11a
214
(K11a
214
)
1
Arc Sequences
7 1 8 11 10 2 9 3 6 5 4
Solving Sequence
2,6 7,9
10 1 3 5 11 4 8
c
6
c
9
c
1
c
2
c
5
c
10
c
4
c
8
c
3
, c
7
, c
11
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hb
4
+ 2b
3
+ b
2
+ 5, 2b
3
+ 3b
2
4b + 9a + 2, 2b
3
+ 3b
2
+ 5b + 9u + 2i
I
u
2
= hu
16
+ 3u
14
u
13
+ 8u
12
2u
11
+ 11u
10
4u
9
+ 15u
8
2u
7
+ 13u
6
2u
5
+ 11u
4
+ 5u
2
u + 1,
u
15
u
14
+ 2u
13
3u
12
+ 7u
11
7u
10
+ 6u
9
8u
8
+ 13u
7
9u
6
+ 2u
5
6u
4
+ 7u
3
5u
2
+ 4a 6u 1,
u
15
u
14
+ 2u
13
3u
12
+ 7u
11
7u
10
+ 6u
9
8u
8
+ 13u
7
9u
6
+ 2u
5
6u
4
+ 7u
3
5u
2
+ 4b 2u 1i
I
u
3
= hu
22
+ u
21
+ ··· + 6u + 5, 160508u
21
283168u
20
+ ··· + 2148665a 366973,
211946u
21
+ 275871u
20
+ ··· + 429733b + 1188174i
There are 3 irreducible components with 42 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
= hb
4
+ 2b
3
+ b
2
+ 5, 2b
3
+ 3b
2
4b + 9a + 2, 2b
3
+ 3b
2
+ 5b + 9u + 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
2
9
b
3
1
3
b
2
5
9
b
2
9
a
7
=
2
9
b
3
1
3
b
2
5
9
b
2
9
2
9
b
3
1
3
b
2
5
9
b
2
9
a
9
=
2
9
b
3
1
3
b
2
+
4
9
b
2
9
b
a
10
=
2
9
b
3
1
3
b
2
+
4
9
b
2
9
2
9
b
3
+
1
3
b
2
+
5
9
b +
2
9
a
1
=
0
1
a
3
=
1
1
a
5
=
1
3
b
3
1
3
b
1
3
4
9
b
3
2
3
b
2
1
9
b
4
9
a
11
=
2
9
b
3
+
1
3
b
2
4
9
b +
11
9
1
9
b
3
+
2
3
b
2
2
9
b +
1
9
a
4
=
1
9
b
3
1
3
b
2
2
9
b +
1
9
1
9
b
3
1
3
b
2
2
9
b +
10
9
a
8
=
4
9
b
3
2
3
b
2
1
9
b
4
9
2
9
b
3
1
3
b
2
+
4
9
b
2
9
a
8
=
4
9
b
3
2
3
b
2
1
9
b
4
9
2
9
b
3
1
3
b
2
+
4
9
b
2
9
(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 = 1.00000I
a = 1.61803
b = 1.61803 1.00000I
5.59278 4.00000
u = 1.00000I
a = 1.61803
b = 1.61803 + 1.00000I
5.59278 4.00000
u = 1.00000I
a = 0.618034
b = 0.618034 1.000000I
2.30291 4.00000
u = 1.00000I
a = 0.618034
b = 0.618034 + 1.000000I
2.30291 4.00000
3
II.
I
u
2
= hu
16
+ 3u
14
+ · · · u + 1, u
15
u
14
+ · · · + 4a 1, u
15
u
14
+ · · · + 4b 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
9
=
1
4
u
15
+
1
4
u
14
+ ··· +
3
2
u +
1
4
1
4
u
15
+
1
4
u
14
+ ··· +
1
2
u +
1
4
a
10
=
1
4
u
15
+
1
4
u
14
+ ··· +
3
2
u +
1
4
u
5
+ u
3
+ u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
5
=
1
2
u
15
u
14
+ ··· +
5
2
u
3
2
1
4
u
15
1
4
u
14
+ ··· +
3
2
u
1
4
a
11
=
u
15
+
5
2
u
13
+ ··· + u +
3
2
3
4
u
15
1
4
u
14
+ ··· + u +
1
4
a
4
=
1
4
u
15
+
1
4
u
14
+ ··· +
3
4
u
2
3
4
1
4
u
15
+
1
4
u
14
+ ··· +
7
4
u
2
+
1
4
a
8
=
1
4
u
15
+
1
4
u
14
+ ··· +
1
2
u +
1
4
1
4
u
15
+
1
4
u
14
+ ··· +
1
2
u +
1
4
a
8
=
1
4
u
15
+
1
4
u
14
+ ··· +
1
2
u +
1
4
1
4
u
15
+
1
4
u
14
+ ··· +
1
2
u +
1
4
(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 = 0.739034 0.627334I
a = 0.841258 0.815572I
b = 0.102224 0.188238I
5.48130 + 1.05317I 4.45688 2.38990I
u = 0.739034 + 0.627334I
a = 0.841258 + 0.815572I
b = 0.102224 + 0.188238I
5.48130 1.05317I 4.45688 + 2.38990I
u = 0.691623 1.176671I
a = 1.052037 + 0.704615I
b = 1.74366 + 1.88129I
12.2077 + 11.7947I 0.96071 6.63599I
u = 0.691623 + 1.176671I
