11a
185
(K11a
185
)
1
Arc Sequences
7 1 11 10 9 2 3 4 5 8 6
Solving Sequence
2,7
1 3 8 6 11 4 9 5 10
c
1
c
2
c
7
c
6
c
11
c
3
c
8
c
5
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
54
u
53
+ ··· u + 1i
There are 1 irreducible components with 54 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
54
u
53
+ · · · u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
8
=
u
5
2u
3
u
u
7
u
5
+ u
a
6
=
u
u
a
11
=
u
4
+ u
2
+ 1
u
4
a
4
=
u
12
3u
10
5u
8
4u
6
2u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
+ u
4
a
9
=
u
31
8u
29
+ ··· 12u
7
4u
5
u
31
+ 7u
29
+ ··· 2u
13
+ u
a
5
=
u
46
+ 13u
44
+ ··· 2u
4
+ 1
u
48
+ 12u
46
+ ··· + 20u
10
+ 8u
8
a
10
=
u
16
+ 5u
14
+ 11u
12
+ 12u
10
+ 5u
8
2u
6
2u
4
+ 1
u
18
+ 4u
16
+ 7u
14
+ 4u
12
3u
10
6u
8
2u
6
+ u
2
a
10
=
u
16
+ 5u
14
+ 11u
12
+ 12u
10
+ 5u
8
2u
6
2u
4
+ 1
u
18
+ 4u
16
+ 7u
14
+ 4u
12
3u
10
6u
8
2u
6
+ u
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 = 0.803336 0.074667I
8.69949 + 0.21899I 3.12382 0.07866I
u = 0.803336 + 0.074667I
8.69949 0.21899I 3.12382 + 0.07866I
u = 0.793006 0.135744I
1.35714 5.52569I 3.45218 + 5.82582I
u = 0.793006 + 0.135744I
1.35714 + 5.52569I 3.45218 5.82582I
u = 0.555404 0.618983I
2.66786 4.19841I 2.85328 + 2.26313I
u = 0.555404 + 0.618983I
2.66786 + 4.19841I 2.85328 2.26313I
u = 0.542871 0.222612I
1.223041 + 0.207996I 8.65252 1.10768I
u = 0.542871 + 0.222612I
1.223041 0.207996I 8.65252 + 1.10768I
u = 0.542026 0.876210I
3.38874 + 8.60756I 0.88746 8.62489I
u = 0.542026 + 0.876210I
3.38874 8.60756I 0.88746 + 8.62489I
u = 0.514528 0.758613I
0.15792 + 2.10554I 4.75076 4.16265I
u = 0.514528 + 0.758613I
0.15792 2.10554I 4.75076 + 4.16265I
u = 0.508429 1.190653I
4.45647 + 10.31745I 0.34822 8.78564I
u = 0.508429 + 1.190653I
4.45647 10.31745I 0.34822 + 8.78564I
u = 0.486868 1.204309I
12.02494 + 4.47153I 6.19061 3.19196I
u = 0.486868 + 1.204309I
12.02494 4.47153I 6.19061 + 3.19196I
u = 0.465718 1.132140I
1.40488 + 3.87836I 4.23189 3.27485I
u = 0.465718 + 1.132140I
1.40488 3.87836I 4.23189 + 3.27485I
u = 0.459955 0.798537I
0.23556 + 1.92632I 2.54464 3.58852I
u = 0.459955 + 0.798537I
0.23556 1.92632I 2.54464 + 3.58852I
u = 0.415619 1.215680I
12.53211 + 4.46314I 6.98408 3.48914I
u = 0.415619 + 1.215680I
12.53211 4.46314I 6.98408 + 3.48914I
u = 0.382721 1.204175I
5.34368 1.56137I 1.34670 + 2.59690I
u = 0.382721 + 1.204175I
5.34368 + 1.56137I 1.34670 2.59690I
u = 0.063963 0.969473I
2.01199 + 1.57241I 2.93647 4.70910I
u = 0.063963 + 0.969473I
