11a
144
(K11a
144
)
1
Arc Sequences
6 1 9 10 2 5 11 3 4 8 7
Solving Sequence
1,6
2 3 5 7 11 8 9 10 4
c
1
c
2
c
5
c
6
c
11
c
7
c
8
c
10
c
4
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
36
+ u
35
+ ··· 2u 1i
There are 1 irreducible components with 36 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
36
+ u
35
+ · · · 2u 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
5
=
u
u
3
+ u
a
7
=
u
3
u
5
+ u
3
+ u
a
11
=
u
8
u
6
u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
8
=
u
13
2u
11
3u
9
2u
7
+ u
u
15
+ 3u
13
+ 6u
11
+ 7u
9
+ 6u
7
+ 4u
5
+ 2u
3
+ u
a
9
=
u
19
+ 4u
17
+ 10u
15
+ 16u
13
+ 19u
11
+ 18u
9
+ 14u
7
+ 10u
5
+ 5u
3
+ 2u
u
19
3u
17
6u
15
7u
13
5u
11
3u
9
+ u
3
+ u
a
10
=
u
18
3u
16
6u
14
7u
12
5u
10
3u
8
+ u
2
+ 1
u
20
+ 4u
18
+ 10u
16
+ 16u
14
+ 19u
12
+ 18u
10
+ 14u
8
+ 10u
6
+ 5u
4
+ 2u
2
a
4
=
u
35
+ 6u
33
+ ··· 5u
3
2u
u
35
u
34
+ ··· + 2u + 1
a
4
=
u
35
+ 6u
33
+ ··· 5u
3
2u
u
35
u
34
+ ··· + 2u + 1
(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 = 0.797844 0.581711I
4.47120 6.26474I 10.83951 + 2.93620I
u = 0.797844 + 0.581711I
4.47120 + 6.26474I 10.83951 2.93620I
u = 0.745932 0.776140I
10.58170 0.71346I 14.5980 + 0.1805I
u = 0.745932 + 0.776140I
10.58170 + 0.71346I 14.5980 0.1805I
u = 0.740774 0.521458I
2.65222 + 0.70366I 6.36717 3.04538I
u = 0.740774 + 0.521458I
2.65222 0.70366I 6.36717 + 3.04538I
u = 0.715018 0.930256I
10.11544 + 6.26287I 13.3685 5.9468I
u = 0.715018 + 0.930256I
10.11544 6.26287I 13.3685 + 5.9468I
u = 0.677606 1.049083I
3.07837 + 11.82286I 8.77665 7.47971I
u = 0.677606 + 1.049083I
3.07837 11.82286I 8.77665 + 7.47971I
u = 0.643360 1.045175I
4.15822 + 4.56725I 4.13742 2.02324I
u = 0.643360 + 1.045175I
4.15822 4.56725I 4.13742 + 2.02324I
u = 0.610887 0.861297I
0.72337 + 2.40081I 4.52745 2.97125I
u = 0.610887 + 0.861297I
0.72337 2.40081I 4.52745 + 2.97125I
u = 0.300399
0.618616 16.2520
u = 0.123410 0.794730I
1.48090 + 1.31158I 2.04069 6.11196I
u = 0.123410 + 0.794730I
1.48090 1.31158I 2.04069 + 6.11196I
u = 0.013383 1.120543I
8.13948 + 2.15908I 0.61666 3.24444I
u = 0.013383 + 1.120543I
8.13948 2.15908I 0.61666 + 3.24444I
u = 0.041910 1.122207I
1.54097 5.15567I 4.24292 + 3.22654I
u = 0.041910 + 1.122207I
1.54097 + 5.15567I 4.24292 3.22654I
u = 0.294729 0.907394I
4.63881 2.63367I 6.64909 + 4.26268I
u = 0.294729 + 0.907394I
4.63881 + 2.63367I 6.64909 4.26268I
u = 0.527603
7.24314 14.1447
u = 0.617505 1.043723I
2.05877 1.63752I 7.52025 + 2.08477I
u = 0.617505 + 1.043723I
2.05877 + 1.63752I 7.52025 2.08477I
u = 0.661656 1.047538I
3.83553 8.85264I 5.15779 + 8.13246I
u = 0.661656 + 1.047538I
3.83553 + 8.85264I 5.15779 8.13246I
u = 0.669880 0.917013I
2.57098 4.98460I 11.29661 + 8.23770I
u = 0.669880 + 0.917013I
2.57098 + 4.98460I 11.29661 8.23770I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.679511 0.773446I
3.00630 0.23147I 13.24902 1.70066I
u = 0.679511 + 0.773446I
3.00630 + 0.23147I 13.24902 + 1.70066I
u = 0.717690 0.456936I
3.69893 3.42946I 10.21925 + 3.00785I
u = 0.717690 + 0.456936I
3.69893 + 3.42946I 10.21925 3.00785I
u = 0.771732 0.557099I
2.39341 + 3.42442I 7.19469 3.59924I
u = 0.771732 + 0.557099I
2.39341 3.42442I 7.19469 + 3.59924I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
36
+ u
35
+ ··· 2u 1)
c
2
, c
6
(u
36
+ 13u
35
+ ··· 6u + 1)
c
3
, c
4
, c
8
c
9
(u
36
+ u
35
+ ··· + 3u
2
1)
c
7
, c
10
, c
11
(u
36
+ 5u
35
+ ··· 28u 7)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
36
+ 13y
35
+ ··· 6y + 1)
c
2
, c
6
(y
36
+ 21y
35
+ ··· 126y + 1)
c
3
, c
4
, c
8
c
9
(y
36
39y
35
+ ··· 6y + 1)
c
7
, c
10
, c
11
(y
36
+ 33y
35
+ ··· 406y + 49)
5