a = 1.052037 0.704615I
b = 1.74366 1.88129I
12.2077 11.7947I 0.96071 + 6.63599I
u = 0.596655 1.032137I
a = 0.109726 + 0.540280I
b = 0.48693 + 1.57242I
1.29053 + 6.45307I 4.44807 7.45131I
u = 0.596655 + 1.032137I
a = 0.109726 0.540280I
b = 0.48693 1.57242I
1.29053 6.45307I 4.44807 + 7.45131I
u = 0.317155 0.789225I
a = 1.72238 0.65818I
b = 1.405228 + 0.131045I
6.59915 + 1.30998I 1.95561 5.45778I
u = 0.317155 + 0.789225I
a = 1.72238 + 0.65818I
b = 1.405228 0.131045I
6.59915 1.30998I 1.95561 + 5.45778I
u = 0.209770 0.436269I
a = 0.568820 0.850997I
b = 0.359050 0.414727I
0.004513 0.990902I 0.07468 + 7.34190I
u = 0.209770 + 0.436269I
a = 0.568820 + 0.850997I
b = 0.359050 + 0.414727I
0.004513 + 0.990902I 0.07468 7.34190I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.555046 0.909908I
a = 0.688090 + 0.110259I
b = 0.133044 + 1.020167I
0.19881 2.75301I 1.57245 + 2.26508I
u = 0.555046 + 0.909908I
a = 0.688090 0.110259I
b = 0.133044 1.020167I
0.19881 + 2.75301I 1.57245 2.26508I
u = 0.652805 1.114226I
a = 0.533500 + 0.650708I
b = 1.18631 + 1.76493I
2.50481 9.84228I 0.10556 + 8.25112I
u = 0.652805 + 1.114226I
a = 0.533500 0.650708I
b = 1.18631 1.76493I
2.50481 + 9.84228I 0.10556 8.25112I
u = 0.926846 0.626361I
a = 0.89792 1.27849I
b = 0.028925 0.652126I
15.8152 0.4292I 4.82755 + 2.00465I
u = 0.926846 + 0.626361I
a = 0.89792 + 1.27849I
b = 0.028925 + 0.652126I
15.8152 + 0.4292I 4.82755 2.00465I
6
III.
I
u
3
= hu
22
+ u
21
+ · · · + 6u + 5, 1.61 × 10
5
u
21
2.83 × 10
5
u
20
+ · · · + 2.15 ×
10
6
a 3.67 ×10
5
, 2.12× 10
5
u
21
+2.76× 10
5
u
20
+· · ·+4.30 ×10
5
b +1.19 ×10
6
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
9
=
0.0747013u
21
+ 0.131788u
20
+ ··· 0.874577u + 0.170791
0.493204u
21
0.641959u
20
+ ··· 6.08237u 2.76491
a
10
=
0.0747013u
21
+ 0.131788u
20
+ ··· 0.874577u + 0.170791
0.782970u
21
0.955766u
20
+ ··· 6.79840u 3.05035
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
5
=
0.331109u
21
+ 0.413583u
20
+ ··· + 2.78813u + 1.30908
0.214435u
21
+ 0.800367u
20
+ ··· 0 .0196448u + 1.48856
a
11
=
0.205744u
21
0.326088u
20
+ ··· + 0.156570u 1.22255
0.503457u
21
0.242811u
20
+ ··· + 0 .879521u + 0.583367
a
4
=
0.380187u
21
0.0215362u
20
+ ··· 0 .0453789u 1.15037
0.229882u
21
0.194437u
20
+ ··· 1.92489u 4.28836
a
8
=
0.0275418u
21
+ 0.323516u
20
+ ··· 0.657386u + 0.591853
0.782970u
21
0.955766u
20
+ ··· 5.79840u 3.05035
a
8
=
0.0275418u
21
+ 0.323516u
20
+ ··· 0.657386u + 0.591853
0.782970u
21
0.955766u
20
+ ··· 5.79840u 3.05035
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.986171 0.439556I
a = 0.71539 + 1 .44238I
b = 0.370454 + 0.315681I
14.4695 5.6984I 3.54476 + 2.83577I
u = 0.986171 + 0.439556I
a = 0.71539 1.44238I
b = 0.370454 0.315681I
14.4695 + 5.6984I 3.54476 2.83577I
u = 0.662778 0.976432I
a = 0.613122 0.698594I
b = 0.90348 1.42464I
4.47712 + 4.26374I 2.95029 4.02329I
u = 0.662778 + 0.976432I
a = 0.613122 + 0.698594I
