11a
75
(K11a
75
)
1
Arc Sequences
6 1 7 10 2 3 4 11 5 9 8
Solving Sequence
2,5
6 1 3 7 4 8 11 9 10
c
5
c
1
c
2
c
6
c
3
c
7
c
11
c
8
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
41
u
40
+ ··· + u + 1i
There are 1 irreducible components with 41 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
41
u
40
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
+ u
2
+ 1
u
4
a
7
=
u
7
2u
5
2u
3
u
7
u
5
+ u
a
4
=
u
10
3u
8
4u
6
u
4
+ u
2
+ 1
u
10
2u
8
u
6
+ 2u
4
+ u
2
a
8
=
u
13
+ 4u
11
+ 7u
9
+ 4u
7
2u
5
4u
3
u
u
13
+ 3u
11
+ 3u
9
2u
7
4u
5
u
3
+ u
a
11
=
u
24
+ 7u
22
+ ··· + 2u
2
+ 1
u
24
+ 6u
22
+ 16u
20
+ 20u
18
+ 4u
16
22u
14
26u
12
6u
10
+ 9u
8
+ 6u
6
a
9
=
u
35
+ 10u
33
+ ··· 7u
3
2u
u
35
+ 9u
33
+ ··· u
3
+ u
a
10
=
u
35
+ 10u
33
+ ··· 7u
3
2u
u
37
9u
35
+ ··· + u
3
+ u
a
10
=
u
35
+ 10u
33
+ ··· 7u
3
2u
u
37
9u
35
+ ··· + u
3
+ u
(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 = 0.826759 0.093182I
1.03604 1.75419I 1.142381 + 0.318926I
u = 0.826759 + 0.093182I
1.03604 + 1.75419I 1.142381 0.318926I
u = 0.805584
3.07852 1.30901
u = 0.579687 0.495426I
6.01823 3.75969I 2.08469 + 2.66327I
u = 0.579687 + 0.495426I
6.01823 + 3.75969I 2.08469 2.66327I
u = 0.521087 0.951326I
4.74123 + 8.14027I 0.92451 8.45750I
u = 0.521087 + 0.951326I
4.74123 8.14027I 0.92451 + 8.45750I
u = 0.498407 1.213509I
2.29038 + 6.57620I 4.18692 3.44855I
u = 0.498407 + 1.213509I
2.29038 6.57620I 4.18692 + 3.44855I
u = 0.458447 1.217193I
6.66197 + 4.52417I 4.64346 3.30102I
u = 0.458447 + 1.217193I
6.66197 4.52417I 4.64346 + 3.30102I
u = 0.419680 0.282475I
0.31190 1.38897I 2.22878 + 5.19649I
u = 0.419680 + 0.282475I
0.31190 + 1.38897I 2.22878 5.19649I
u = 0.413452 0.991560I
2.13456 + 4.94858I 7.01922 9.44337I
u = 0.413452 + 0.991560I
2.13456 4.94858I 7.01922 + 9.44337I
u = 0.408443 1.226141I
2.92978 + 2.50596I 5.15377 2.93090I
u = 0.408443 + 1.226141I
2.92978 2.50596I 5.15377 + 2.93090I
u = 0.235339 0.999224I
3.36085 + 0.49947I 12.33273 0.13229I
u = 0.235339 + 0.999224I
3.36085 0.49947I 12.33273 + 0.13229I
u = 0.028011 1.058192I
1.40338 2.86651I 6.38250 + 2.83312I
u = 0.028011 + 1.058192I
1.40338 + 2.86651I 6.38250 2.83312I
u = 0.319249 0.659184I
0.258138 1.315180I 0.82726 + 5.55607I
u = 0.319249 + 0.659184I
0.258138 + 1.315180I 0.82726 5.55607I
u = 0.364646 0.884514I
0.38333 1.88364I 0.67137 + 3.86434I
u = 0.364646 + 0.884514I
0.38333 + 1.88364I 0.67137 3.86434I
u = 0.409607 1.239190I
3.60687 + 3.46651I 6.32048 2.17214I
u = 0.409607 + 1.239190I
3.60687 3.46651I 6.32048 + 2.17214I
u = 0.445383 1.237319I
10.01039 1.50035I 11.08025 0.35088I
u = 0.445383 + 1.237319I
10.01039 + 1.50035I 11.08025 + 0.35088I
u = 0.475149 1.231301I
9.79545 7.79305I 10.43974 + 6.91622I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.475149 + 1.231301I
9.79545 + 7.79305I 10.43974 6.91622I
u = 0.501424 1.221002I
2.94834 12.69196I 5.29244 + 8.24315I
u = 0.501424 + 1.221002I
2.94834 + 12.69196I 5.29244 8.24315I
u = 0.519368 0.929928I
5.01543 2.00642I 0.12467 + 3.31909I
u = 0.519368 + 0.929928I
5.01543 + 2.00642I 0.12467 3.31909I
u = 0.568080 0.528628I
6.13950 2.34478I 2.43085 + 2.90580I
u = 0.568080 + 0.528628I
6.13950 + 2.34478I 2.43085 2.90580I
u = 0.844312 0.030001I
6.20529 + 3.05813I 7.49814 3.80729I
u = 0.844312 + 0.030001I
6.20529 3.05813I 7.49814 + 3.80729I
u = 0.844886 0.090367I
0.42502 + 7.80969I 2.24693 5.23664I
u = 0.844886 + 0.090367I
0.42502 7.80969I 2.24693 + 5.23664I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
41
+ u
40
+ ··· + u 1)
c
2
(u
41
+ 23u
40
+ ··· 3u 1)
c
3
, c
6
, c
7
(u
41
+ u
40
+ ··· 7u + 1)
c
4
, c
9
(u
41
+ u
40
+ ··· + u + 1)
c
8
, c
10
, c
11
(u
41
+ 11u
40
+ ··· 3u 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
41
+ 23y
40
+ ··· 3y 1)
c
2
(y
41
9y
40
+ ··· 19y 1)
c
3
, c
6
, c
7
(y
41
41y
40
+ ··· 51y 1)
c
4
, c
9
(y
41
+ 11y
40
+ ··· 3y 1)
c
8
, c
11
(y
41
+ 39y
40
+ ··· 11y 1)
c
10
(y
41
+ 39y
40
+ ··· 11y 1)
6