11a
192
(K11a
192
)
1
Arc Sequences
6 1 10 9 7 2 3 11 4 5 8
Solving Sequence
2,6
7 1 3 8 5 11 9 4 10
c
6
c
1
c
2
c
7
c
5
c
11
c
8
c
4
c
10
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
48
+ u
47
+ ··· + 4u
2
1i
There are 1 irreducible components with 48 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
48
+ u
47
+ · · · + 4u
2
1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
7
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
8
=
u
7
2u
5
+ 2u
3
2u
u
9
+ u
7
u
5
+ u
a
5
=
u
3
u
3
+ u
a
11
=
u
14
3u
12
+ 6u
10
9u
8
+ 8u
6
6u
4
+ 2u
2
+ 1
u
16
+ 2u
14
4u
12
+ 4u
10
2u
8
+ 2u
4
2u
2
a
9
=
u
21
4u
19
+ ··· + 2u
3
3u
u
23
+ 3u
21
+ ··· + 2u
3
+ u
a
4
=
u
47
8u
45
+ ··· 18u
5
+ 10u
3
u
47
u
46
+ ··· 4u
2
+ 1
a
10
=
u
22
+ 3u
20
+ ··· + 2u
2
+ 1
u
22
4u
20
+ ··· + 2u
4
3u
2
a
10
=
u
22
+ 3u
20
+ ··· + 2u
2
+ 1
u
22
4u
20
+ ··· + 2u
4
3u
2
(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 = 1.005798 0.748763I
11.2407 13.2008I 4.69604 + 8.20742I
u = 1.005798 + 0.748763I
11.2407 + 13.2008I 4.69604 8.20742I
u = 1.004247 0.197756I
0.68024 4.58900I 13.6527 + 7.1281I
u = 1.004247 + 0.197756I
0.68024 + 4.58900I 13.6527 7.1281I
u = 0.984346 0.747272I
5.67693 5.57732I 6.94459 + 2.40000I
u = 0.984346 + 0.747272I
5.67693 + 5.57732I 6.94459 2.40000I
u = 0.982394
4.36789 20.8284
u = 0.977276 0.681640I
3.84600 8.17225I 8.45707 + 8.28509I
u = 0.977276 + 0.681640I
3.84600 + 8.17225I 8.45707 8.28509I
u = 0.969812 0.290267I
5.75150 + 1.80433I 8.37889 + 0.64615I
u = 0.969812 + 0.290267I
5.75150 1.80433I 8.37889 0.64615I
u = 0.908318 0.607143I
2.32852 2.32135I 10.38591 + 2.77129I
u = 0.908318 + 0.607143I
2.32852 + 2.32135I 10.38591 2.77129I
u = 0.863433 0.671565I
2.01219 2.59814I 6.70685 + 3.63850I
u = 0.863433 + 0.671565I
2.01219 + 2.59814I 6.70685 3.63850I
u = 0.750738 0.818055I
6.39491 0.29411I 5.62712 + 2.80614I
u = 0.750738 + 0.818055I
6.39491 + 0.29411I 5.62712 2.80614I
u = 0.726260 0.838751I
12.09985 + 7.26678I 3.13252 3.28758I
u = 0.726260 + 0.838751I
12.09985 7.26678I 3.13252 + 3.28758I
u = 0.687005 0.705958I
4.69521 + 2.82559I 6.42254 2.96931I
u = 0.687005 + 0.705958I
4.69521 2.82559I 6.42254 + 2.96931I
u = 0.321214 0.453052I
3.24763 1.60907I 6.12064 + 4.01987I
u = 0.321214 + 0.453052I
3.24763 + 1.60907I 6.12064 4.01987I
u = 0.052937 0.663054I
8.65974 4.98357I 2.57496 + 3.43258I
u = 0.052937 + 0.663054I
8.65974 + 4.98357I 2.57496 3.43258I
u = 0.035513 0.617174I
2.62424 + 1.94253I 5.82906 3.77516I
u = 0.035513 + 0.617174I
2.62424 1.94253I 5.82906 + 3.77516I
u = 0.390764
0.601903 16.4765
u = 0.731389 0.825033I
6.02949 3.89902I 6.63992 + 3.50313I
u = 0.731389 + 0.825033I
6.02949 + 3.89902I 6.63992 3.50313I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.742608 0.631933I
0.1388915 + 0.0056976I 12.76408 + 1.77198I
u = 0.742608 + 0.631933I
0.1388915 0.0056976I 12.76408 1.77198I
u = 0.765161 0.831752I
12.80673 + 3.15758I 2.24302 2.74942I
u = 0.765161 + 0.831752I
12.80673 3.15758I 2.24302 + 2.74942I
u = 0.870479 0.749319I
7.96823 + 2.83806I 2.43161 2.98157I
u = 0.870479 + 0.749319I
7.96823 2.83806I 2.43161 + 2.98157I
u = 0.940603 0.220725I
0.223689 + 0.846659I 12.11040 0.46472I
u = 0.940603 + 0.220725I
0.223689 0.846659I 12.11040 + 0.46472I
u = 0.951082 0.661265I
0.50327 + 5.09371I 14.3561 6.8355I
u = 0.951082 + 0.661265I
0.50327 5.09371I 14.3561 + 6.8355I
u = 0.981347 0.761736I
12.14028 + 2.80062I 3.38890 2.38417I
u = 0.981347 + 0.761736I
12.14028 2.80062I 3.38890 + 2.38417I
u = 0.997744 0.743909I
5.21260 + 9.77857I 8.26482 8.48475I
u = 0.997744 + 0.743909I
5.21260 9.77857I 8.26482 + 8.48475I
u = 0.999716 0.062266I
0.64228 + 2.86520I 14.6176 4.2078I
u = 0.999716 + 0.062266I
0.64228 2.86520I 14.6176 + 4.2078I
u = 1.031557 0.212124I
5.16114 + 7.81947I 9.60222 6.57989I
u = 1.031557 + 0.212124I
5.16114 7.81947I 9.60222 + 6.57989I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
48
+ u
47
+ ··· + 4u
2
1)
c
2
, c
5
(u
48
+ 15u
47
+ ··· + 8u + 1)
c
3
, c
4
, c
9
(u
48
+ u
47
+ ··· 4u 1)
c
7
(u
48
+ u
47
+ ··· 282u 61)
c
8
, c
11
(u
48
+ 7u
47
+ ··· + 16u + 1)
c
10
(u
48
+ u
47
+ ··· + 198u 37)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
48
15y
47
+ ··· 8y + 1)
c
2
, c
5
(y
48
+ 37y
47
+ ··· 40y + 1)
c
3
(y
48
+ 45y
47
+ ··· 8y + 1)
c
4
, c
9
(y
48
+ 45y
47
+ ··· 8y + 1)
c
7
(y
48
+ 13y
47
+ ··· 22428y + 3721)
c
8
, c
11
(y
48
+ 41y
47
+ ··· + 200y + 1)
c
10
(y
48
+ 17y
47
+ ··· + 24140y + 1369)
6