b = 0.90348 + 1.42464I
4.47712 4.26374I 2.95029 + 4.02329I
u = 0.610796 0.518790I
a = 0.732873 0.099949I
b = 0.299838 0.613611I
0.18031 1.62554I 1.42199 + 3.91435I
u = 0.610796 + 0.518790I
a = 0.732873 + 0 .099949I
b = 0.299838 + 0.613611I
0.18031 + 1.62554I 1.42199 3.91435I
u = 0.579803 0.857238I
a = 1.34246 + 0 .94342I
b = 0.10974 + 2 .24371I
7.95553 + 2.30219I 0.32022 2.86330I
u = 0.579803 + 0.857238I
a = 1.34246 0.94342I
b = 0.10974 2.24371I
7.95553 2.30219I 0.32022 + 2.86330I
u = 0.197868 1.057098I
a = 0.057779 + 0.308683I
b = 0.624592 + 1.222647I
3.92670 11.6982
u = 0.197868 + 1.057098I
a = 0.057779 0.308683I
b = 0.624592 1.222647I
3.92670 11.6982
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.111564 1.357145I
a = 1.244438 0.079920I
b = 1.99597 + 0 .15207I
7.95553 2.30219I 0.32022 + 2.86330I
u = 0.111564 + 1.357145I
a = 1.244438 + 0.079920I
b = 1.99597 0.15207I
7.95553 + 2 .30219I 0.32022 2.86330I
u = 0.125296 1.244617I
a = 0.715202 + 0 .046512I
b = 1.320485 + 0 .472454I
1.26759 + 1 .65848I 0.54419 4.72916I
u = 0.125296 + 1 .244617I
a = 0.715202 0.046512I
b = 1.320485 0.472454I
1.26759 1.65848I 0.54419 + 4 .72916I
u = 0.399913 0.875160I
a = 0.772209 + 0.521411I
b = 0.18495 + 1 .83613I
1.26759 1.65848I 0.54419 + 4 .72916I
u = 0.399913 + 0 .875160I
a = 0.772209 0.521411I
b = 0.18495 1 .83613I
1.26759 + 1 .65848I 0.54419 4.72916I
u = 0.529162 0.802687I
a = 0.008791 0.616475I
b = 0.482064 1.069543I
0.18031 1.62554I 1.42199 + 3 .91435I
u = 0.529162 + 0 .802687I
a = 0.008791 + 0.616475I
b = 0.482064 + 1 .069543I
0.18031 + 1 .62554I 1.42199 3.91435I
u = 0.746289 1.064202I
a = 1.062488 0.812263I
b = 1.26433 1 .68612I
14.4695 5.6984I 3.54476 + 2.83577I
u = 0.746289 + 1 .064202I
a = 1.062488 + 0 .812263I
b = 1.26433 + 1 .68612I
14.4695 + 5.6984I 3.54476 2.83577I
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.848321 0.450725I
a = 0.772068 + 0.841303I
b = 0.332764 0.097424I
4.47712 + 4 .26374I 2.95029 4.02329I
u = 0.848321 + 0 .450725I
a = 0.772068 0.841303I
b = 0.332764 + 0 .097424I
4.47712 4.26374I 2.95029 + 4.02329I
9
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
3
, c
6
c
8
(u
2
+ 1)
2
(u
16
+ 3u
14
+ ··· u + 1)(u
22
+ u
21
+ ··· + 6u + 5)
c
2
(u + 1)
4
(u
16
+ 6u
15
+ ··· + 9u + 1)(u
22
+ 11u
21
+ ··· + 124u + 25)
c
4
, c
5
, c
9
c
10
, c
11
(u
4
+ 3u
2
+ 1)
(u
11
u
10
+ 8u
9
7u
8
+ 22u
7
16u
6
+ 24u
5
13u
4
+ 9u
3
3u
2
+ 1)
2
(u
16
+ 3u
15
+ ··· + 7u + 2)
c
7
(u 1)
4
(u
16
+ 6u
15
+ ··· + 9u + 1)(u
22
+ 11u
21
+ ··· + 124u + 25)
10
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
, c
6
c
8
(y + 1)
4
(y
16
+ 6y
15
+ ··· + 9 y + 1)(y
22
+ 11y
21
+ ··· + 124y + 25)
c
2
, c
7
(y 1)
4
(y
16
+ 14y
15
+ ··· + 13y + 1)(y
22
y
21
+ ··· + 4824 y + 625)
c
4
, c
5
, c
9
c
10
, c
11
(y
2
+ 3y + 1)
2
(1 + 6y + 17y
2
+ 35y
3
+ 181y
4
+ 516y
5
+ 756y
6
+ 636y
7
+ 319y
8
+ 94y
9
+ 15y
10
+ y
11
)
2
(y
16
+ 21y
15
+ ··· + 23y + 4)
11