
2.28510 14.8691
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.151921 + 0.412149I
a = 0.360904 0.247048I
b = 0.000711 + 0.366208I
0.85249 2.05778I 13.01930 + 0.37816I
u = 1.151921 0.412149I
a = 0.360904 + 0.247048I
b = 0.000711 0.366208I
0.85249 + 2.05778I 13.01930 0.37816I
u = 1.156823 0.481476I
a = 0.661048 0.365125I
b = 0.307436 0.094632I
0.35577 6.09306I 11.29297 + 6.87425I
u = 1.156823 + 0.481476I
a = 0.661048 + 0.365125I
b = 0.307436 + 0.094632I
0.35577 + 6.09306I 11.29297 6.87425I
u = 1.162589 + 0.537552I
a = 0.869248 0.432337I
b = 0.518989 0.345285I
6.70220 8.83664I 7.62632 + 5.87120I
u = 1.162589 0.537552I
a = 0.869248 + 0.432337I
b = 0.518989 + 0.345285I
6.70220 + 8.83664I 7.62632 5.87120I
u = 0.758174 + 0.422247I
a = 1.066070 0.797449I
b = 1.67413 0.12115I
4.41315 + 1.83062I 4.40697 5.22267I
u = 0.758174 0.422247I
a = 1.066070 + 0.797449I
b = 1.67413 + 0.12115I
4.41315 1.83062I 4.40697 + 5.22267I
u = 0.774885 0.615952I
a = 1.41606 0.55021I
b = 1.54855 0.00624I
12.06087 + 2.39923I 3.13400 3.27109I
u = 0.774885 + 0.615952I
a = 1.41606 + 0.55021I
b = 1.54855 + 0.00624I
12.06087 2.39923I 3.13400 + 3.27109I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.231761 0.782357I
a = 1.57474 0.86560I
b = 1.347493 0.257267I
9.44087 3.91820I 4.40216 + 2.39256I
u = 0.231761 + 0.782357I
a = 1.57474 + 0.86560I
b = 1.347493 + 0.257267I
9.44087 + 3.91820I 4.40216 2.39256I
u = 0.112463 + 0.679715I
a = 1.60153 0.50003I
b = 1.227057 0.115531I
2.59185 1.70542I 8.10923 + 4.02096I
u = 0.112463 0.679715I
a = 1.60153 + 0.50003I
b = 1.227057 + 0.115531I
2.59185 + 1.70542I 8.10923 4.02096I
9
III. I
u
3
= hu 1, a + 1, 2b + 1i
(i) Arc colorings
a
5
=
0
1
a
10
=
1
1
2
a
2
=
1
0
a
6
=
1
1
2
a
7
=
3
2
1
2
a
1
=
1
1
a
4
=
1
0
a
9
=
2
0
a
3
=
1
0
a
8
=
2
0
a
11
=
1
2
1
2
a
11
=
1
2
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0.500000
3.28987 7.50000
11
IV. I
u
4
= h4b
2
+ 4b + 3, a + 1, u + 1i
(i) Arc colorings
a
5
=
0
1
a
10
=
1
b
a
2
=
1
0
a
6
=
1
b 1
a
7
=
b + 2
b 1
a
1
=
1
1
a
4
=
1
0
a
9
=
2
2b + 1
a
3
=
4b 1
2
a
8
=
2b + 3
2b 1
a
11
=
b 1
b
a
11
=
b 1
b
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
12
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 0.500000 0.707107I
1.64493 12.0000
u = 1.00000
a = 1.00000
b = 0.500000 + 0.707107I
1.64493 12.0000
13
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)(u + 1)
2
(1 + u 2u
4
2u
5
+ 2u
6
+ 6u
7
+ 5u
8
3u
9
12u
10
4u
11
+ 11u
12
+ 7u
13
5u
14
4u
15
+ u
16
+ u
17
)
2
(u
21
6u
19
+ ··· + 57u + 24)
c
2
, c
3
, c
8
u(u
2
+ 2)
(1 + u + 4u
3
4u
4
+ 18u
5
12u
6
+ 38u
7
37u
8
+ 71u
9
50u
10
+ 74u
11
31u
12
+ 39u
13
9u
14
+ 10u
15
u
16
+ u
17
)
2
(u
21
+ 3u
20
+ ··· 24u 8)
c
4
(u 1)
2
(u + 1)
(1 + u 2u
4
2u
5
+ 2u
6
+ 6u
7
+ 5u
8
3u
9
12u
10
4u
11
+ 11u
12
+ 7u
13
5u
14
4u
15
+ u
16
+ u
17
)
2
(u
21
6u
19
+ ··· + 57u + 24)
c
5
, c
7
(u 1)(u + 1)
2
(u
21
u
20
+ ··· u + 3)(u
34
+ 3u
33
+ ··· + 8u + 1)
c
6
(2u + 1)(4u
2
4u + 3)(8u
21
+ 4u
20
+ ··· 2u 4)
(9u
34
+ 45u
33
+ ··· 5844u + 4123)
c
9
, c
11
(u 1)
2
(u + 1)(u
21
u
20
+ ··· u + 3)(u
34
+ 3u
33
+ ··· + 8u + 1)
c
10
(2u 1)(4u
2
+ 4u + 3)(8u
21
+ 4u
20
+ ··· 2u 4)
(9u
34
+ 45u
33
+ ··· 5844u + 4123)
14
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y 1)
3
(1 + y + 4y
2
8y
3
2y
4
+ 30y
5
38y
6
+ 4y
7
+ 37y
8
9y
9
106y
10
+ 232y
11
271y
12
+ 209y
13
111y
14
+ 40y
15
9y
16
+ y
17
)
2
(y
21
12y
20
+ ··· + 13233y 576)
c
2
, c
3
, c
8
y(y + 2)
2
(1 + y + 16y
2
+ 76y
3
+ 278y
4
+ 774y
5
+ 1706y
6
+ 3400y
7
+ 5577y
8
+ 7635y
9
+ 8822y
10
+ 8020y
11
+ 5333y
12
+ 2485y
13
+ 785y
14
+ 160y
15
+ 19y
16
+ y
17
)
2
(y
21
+ 23y
20
+ ··· + 96y 64)
c
5
, c
7
, c
9
c
11
(y 1)
3
(y
21
+ 11y
20
+ ··· + 85y 9)(y
34
+ 23y
33
+ ··· 16y + 1)
c
6
, c
10
(4y 1)(16y
2
+ 8y + 9)(64y
21
+ 656y
20
+ ··· + 60y 16)
(81y
34
+ 1539y
33
+ ··· + 218604056y + 16999129)
15