11a
178
(K11a
178
)
1
Arc Sequences
6 1 11 10 9 2 3 4 5 8 7
Solving Sequence
2,7
6 1 3 8 11 4 9 5 10
c
6
c
1
c
2
c
7
c
11
c
3
c
8
c
5
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
61
+ u
60
+ ··· u 1i
There are 1 irreducible components with 61 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
61
+ u
60
+ · · · u 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
6
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
u
2
+ 1
u
4
a
8
=
u
9
2u
7
+ 3u
5
2u
3
+ u
u
9
u
7
+ u
5
+ u
a
11
=
u
2
+ 1
u
4
a
4
=
u
10
+ 3u
8
4u
6
+ 3u
4
u
2
+ 1
u
12
+ 2u
10
2u
8
+ u
4
a
9
=
u
31
8u
29
+ ··· + 12u
7
4u
5
u
33
7u
31
+ ··· + 2u
13
+ u
a
5
=
u
56
13u
54
+ ··· 2u
2
+ 1
u
56
12u
54
+ ··· + 5u
8
+ 2u
4
a
10
=
u
22
+ 5u
20
+ ··· 2u
2
+ 1
u
22
+ 4u
20
9u
18
+ 12u
16
12u
14
+ 10u
12
9u
10
+ 6u
8
3u
6
u
2
a
10
=
u
22
+ 5u
20
+ ··· 2u
2
+ 1
u
22
+ 4u
20
9u
18
+ 12u
16
12u
14
+ 10u
12
9u
10
+ 6u
8
3u
6
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 = 1.124888 0.572801I
3.4458 14.6424I 2.99891 + 9.76642I
u = 1.124888 + 0.572801I
3.4458 + 14.6424I 2.99891 9.76642I
u = 1.120395 0.239796I
4.20404 + 3.36287I 10.96658 4.02408I
u = 1.120395 + 0.239796I
4.20404 3.36287I 10.96658 + 4.02408I
u = 1.118685 0.534112I
1.26791 7.55537I 6.72993 + 7.23830I
u = 1.118685 + 0.534112I
1.26791 + 7.55537I 6.72993 7.23830I
u = 1.115369 0.342685I
5.28239 3.39079I 12.90700 + 4.89383I
u = 1.115369 + 0.342685I
5.28239 + 3.39079I 12.90700 4.89383I
u = 1.113390 0.485777I
0.382880 0.851377I 6.25659 + 1.05739I
u = 1.113390 + 0.485777I
0.382880 + 0.851377I 6.25659 1.05739I
u = 1.111264 0.557520I
0.69264 7.18756I 4.76998 + 4.51746I
u = 1.111264 + 0.557520I
0.69264 + 7.18756I 4.76998 4.51746I
u = 1.033104 0.187577I
3.27959 1.47237I 3.77294 + 0.98684I
u = 1.033104 + 0.187577I
3.27959 + 1.47237I 3.77294 0.98684I
u = 1.003474 0.545968I
1.15617 4.09014I 2.37608 + 6.61721I
u = 1.003474 + 0.545968I
1.15617 + 4.09014I 2.37608 6.61721I
u = 0.948153 0.574834I
6.18322 + 2.55917I 0.353871 0.495602I
u = 0.948153 + 0.574834I
6.18322 2.55917I 0.353871 + 0.495602I
u = 0.702655 0.463134I
2.64368 1.93405I 1.89634 + 4.21284I
u = 0.702655 + 0.463134I
2.64368 + 1.93405I 1.89634 4.21284I
u = 0.621785 0.658999I
7.14477 7.36689I 1.83265 + 6.49541I
u = 0.621785 + 0.658999I
7.14477 + 7.36689I 1.83265 6.49541I
u = 0.552270 0.617769I
2.48756 0.50881I 0.570526 0.185507I
u = 0.552270 + 0.617769I
2.48756 + 0.50881I 0.570526 + 0.185507I
u = 0.345416 0.715523I
1.53930 + 2.31744I 1.192371 0.636222I
u = 0.345416 + 0.715523I
1.53930 2.31744I 1.192371 + 0.636222I
u = 0.343323 0.767640I
5.74647 + 9.59086I 0.22395 6.02636I
u = 0.343323 + 0.767640I
5.74647 9.59086I 0.22395 + 6.02636I
u = 0.277033 0.691934I
1.13938 + 2.86125I 3.45602 3.52851I
u = 0.277033 + 0.691934I
