11a
335
(K11a
335
)
1
Arc Sequences
7 8 1 11 10 9 2 3 4 5 6
Solving Sequence
4,11
5 10 6 1 3 9 7 2 8
c
4
c
10
c
5
c
11
c
3
c
9
c
6
c
1
c
8
c
2
, c
7
Representation Ideals
I = I
u
1
I
u
1
= hu
37
u
36
+ ··· 3u + 1i
There are 1 irreducible components with 37 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
37
u
36
+ · · · 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
10
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
u
5
2u
3
u
u
7
3u
5
2u
3
+ u
a
3
=
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
3
+ 2u
u
3
+ u
a
7
=
u
10
5u
8
8u
6
3u
4
+ 3u
2
+ 1
u
10
4u
8
5u
6
+ 3u
2
a
2
=
u
27
+ 12u
25
+ ··· 9u
3
2u
u
27
+ 11u
25
+ ··· 5u
3
+ u
a
8
=
u
29
12u
27
+ ··· + 6u
3
+ 3u
u
31
13u
29
+ ··· + 24u
7
+ u
a
8
=
u
29
12u
27
+ ··· + 6u
3
+ 3u
u
31
13u
29
+ ··· + 24u
7
+ 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 = 0.761012 0.145124I
1.30987 5.10979I 14.0141 + 6.9625I
u = 0.761012 + 0.145124I
1.30987 + 5.10979I 14.0141 6.9625I
u = 0.741349
4.65627 19.8707
u = 0.600959 0.215194I
6.30817 + 0.50143I 15.7929 + 1.6593I
u = 0.600959 + 0.215194I
6.30817 0.50143I 15.7929 1.6593I
u = 0.323260 1.352453I
3.41113 9.03749I 9.15046 + 8.29355I
u = 0.323260 + 1.352453I
3.41113 + 9.03749I 9.15046 8.29355I
u = 0.303719 1.260876I
0.75596 3.77593I 14.9240 + 4.3419I
u = 0.303719 + 1.260876I
0.75596 + 3.77593I 14.9240 4.3419I
u = 0.302108 0.618325I
4.95014 3.74741I 12.71662 + 4.63648I
u = 0.302108 + 0.618325I
4.95014 + 3.74741I 12.71662 4.63648I
u = 0.261585 1.346480I
1.46648 2.68282I 10.45967 + 2.37347I
u = 0.261585 + 1.346480I
1.46648 + 2.68282I 10.45967 2.37347I
u = 0.247587 1.099148I
1.51106 + 1.30299I 11.08606 3.41779I
u = 0.247587 + 1.099148I
1.51106 1.30299I 11.08606 + 3.41779I
u = 0.044413 1.402125I
1.30989 4.63234I 8.40491 + 3.31398I
u = 0.044413 + 1.402125I
1.30989 + 4.63234I 8.40491 3.31398I
u = 0.014593 1.395727I
7.89022 + 1.99397I 4.51029 3.60908I
u = 0.014593 + 1.395727I
7.89022 1.99397I 4.51029 + 3.60908I
u = 0.132400 0.636798I
1.72361 + 1.67469I 8.06184 5.20256I
u = 0.132400 + 0.636798I
1.72361 1.67469I 8.06184 + 5.20256I
u = 0.209723 1.214468I
2.54473 + 1.90283I 7.07864 3.49708I
u = 0.209723 + 1.214468I
2.54473 1.90283I 7.07864 + 3.49708I
u = 0.276289
0.504726 19.7383
u = 0.303191 1.346634I
4.15088 + 5.05582I 6.99986 2.20493I
u = 0.303191 + 1.346634I
4.15088 5.05582I 6.99986 + 2.20493I
u = 0.322667 1.080030I
5.73875 3.53679I 14.2053 + 1.5505I
u = 0.322667 + 1.080030I
5.73875 + 3.53679I 14.2053 1.5505I
u = 0.338576 1.356182I
3.83357 + 11.73380I 12.4832 7.0367I
u = 0.338576 + 1.356182I
3.83357 11.73380I 12.4832 + 7.0367I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.351528 1.257024I
8.89081 + 4.15452I 16.1817 3.4204I
u = 0.351528 + 1.257024I
8.89081 4.15452I 16.1817 + 3.4204I
u = 0.711095 0.138353I
0.53120 + 1.35599I 11.83231 0.62165I
u = 0.711095 + 0.138353I
0.53120 1.35599I 11.83231 + 0.62165I
u = 0.792373 0.146649I
8.57063 + 7.64850I 17.1130 5.4186I
u = 0.792373 + 0.146649I
8.57063 7.64850I 17.1130 + 5.4186I
u = 0.802054
12.7836 20.3610
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
7
c
8
(u
37
+ u
36
+ ··· u 1)
c
3
, c
6
(u
37
+ 7u
36
+ ··· + u + 7)
c
4
, c
5
, c
10
(u
37
+ u
36
+ ··· 3u 1)
c
9
, c
11
(u
37
+ u
36
+ ··· 3u + 2)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
7
c
8
(y
37
41y
36
+ ··· + 11y 1)
c
3
, c
6
(y
37
+ 19y
36
+ ··· + 239y 49)
c
4
, c
5
, c
10
(y
37
+ 31y
36
+ ··· + 11y 1)
c
9
, c
11
(y
37
21y
36
+ ··· + 41y 4)
5