11a
235
(K11a
235
)
1
Arc Sequences
7 1 9 11 10 8 2 3 4 5 6
Solving Sequence
2,7
8 1 3 9 4 10 6 5 11
c
7
c
1
c
2
c
8
c
3
c
9
c
6
c
5
c
11
c
4
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
35
u
34
+ ··· 2u + 1i
There are 1 irreducible components with 35 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
35
u
34
+ · · · 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
8
=
u
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
9
=
u
7
2u
5
+ 2u
3
2u
u
9
+ u
7
u
5
+ u
a
4
=
u
12
3u
10
+ 5u
8
6u
6
+ 4u
4
3u
2
+ 1
u
14
+ 2u
12
3u
10
+ 2u
8
+ u
2
a
10
=
u
17
+ 4u
15
9u
13
+ 14u
11
15u
9
+ 14u
7
10u
5
+ 6u
3
3u
u
19
3u
17
+ 6u
15
7u
13
+ 5u
11
3u
9
u
3
+ u
a
6
=
u
3
u
3
+ u
a
5
=
u
30
5u
28
+ ··· 6u
2
+ 1
u
30
+ 6u
28
+ ··· + 6u
4
+ u
2
a
11
=
u
8
+ u
6
u
4
+ 1
u
8
2u
6
+ 2u
4
2u
2
a
11
=
u
8
+ u
6
u
4
+ 1
u
8
2u
6
+ 2u
4
2u
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 = 1.151005 0.016756I
9.27089 4.80858I 16.4615 + 3.1101I
u = 1.151005 + 0.016756I
9.27089 + 4.80858I 16.4615 3.1101I
u = 1.069139 0.654044I
9.04332 7.10158I 16.2339 + 4.8820I
u = 1.069139 + 0.654044I
9.04332 + 7.10158I 16.2339 4.8820I
u = 0.971488 0.678067I
3.85759 8.16795I 8.47769 + 8.32654I
u = 0.971488 + 0.678067I
3.85759 + 8.16795I 8.47769 8.32654I
u = 0.962972
4.33695 20.8197
u = 0.924502 0.548752I
1.47757 2.06754I 12.18012 + 2.63820I
u = 0.924502 + 0.548752I
1.47757 + 2.06754I 12.18012 2.63820I
u = 0.841454 0.599631I
1.48613 2.36443I 8.99438 + 4.59259I
u = 0.841454 + 0.599631I
1.48613 + 2.36443I 8.99438 4.59259I
u = 0.695903 0.720589I
4.68045 + 2.80636I 6.46642 3.03616I
u = 0.695903 + 0.720589I
4.68045 2.80636I 6.46642 + 3.03616I
u = 0.515759 0.801227I
7.40598 + 1.64045I 14.07012 0.25947I
u = 0.515759 + 0.801227I
7.40598 1.64045I 14.07012 + 0.25947I
u = 0.242634 0.466548I
2.79133 1.62971I 6.97786 + 4.00042I
u = 0.242634 + 0.466548I
2.79133 + 1.62971I 6.97786 4.00042I
u = 0.383885
0.541818 18.3301
u = 0.492158 0.787784I
3.57477 + 3.06228I 10.68806 2.96548I
u = 0.492158 + 0.787784I
3.57477 3.06228I 10.68806 + 2.96548I
u = 0.537942 0.808962I
3.29192 6.31527I 10.32852 + 3.15989I
u = 0.537942 + 0.808962I
3.29192 + 6.31527I 10.32852 3.15989I
u = 0.675472 0.621297I
0.117264 0.215670I 13.04627 + 2.21794I
u = 0.675472 + 0.621297I
0.117264 + 0.215670I 13.04627 2.21794I
u = 0.851731 0.700357I
6.80865 + 2.68270I 3.85369 3.32127I
u = 0.851731 + 0.700357I
6.80865 2.68270I 3.85369 + 3.32127I
u = 0.965023 0.117776I
0.75414 + 3.23838I 15.3127 4.6996I
u = 0.965023 + 0.117776I
0.75414 3.23838I 15.3127 + 4.6996I
u = 0.967337 0.632060I
0.75413 + 5.18051I 14.8353 7.3100I
u = 0.967337 + 0.632060I
0.75413 5.18051I 14.8353 + 7.3100I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.066496 0.664855I
4.86404 + 11.84451I 12.4530 7.6430I
u = 1.066496 + 0.664855I
4.86404 11.84451I 12.4530 + 7.6430I
u = 1.068609 0.641330I
5.26665 + 2.30484I 13.10183 1.73912I
u = 1.068609 + 0.641330I
5.26665 2.30484I 13.10183 + 1.73912I
u = 1.15332
13.2599 19.8875
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
7
(u
35
+ u
34
+ ··· 2u 1)
c
2
, c
6
(u
35
+ 13u
34
+ ··· + 10u + 1)
c
3
, c
8
, c
9
c
11
(u
35
+ u
34
+ ··· 8u + 1)
c
4
, c
5
, c
10
(u
35
+ u
34
+ ··· 4u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
7
(y
35
13y
34
+ ··· + 10y 1)
c
2
, c
6
(y
35
+ 19y
34
+ ··· + 26y 1)
c
3
, c
8
, c
9
c
11
(y
35
41y
34
+ ··· + 26y 1)
c
4
, c
5
, c
10
(y
35
+ 27y
34
+ ··· + 10y 1)
5