1.13938 2.86125I 3.45602 + 3.52851I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.126206 0.638743I
3.06025 3.37781I 2.51099 + 2.74692I
u = 0.126206 + 0.638743I
3.06025 + 3.37781I 2.51099 2.74692I
u = 0.210413 0.629262I
1.67346 + 0.23991I 8.17483 1.24926I
u = 0.210413 + 0.629262I
1.67346 0.23991I 8.17483 + 1.24926I
u = 0.336261 0.751744I
0.27382 6.06188I 4.21507 + 6.02215I
u = 0.336261 + 0.751744I
0.27382 + 6.06188I 4.21507 6.02215I
u = 0.394147 0.730677I
7.77499 0.61886I 2.98419 + 0.41079I
u = 0.394147 + 0.730677I
7.77499 + 0.61886I 2.98419 0.41079I
u = 0.541944 0.674012I
8.48817 1.61774I 3.86252 + 0.20232I
u = 0.541944 + 0.674012I
8.48817 + 1.61774I 3.86252 0.20232I
u = 0.612486 0.631132I
1.61526 + 4.05129I 2.39277 6.82409I
u = 0.612486 + 0.631132I
1.61526 4.05129I 2.39277 + 6.82409I
u = 0.612895
0.928331 10.6736
u = 0.957071 0.545546I
0.605205 + 0.585495I 3.92457 + 0.79443I
u = 0.957071 + 0.545546I
0.605205 0.585495I 3.92457 0.79443I
u = 1.010657 0.577213I
7.10735 + 6.46891I 1.23961 5.95841I
u = 1.010657 + 0.577213I
7.10735 6.46891I 1.23961 + 5.95841I
u = 1.089712 0.268806I
2.65665 + 0.24134I 8.01162 1.24581I
u = 1.089712 + 0.268806I
2.65665 0.24134I 8.01162 + 1.24581I
u = 1.096941 0.573191I
5.71025 + 5.58980I 0.33382 4.72255I
u = 1.096941 + 0.573191I
5.71025 5.58980I 0.33382 + 4.72255I
u = 1.112282 0.300936I
2.83860 + 0.05729I 9.38968 + 0.27153I
u = 1.112282 + 0.300936I
2.83860 0.05729I 9.38968 0.27153I
u = 1.112330 0.510589I
4.14943 + 4.18449I 11.34771 2.91609I
u = 1.112330 + 0.510589I
4.14943 4.18449I 11.34771 + 2.91609I
u = 1.122408 0.565959I
2.03053 + 11.04655I 7.45993 9.63925I
u = 1.122408 + 0.565959I
2.03053 11.04655I 7.45993 + 9.63925I
u = 1.124705 0.366091I
0.41617 + 6.80603I 7.46016 6.19926I
u = 1.124705 + 0.366091I
0.41617 6.80603I 7.46016 + 6.19926I
u = 1.129605 0.223326I
1.12751 6.89407I 6.18661 + 4.38730I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.129605 + 0.223326I
1.12751 + 6.89407I 6.18661 4.38730I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
61
+ u
60
+ ··· u 1)
c
2
(u
61
+ 29u
60
+ ··· + 3u + 1)
c
3
(u
61
+ 7u
60
+ ··· + 433u + 37)
c
4
(u
61
+ u
60
+ ··· + 3u + 1)
c
5
(u
61
+ u
60
+ ··· + 3u + 1)
c
7
(u
61
+ u
60
+ ··· 211u + 61)
c
8
(u
61
+ u
60
+ ··· + 11u 2)
c
9
(u
61
+ u
60
+ ··· + 3u + 1)
c
10
(u
61
+ 13u
60
+ ··· 3083u 283)
c
11
(u
61
+ 3u
60
+ ··· 89u 56)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
61
29y
60
+ ··· + 3y 1)
c
2
(y
61
+ 7y
60
+ ··· y 1)
c
3
(y
61
+ 11y
60
+ ··· 18009y 1369)
c
4
(y
61
+ 55y
60
+ ··· + 3y 1)
c
5
, c
9
(y
61
+ 55y
60
+ ··· + 3y 1)
c
7
(y
61
13y
60
+ ··· + 176159y 3721)
c
8
(y
61
+ 3y
60
+ ··· + 57y 4)
c
10
(y
61
+ 19y
60
+ ··· 760653y 80089)
c
11
(y
61
+ 15y
60
+ ··· 75183y 3136)
6