11a
359
(K11a
359
)
1
Arc Sequences
7 9 8 1 11 10 2 3 4 6 5
Solving Sequence
4,8
3 9 10 2 7 1 6 11 5
c
3
c
8
c
9
c
2
c
7
c
1
c
6
c
10
c
5
c
4
, c
11
Representation Ideals
I = I
u
1
I
u
1
= hu
26
+ u
25
+ ··· + u 1i
There are 1 irreducible components with 26 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
26
+ u
25
+ · · · + u 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
9
=
u
u
3
+ u
a
10
=
u
3
2u
u
3
+ u
a
2
=
u
2
+ 1
u
4
2u
2
a
7
=
u
5
+ 2u
3
+ u
u
7
3u
5
2u
3
+ u
a
1
=
u
8
3u
6
3u
4
+ 1
u
10
+ 4u
8
+ 5u
6
3u
2
a
6
=
u
13
6u
11
13u
9
10u
7
+ 4u
5
+ 8u
3
+ u
u
13
+ 5u
11
+ 9u
9
+ 4u
7
6u
5
5u
3
+ u
a
11
=
u
23
10u
21
+ ··· 4u
3
2u
u
23
+ 9u
21
+ ··· 2u
3
+ u
a
5
=
u
18
7u
16
20u
14
27u
12
11u
10
+ 13u
8
+ 14u
6
3u
2
+ 1
u
20
+ 8u
18
+ 26u
16
+ 40u
14
+ 19u
12
24u
10
30u
8
+ 9u
4
a
5
=
u
18
7u
16
20u
14
27u
12
11u
10
+ 13u
8
+ 14u
6
3u
2
+ 1
u
20
+ 8u
18
+ 26u
16
+ 40u
14
+ 19u
12
24u
10
30u
8
+ 9u
4
(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 = 0.841791 0.094185I
5.20604 5.29901I 9.93823 + 3.19957I
u = 0.841791 + 0.094185I
5.20604 + 5.29901I 9.93823 3.19957I
u = 0.829469
6.03489 16.5469
u = 0.392131 1.168430I
8.49921 + 0.85694I 6.81756 + 0.45709I
u = 0.392131 + 1.168430I
8.49921 0.85694I 6.81756 0.45709I
u = 0.374153 1.333357I
9.68283 9.67188I 5.67938 + 5.45420I
u = 0.374153 + 1.333357I
9.68283 + 9.67188I 5.67938 5.45420I
u = 0.373903 1.269516I
2.09387 4.32460I 12.48733 + 3.68089I
u = 0.373903 + 1.269516I
2.09387 + 4.32460I 12.48733 3.68089I
u = 0.373827 0.329514I
1.88313 1.28751I 6.75058 + 5.74185I
u = 0.373827 + 0.329514I
1.88313 + 1.28751I 6.75058 5.74185I
u = 0.116826 1.320417I
6.90824 2.96972I 1.89605 + 4.34441I
u = 0.116826 + 1.320417I
6.90824 + 2.96972I 1.89605 4.34441I
u = 0.063117 1.217597I
3.01166 + 1.26256I 8.17654 5.12241I
u = 0.063117 + 1.217597I
3.01166 1.26256I 8.17654 + 5.12241I
u = 0.127500 1.375757I
16.3951 + 3.6931I 1.57713 3.06120I
u = 0.127500 + 1.375757I
16.3951 3.6931I 1.57713 + 3.06120I
u = 0.301902
0.485500 20.4448
u = 0.370693 1.222998I
0.117817 + 0.889406I 8.45807 + 0.89318I
u = 0.370693 + 1.222998I
0.117817 0.889406I 8.45807 0.89318I
u = 0.371528 1.305528I
0.74252 + 7.74244I 7.42357 6.92511I
u = 0.371528 + 1.305528I
0.74252 7.74244I 7.42357 + 6.92511I
u = 0.475175 0.446398I
10.68297 + 1.72593I 6.44509 3.70709I
u = 0.475175 + 0.446398I
10.68297 1.72593I 6.44509 + 3.70709I
u = 0.828402 0.050333I
3.49265 + 3.42603I 11.85459 4.34345I
u = 0.828402 + 0.050333I
3.49265 3.42603I 11.85459 + 4.34345I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
7
, c
9
(u
26
+ u
25
+ ··· 9u 5)
c
2
, c
3
, c
8
(u
26
+ u
25
+ ··· + u 1)
c
4
, c
5
, c
6
c
10
, c
11
(u
26
+ u
25
+ ··· 3u 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
7
, c
9
(y
26
23y
25
+ ··· 151y + 25)
c
2
, c
3
, c
8
(y
26
+ 21y
25
+ ··· 11y + 1)
c
4
, c
5
, c
6
c
10
, c
11
(y
26
+ 33y
25
+ ··· 11y + 1)
5