11a
91
(K11a
91
)
1
Arc Sequences
6 1 10 9 2 3 11 4 8 5 7
Solving Sequence
4,9
5 8 10 11 3 7 1 2 6
c
4
c
8
c
9
c
10
c
3
c
7
c
11
c
2
c
6
c
1
, c
5
Representation Ideals
I = I
u
1
I
u
1
= hu
64
+ u
63
+ ··· + 2u + 1i
There are 1 irreducible components with 64 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
64
+ u
63
+ · · · + 2u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
8
=
u
u
a
10
=
u
3
u
3
+ u
a
11
=
u
5
+ 2u
3
u
u
7
u
5
+ u
a
3
=
u
6
u
4
+ 1
u
6
+ 2u
4
u
2
a
7
=
u
13
+ 4u
11
7u
9
+ 6u
7
2u
5
u
u
15
3u
13
+ 4u
11
u
9
2u
7
+ 2u
5
+ u
a
1
=
u
21
+ 6u
19
+ ··· + 2u
3
u
u
23
5u
21
+ 12u
19
15u
17
+ 8u
15
+ 4u
13
8u
11
+ 5u
9
u
7
+ u
5
+ u
a
2
=
u
50
13u
48
+ ··· + u
2
+ 1
u
52
+ 12u
50
+ ··· + 3u
4
2u
2
a
6
=
u
27
6u
25
+ ··· + 4u
7
u
3
u
27
+ 7u
25
+ ··· u
3
+ u
a
6
=
u
27
6u
25
+ ··· + 4u
7
u
3
u
27
+ 7u
25
+ ··· 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 = 1.154848 0.273654I
7.87867 1.87799I 7.15598 + 0.14160I
u = 1.154848 + 0.273654I
7.87867 + 1.87799I 7.15598 0.14160I
u = 1.154461 0.302003I
8.21168 + 1.00289I 7.61916 0.53272I
u = 1.154461 + 0.302003I
8.21168 1.00289I 7.61916 + 0.53272I
u = 1.142882 0.528499I
5.14617 + 1.86555I 3.16993 0.93860I
u = 1.142882 + 0.528499I
5.14617 1.86555I 3.16993 + 0.93860I
u = 1.140525 0.558856I
3.9773 + 15.1327I 1.28834 10.54235I
u = 1.140525 + 0.558856I
3.9773 15.1327I 1.28834 + 10.54235I
u = 1.126514 0.550942I
0.88876 + 7.79459I 1.99768 5.95013I
u = 1.126514 + 0.550942I
0.88876 7.79459I 1.99768 + 5.95013I
u = 1.090792 0.461542I
2.45432 + 5.70994I 4.07220 7.50917I
u = 1.090792 + 0.461542I
2.45432 5.70994I 4.07220 + 7.50917I
u = 1.064503 0.535808I
0.17913 + 5.31802I 0.01812 6.01630I
u = 1.064503 + 0.535808I
0.17913 5.31802I 0.01812 + 6.01630I
u = 0.948812 0.510706I
1.98631 + 3.10078I 5.45245 3.88979I
u = 0.948812 + 0.510706I
1.98631 3.10078I 5.45245 + 3.88979I
u = 0.925067 0.156259I
0.18490 3.01523I 0.51085 + 4.08868I
u = 0.925067 + 0.156259I
0.18490 + 3.01523I 0.51085 4.08868I
u = 0.844956 0.545528I
0.03472 3.65450I 2.09839 + 2.07040I
u = 0.844956 + 0.545528I
0.03472 + 3.65450I 2.09839 2.07040I
u = 0.691782 0.617995I
0.43420 + 8.26774I 3.18319 8.31495I
u = 0.691782 + 0.617995I
0.43420 8.26774I 3.18319 + 8.31495I
u = 0.622278 0.585266I
2.93619 + 1.29722I 7.30833 2.92067I
u = 0.622278 + 0.585266I
2.93619 1.29722I 7.30833 + 2.92067I
u = 0.421396 0.617038I
1.69065 0.75291I 4.16901 + 1.04385I
u = 0.421396 + 0.617038I
1.69065 + 0.75291I 4.16901 1.04385I
u = 0.304810 0.731968I
1.50287 2.92329I 5.31775 + 2.36689I
u = 0.304810 + 0.731968I
1.50287 + 2.92329I 5.31775 2.36689I
u = 0.294713 0.772195I
1.49417 10.13743I 1.81004 + 7.03416I
u = 0.294713 + 0.772195I
1.49417 + 10.13743I 1.81004 7.03416I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.226658 0.736100I
