11a
95
(K11a
95
)
1
Arc Sequences
5 1 9 6 2 3 11 10 4 8 7
Solving Sequence
2,6
5 1 3 7 4 11 8 10 9
c
5
c
1
c
2
c
6
c
4
c
11
c
7
c
10
c
8
c
3
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
36
+ u
35
+ ··· 4u 1i
There are 1 irreducible components with 36 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
36
+ u
35
+ · · · 4u 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
5
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
u
2
+ 1
u
4
a
7
=
u
9
+ 2u
7
3u
5
+ 2u
3
u
u
9
+ u
7
u
5
+ u
a
4
=
u
u
3
+ u
a
11
=
u
16
+ 3u
14
7u
12
+ 10u
10
11u
8
+ 8u
6
4u
4
+ 1
u
16
+ 2u
14
4u
12
+ 4u
10
2u
8
+ 2u
4
2u
2
a
8
=
u
23
+ 4u
21
+ ··· + 4u
3
2u
u
23
+ 3u
21
+ ··· + 2u
3
+ u
a
10
=
u
30
+ 5u
28
+ ··· + 2u
2
+ 1
u
30
+ 4u
28
+ ··· + 2u
4
3u
2
a
9
=
u
34
+ 5u
32
+ ··· + u
2
+ 1
u
35
u
34
+ ··· + 4u + 1
a
9
=
u
34
+ 5u
32
+ ··· + u
2
+ 1
u
35
u
34
+ ··· + 4u + 1
(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 = 1.029711 0.270133I
6.73510 + 0.05242I 9.91031 + 1.11538I
u = 1.029711 + 0.270133I
6.73510 0.05242I 9.91031 1.11538I
u = 1.005164 0.763200I
13.0885 11.7607I 5.64793 + 7.43079I
u = 1.005164 + 0.763200I
13.0885 + 11.7607I 5.64793 7.43079I
u = 0.978294 0.723773I
3.52152 9.06176I 8.19420 + 9.30306I
u = 0.978294 + 0.723773I
3.52152 + 9.06176I 8.19420 9.30306I
u = 0.931320 0.665651I
0.44906 4.79281I 14.2901 + 6.9019I
u = 0.931320 + 0.665651I
0.44906 + 4.79281I 14.2901 6.9019I
u = 0.827979 0.168454I
0.731880 0.351895I 10.65376 + 0.66893I
u = 0.827979 + 0.168454I
0.731880 + 0.351895I 10.65376 0.66893I
u = 0.795382 0.633860I
0.001943 0.306901I 12.89345 1.58755I
u = 0.795382 + 0.633860I
0.001943 + 0.306901I 12.89345 + 1.58755I
u = 0.741334 0.854303I
13.9035 + 5.7329I 4.26372 2.53612I
u = 0.741334 + 0.854303I
13.9035 5.7329I 4.26372 + 2.53612I
u = 0.733515 0.778479I
4.26116 + 3.38021I 6.36942 4.06127I
u = 0.733515 + 0.778479I
4.26116 3.38021I 6.36942 + 4.06127I
u = 0.404870
0.709168 14.3098
u = 0.086623 0.514598I
1.42228 2.05301I 4.86610 + 4.82950I
u = 0.086623 + 0.514598I
1.42228 + 2.05301I 4.86610 4.82950I
u = 0.011219 0.704019I
10.03415 3.29411I 3.98637 + 2.43304I
u = 0.011219 + 0.704019I
10.03415 + 3.29411I 3.98637 2.43304I
u = 0.750710 0.853582I
14.07567 + 0.94615I 3.96028 2.12397I
u = 0.750710 + 0.853582I
14.07567 0.94615I 3.96028 + 2.12397I
u = 0.782430 0.779304I
5.14913 + 1.38552I 3.93165 2.60854I
u = 0.782430 + 0.779304I
5.14913 1.38552I 3.93165 + 2.60854I
u = 0.870204 0.708836I
2.46542 + 2.71564I 4.42006 3.22989I
u = 0.870204 + 0.708836I
2.46542 2.71564I 4.42006 + 3.22989I
u = 0.951308 0.739370I
4.63406 + 4.35057I 4.96741 3.00405I
u = 0.951308 + 0.739370I
4.63406 4.35057I 4.96741 + 3.00405I
u = 0.957347
4.25142 21.1242
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.970808 0.146946I
1.79064 + 4.12069I 14.4783 7.6804I
u = 0.970808 + 0.146946I
1.79064 4.12069I 14.4783 + 7.6804I
u = 0.999925 0.767262I
13.3053 + 5.0936I 5.21713 2.79441I
u = 0.999925 + 0.767262I
13.3053 5.0936I 5.21713 + 2.79441I
u = 1.038917 0.253422I
6.61933 + 6.45885I 10.23279 5.88059I
u = 1.038917 + 0.253422I
6.61933 6.45885I 10.23279 + 5.88059I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
5
(u
36
+ u
35
+ ··· 4u 1)
c
2
, c
4
(u
36
+ 11u
35
+ ··· + 6u + 1)
c
3
, c
9
(u
36
+ u
35
+ ··· + 2u 1)
c
6
(u
36
+ u
35
+ ··· + 366u 97)
c
7
, c
8
, c
10
c
11
(u
36
+ 7u
35
+ ··· + 6u + 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
36
11y
35
+ ··· 6y + 1)
c
2
, c
4
(y
36
+ 29y
35
+ ··· 62y + 1)
c
3
, c
9
(y
36
7y
35
+ ··· 6y + 1)
c
6
(y
36
+ 17y
35
+ ··· 13870y + 9409)
c
7
, c
8
, c
10
c
11
(y
36
+ 45y
35
+ ··· 14y + 1)
5