2.01199 1.57241I 2.93647 + 4.70910I
u = 0.068795 1.043574I
7.55344 4.33327I 6.71453 + 3.78697I
u = 0.068795 + 1.043574I
7.55344 + 4.33327I 6.71453 3.78697I
u = 0.378306 1.216653I
11.00630 + 4.98743I 5.44012 2.56031I
u = 0.378306 + 1.216653I
11.00630 4.98743I 5.44012 + 2.56031I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.403427 1.196669I
6.22025 2.29095I 3.47483 + 3.73518I
u = 0.403427 + 1.196669I
6.22025 + 2.29095I 3.47483 3.73518I
u = 0.404606 0.965250I
5.19453 0.85164I 2.69916 + 2.79194I
u = 0.404606 + 0.965250I
5.19453 + 0.85164I 2.69916 2.79194I
u = 0.409939 1.110805I
5.37080 0.77260I 1.83369 + 0.52088I
u = 0.409939 + 1.110805I
5.37080 + 0.77260I 1.83369 0.52088I
u = 0.492150 1.152335I
4.72150 7.14315I 0.51437 + 6.91242I
u = 0.492150 + 1.152335I
4.72150 + 7.14315I 0.51437 6.91242I
u = 0.494467 1.187320I
5.57287 6.38943I 2.23719 + 3.19897I
u = 0.494467 + 1.187320I
5.57287 + 6.38943I 2.23719 3.19897I
u = 0.513281 1.197090I
10.0524 13.8722I 3.82831 + 8.77565I
u = 0.513281 + 1.197090I
10.0524 + 13.8722I 3.82831 8.77565I
u = 0.521169 0.661679I
2.37968 + 0.93113I 8.32580 1.37232I
u = 0.521169 + 0.661679I
2.37968 0.93113I 8.32580 + 1.37232I
u = 0.526458 0.850149I
1.84506 5.20730I 6.07211 + 8.44255I
u = 0.526458 + 0.850149I
1.84506 + 5.20730I 6.07211 8.44255I
u = 0.553091 0.375407I
3.44062 3.02821I 2.33743 + 2.90410I
u = 0.553091 + 0.375407I
3.44062 + 3.02821I 2.33743 2.90410I
u = 0.688011 0.172752I
1.90661 + 2.65629I 2.99397 3.57576I
u = 0.688011 + 0.172752I
1.90661 2.65629I 2.99397 + 3.57576I
u = 0.768273 0.105402I
2.42732 + 1.73641I 0.699777 + 0.008860I
u = 0.768273 + 0.105402I
2.42732 1.73641I 0.699777 0.008860I
u = 0.812471 0.137850I
6.92259 + 9.00910I 0.82614 5.72677I
u = 0.812471 + 0.137850I
6.92259 9.00910I 0.82614 + 5.72677I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
54
+ u
53
+ ··· + u + 1)
c
2
(u
54
+ 29u
53
+ ··· u + 1)
c
3
(u
54
+ 7u
53
+ ··· + 47u + 5)
c
4
(u
54
+ u
53
+ ··· + u + 1)
c
5
(u
54
+ u
53
+ ··· + u + 1)
c
7
, c
11
(u
54
+ u
53
+ ··· u + 1)
c
8
(u
54
+ u
53
+ ··· + 11u + 1)
c
9
(u
54
+ u
53
+ ··· + u + 1)
c
10
(u
54
+ 11u
53
+ ··· + 1951u + 187)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
54
+ 29y
53
+ ··· y + 1)
c
2
(y
54
7y
53
+ ··· 5y + 1)
c
3
(y
54
3y
53
+ ··· + 631y + 25)
c
4
(y
54
+ 49y
53
+ ··· y + 1)
c
5
, c
9
(y
54
+ 49y
53
+ ··· y + 1)
c
7
, c
11
(y
54
43y
53
+ ··· 97y + 1)
c
8
(y
54
+ 5y
53
+ ··· 49y + 1)
c
10
(y
54
+ 21y
53
+ ··· + 184179y + 34969)
6