2.50217 + 2.88719I 0.11514 2.73367I
u = 0.226658 + 0.736100I
2.50217 2.88719I 0.11514 + 2.73367I
u = 0.109376 0.527151I
0.08646 1.82443I 0.12496 + 3.83658I
u = 0.109376 + 0.527151I
0.08646 + 1.82443I 0.12496 3.83658I
u = 0.248813 0.743811I
4.02540 + 2.21650I 2.22128 2.47627I
u = 0.248813 + 0.743811I
4.02540 2.21650I 2.22128 + 2.47627I
u = 0.284380 0.763443I
3.48322 + 4.95658I 1.27407 2.78403I
u = 0.284380 + 0.763443I
3.48322 4.95658I 1.27407 + 2.78403I
u = 0.423078 0.678155I
4.36286 + 4.56971I 7.67331 4.88314I
u = 0.423078 + 0.678155I
4.36286 4.56971I 7.67331 + 4.88314I
u = 0.487387 0.645472I
4.65712 2.64556I 8.69821 + 3.84156I
u = 0.487387 + 0.645472I
4.65712 + 2.64556I 8.69821 3.84156I
u = 0.701071 0.591063I
1.52804 3.28439I 0.17422 + 4.06730I
u = 0.701071 + 0.591063I
1.52804 + 3.28439I 0.17422 4.06730I
u = 0.784786 0.520323I
1.84271 1.15146I 1.38817 + 3.13013I
u = 0.784786 + 0.520323I
1.84271 + 1.15146I 1.38817 3.13013I
u = 0.939104 0.339205I
1.65512 0.97415I 3.52790 + 1.04712I
u = 0.939104 + 0.339205I
1.65512 + 0.97415I 3.52790 1.04712I
u = 1.036165 0.550652I
3.04852 2.03669I 5.62783 + 1.89915I
u = 1.036165 + 0.550652I
3.04852 + 2.03669I 5.62783 1.89915I
u = 1.070333 0.558396I
2.47375 9.35788I 3.98613 + 9.54182I
u = 1.070333 + 0.558396I
2.47375 + 9.35788I 3.98613 9.54182I
u = 1.071537 0.414993I
2.79512 1.45588I 5.17890 + 0.43885I
u = 1.071537 + 0.414993I
2.79512 + 1.45588I 5.17890 0.43885I
u = 1.122752 0.278948I
2.73183 + 0.05760I 1.067117 + 0.224385I
u = 1.122752 + 0.278948I
2.73183 0.05760I 1.067117 0.224385I
u = 1.140371 0.553325I
5.98813 9.90485I 4.33088 + 6.32075I
u = 1.140371 + 0.553325I
5.98813 + 9.90485I 4.33088 6.32075I
u = 1.141814 0.537319I
6.61499 7.03708I 5.30834 + 6.10318I
u = 1.141814 + 0.537319I
6.61499 + 7.03708I 5.30834 6.10318I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.155880 0.315108I
6.59460 6.19283I 5.07816 + 5.61780I
u = 1.155880 + 0.315108I
6.59460 + 6.19283I 5.07816 5.61780I
u = 1.156904 0.262634I
5.97549 + 7.09510I 4.21507 4.67919I
u = 1.156904 + 0.262634I
5.97549 7.09510I 4.21507 + 4.67919I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
64
+ u
63
+ ··· + 2u + 1)
c
2
(u
64
+ 29u
63
+ ··· 16u
4
+ 1)
c
3
(u
64
+ 3u
63
+ ··· + 467u + 88)
c
4
, c
8
(u
64
+ u
63
+ ··· + 2u + 1)
c
6
(u
64
+ u
63
+ ··· + 11u + 2)
c
7
, c
11
(u
64
+ 5u
63
+ ··· + 32u + 1)
c
9
(u
64
+ 31u
63
+ ··· + 16u
4
+ 1)
c
10
(u
64
+ u
63
+ ··· + 8u + 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
64
+ 29y
63
+ ··· 16y
4
+ 1)
c
2
(y
64
+ 13y
63
+ ··· 32y
2
+ 1)
c
3
(y
64
+ 21y
63
+ ··· + 151687y + 7744)
c
4
, c
8
(y
64
31y
63
+ ··· + 16y
4
+ 1)
c
6
(y
64
3y
63
+ ··· 213y + 4)
c
7
, c
11
(y
64
+ 49y
63
+ ··· 160y + 1)
c
9
(y
64
+ 5y
63
+ ··· + 32y
2
+ 1)
c
10
(y
64
+ y
63
+ ··· + 32y + 1)
6