11a
311
(K11a
311
)
1
Arc Sequences
7 6 1 10 9 2 3 11 5 4 8
Solving Sequence
1,7
2 6 3 4 8 11 9 5 10
c
1
c
6
c
2
c
3
c
7
c
11
c
8
c
5
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
39
u
38
+ ··· + 2u 1i
There are 1 irreducible components with 39 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
39
u
38
+ · · · + 2u 1i
(i) Arc colorings
a
1
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
6
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
u
4
u
2
+ 1
u
4
+ 2u
2
a
8
=
u
5
2u
3
u
u
7
3u
5
2u
3
+ u
a
11
=
u
12
+ 5u
10
+ 9u
8
+ 6u
6
u
2
+ 1
u
14
+ 6u
12
+ 13u
10
+ 10u
8
2u
6
4u
4
+ u
2
a
9
=
u
19
8u
17
26u
15
42u
13
31u
11
2u
9
+ 8u
7
2u
5
5u
3
u
21
9u
19
+ ··· u
3
+ u
a
5
=
u
37
+ 16u
35
+ ··· + 5u
5
+ u
u
38
u
37
+ ··· u + 1
a
10
=
u
22
+ 9u
20
+ ··· 2u
2
+ 1
u
22
10u
20
+ ··· 6u
4
+ u
2
a
10
=
u
22
+ 9u
20
+ ··· 2u
2
+ 1
u
22
10u
20
+ ··· 6u
4
+ 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 = 0.711187 0.246148I
2.96795 5.55181I 9.25872 + 7.70638I
u = 0.711187 + 0.246148I
2.96795 + 5.55181I 9.25872 7.70638I
u = 0.703791 0.153316I
2.59124 + 0.84756I 7.81330 + 0.69971I
u = 0.703791 + 0.153316I
2.59124 0.84756I 7.81330 0.69971I
u = 0.493230 0.294505I
1.37394 1.42753I 1.59581 + 5.78078I
u = 0.493230 + 0.294505I
1.37394 + 1.42753I 1.59581 5.78078I
u = 0.28243 1.39867I
2.26953 9.16193I 4.31482 + 8.21466I
u = 0.28243 + 1.39867I
2.26953 + 9.16193I 4.31482 8.21466I
u = 0.271172 1.346872I
7.31578 2.67288I 2.71632 + 2.30762I
u = 0.271172 + 1.346872I
7.31578 + 2.67288I 2.71632 2.30762I
u = 0.220766 1.027333I
5.20817 4.40207I 3.96308 + 3.90504I
u = 0.220766 + 1.027333I
5.20817 + 4.40207I 3.96308 3.90504I
u = 0.209779 0.732429I
1.18645 + 1.89478I 6.62379 3.07678I
u = 0.209779 + 0.732429I
1.18645 1.89478I 6.62379 + 3.07678I
u = 0.202053 1.394332I
6.72383 4.04302I 1.83134 + 4.62679I
u = 0.202053 + 1.394332I
6.72383 + 4.04302I 1.83134 4.62679I
u = 0.096643 1.387204I
4.84305 + 1.02619I 1.08808 3.88143I
u = 0.096643 + 1.387204I
4.84305 1.02619I 1.08808 + 3.88143I
u = 0.09336 1.42811I
12.14090 3.09884I 1.72513 + 2.07944I
u = 0.09336 + 1.42811I
12.14090 + 3.09884I 1.72513 2.07944I
u = 0.150792 1.343059I
3.63716 + 2.05070I 5.79681 3.19622I
u = 0.150792 + 1.343059I
3.63716 2.05070I 5.79681 + 3.19622I
u = 0.153563 0.930185I
1.29404 + 1.89422I 7.65532 4.23095I
u = 0.153563 + 0.930185I
1.29404 1.89422I 7.65532 + 4.23095I
u = 0.20576 1.43000I
14.7937 + 4.5566I 3.03719 3.41196I
u = 0.20576 + 1.43000I
14.7937 4.5566I 3.03719 + 3.41196I
u = 0.276285 1.381538I
1.59535 + 5.13986I 6.25494 2.11218I
u = 0.276285 + 1.381538I
1.59535 5.13986I 6.25494 + 2.11218I
u = 0.28622 1.41194I
9.4648 + 11.8941I 0.95456 7.01410I
u = 0.28622 + 1.41194I
9.4648 11.8941I 0.95456 + 7.01410I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.333668 0.697395I
5.65303 4.34476I 2.73351 + 1.65632I
u = 0.333668 + 0.697395I
5.65303 + 4.34476I 2.73351 1.65632I
u = 0.436374
0.690035 14.8486
u = 0.550796 0.394545I
8.97845 + 1.78659I 0.73228 3.87489I
u = 0.550796 + 0.394545I
8.97845 1.78659I 0.73228 + 3.87489I
u = 0.699391 0.209840I
3.45995 + 1.60136I 11.19941 0.98974I
u = 0.699391 + 0.209840I
3.45995 1.60136I 11.19941 + 0.98974I
u = 0.723023 0.273449I
4.08876 + 8.22597I 5.46857 6.60973I
u = 0.723023 + 0.273449I
4.08876 8.22597I 5.46857 + 6.60973I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
6
(u
39
+ u
38
+ ··· + 2u + 1)
c
3
(u
39
+ 9u
38
+ ··· 112u 17)
c
4
, c
5
, c
9
c
10
(u
39
+ u
38
+ ··· + 2u + 1)
c
7
(u
39
+ u
38
+ ··· + 2u
2
1)
c
8
, c
11
(u
39
+ 7u
38
+ ··· + 120u + 17)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
(y
39
+ 35y
38
+ ··· + 4y 1)
c
3
(y
39
+ 7y
38
+ ··· 2076y 289)
c
4
, c
5
, c
9
c
10
(y
39
+ 43y
38
+ ··· + 4y 1)
c
7
(y
39
y
38
+ ··· + 4y 1)
c
8
, c
11
(y
39
+ 23y
38
+ ··· + 3588y 289)
5