9
32
(K9a
6
)
1
Arc Sequences
4 5 7 8 3 9 2 1 6
Solving Sequence
6,9 3,7
4 1 5 2 8
c
6
c
3
c
9
c
5
c
2
c
8
c
1
, c
4
, c
7
Representation Ideals
I = I
u
1
I
u
1
= hu
29
+ u
28
+ ··· + 5u 1, 1.06086 × 10
18
u
28
1.36725 × 10
18
u
27
+ ··· + 4.72018 × 10
17
b 1.91003 × 10
18
,
1.76530 × 10
18
u
28
2.68632 × 10
18
u
27
+ ··· + 4.72018 × 10
17
a 5.28983 × 10
18
i
There are 1 irreducible components with 29 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
29
+u
28
+· · ·+5u 1, 1.06×10
18
u
28
1.37× 10
18
u
27
+· · ·+4.72 ×10
17
b
1.91× 10
18
, 1.77× 10
18
u
28
2.69 × 10
18
u
27
+· · · +4.72 × 10
17
a 5.29 × 10
18
i
(i) Arc colorings
a
6
=
0
u
a
9
=
3.73989u
28
+ 5.69114u
27
+ ··· 27.4128u + 11.2068
2.24749u
28
+ 2.89660u
27
+ ··· 10.1401u + 4.04651
a
3
=
1
0
a
7
=
2.45655u
28
+ 4.23332u
27
+ ··· 8.61671u + 5.60054
3.66245u
28
+ 4.72135u
27
+ ··· 16.0925u + 5.63519
a
4
=
0.585318u
28
0.0731353u
27
+ ··· + 5.97606u + 2.14961
2.09904u
28
3.66262u
27
+ ··· + 15.9412u 5.36065
a
1
=
3.73989u
28
+ 5.69114u
27
+ ··· 27.4128u + 11.2068
1.61270u
28
+ 1.75671u
27
+ ··· 4.12373u + 2.09526
a
5
=
u
u
a
2
=
u
2
+ 1
u
2
a
8
=
3.65871u
28
+ 5.96810u
27
+ ··· 15.0192u + 7.76733
3.99315u
28
+ 5.15215u
27
+ ··· 17.7232u + 6.26790
a
8
=
3.65871u
28
+ 5.96810u
27
+ ··· 15.0192u + 7.76733
3.99315u
28
+ 5.15215u
27
+ ··· 17.7232u + 6.26790
(ii) Obstruction class = 1
(iii) Cusp Shapes =
8031518398882121152
472018340535141461
u
28
9961708991889109292
472018340535141461
u
27
+ ··· +
28131352270886790128
472018340535141461
u
9823958551022044026
472018340535141461
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.39544 0.53455I
a = 0.707053 + 0.521191I
b = 2.17283 + 1.13166I
4.19521 + 13.09990I 5.01719 8.12211I
u = 1.39544 + 0.53455I
a = 0.707053 0.521191I
b = 2.17283 1.13166I
4.19521 13.09990I 5.01719 + 8.12211I
u = 1.37838 0.43416I
a = 0.494582 0.557761I
b = 0.196098 + 0.271006I
5.89129 + 7.10658I 7.40494 4.09137I
u = 1.37838 + 0.43416I
a = 0.494582 + 0.557761I
b = 0.196098 0.271006I
5.89129 7.10658I 7.40494 + 4.09137I
u = 1.211659 0.045159I
a = 0.867325 0.368655I
b = 0.364126 + 0.023646I
5.14963 + 1.80223I 13.69706 3.37820I
u = 1.211659 + 0.045159I
a = 0.867325 + 0.368655I
b = 0.364126 0.023646I
5.14963 1.80223I 13.69706 + 3.37820I
u = 1.164369 0.162769I
a = 0.783179 0.870746I
b = 1.24002 0.78663I
3.17430 + 4.69569I 8.95566 8.13169I
u = 1.164369 + 0.162769I
a = 0.783179 + 0.870746I
b = 1.24002 + 0.78663I
3.17430 4.69569I 8.95566 + 8.13169I
u = 1.093357 0.383928I
a = 0.452814 0.999835I
b = 0.94210 1.28179I
1.26594 + 5.18635I 1.49328 7.03100I
u = 1.093357 + 0.383928I
a = 0.452814 + 0.999835I
b = 0.94210 + 1.28179I
1.26594 5.18635I 1.49328 + 7.03100I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.328130 0.742907I
a = 1.221666 + 0.405694I
b = 1.61608 0.22471I
3.62029 0.98610I 3.43918 + 1.15236I
u = 0.328130 + 0.742907I
a = 1.221666 0.405694I
b = 1.61608 + 0.22471I
3.62029 + 0.98610I 3.43918 1.15236I
u = 0.046849 0.301708I
a = 3.43780 + 1.21899I
b = 0.477636 0.689304I
0.15788 2.80514I 1.82209 + 1.85203I
u = 0.046849 + 0.301708I
a = 3.43780 1.21899I
b = 0.477636 + 0.689304I
0.15788 + 2.80514I 1.82209 1.85203I
u = 0.059577 1.184960I
a = 0.881727 0.477829I
b = 1.73107 0.09023I
0.38505 7.12556I 2.65443 + 8.10425I
u = 0.059577 + 1.184960I
a = 0.881727 + 0.477829I
b = 1.73107 + 0.09023I
0.38505 + 7.12556I 2.65443 8.10425I
u = 0.253652 0.975036I
a = 0.382442 0.757041I
b = 0.750999 0.161406I
0.91572 2.15286I 5.11617 + 3.69479I
u = 0.253652 + 0.975036I
a = 0.382442 + 0.757041I
b = 0.750999 + 0.161406I
0.91572 + 2.15286I 5.11617 3.69479I
u = 0.460562 0.048919I
a = 0.80418 + 1.58142I
b = 1.024324 + 0.601865I
0.78940 + 1.37762I 5.11267 4.75149I
u = 0.460562 + 0.048919I
a = 0.80418 1.58142I
b = 1.024324 0.601865I
0.78940 1.37762I 5.11267 + 4.75149I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.620218 0.307429I
a = 0.618578 0.611210I
b = 0.265324 1.140961I
0.70687 1.36069I 4.42210 + 4.47976I
u = 0.620218 + 0.307429I
a = 0.618578 + 0.611210I
b = 0.265324 + 1.140961I
0.70687 + 1.36069I 4.42210 4.47976I
u = 1.079219 0.058684I
a = 0.559926 0.767898I
b = 3.38806 + 1.00489I
1.99105 2.23064I 15.0558 8.8774I
u = 1.079219 + 0.058684I
a = 0.559926 + 0.767898I
b = 3.38806 1.00489I
1.99105 + 2.23064I 15.0558 + 8.8774I
u = 1.16056
a = 0.234413
b = 0.566135
2.30899 2.51256
u = 1.43653 0.66551I
a = 0.608900 + 0.346466I
b = 1.97849 + 0.94868I
4.11625 4.48763I 9.60010 + 6.67821I
u = 1.43653 + 0.66551I
a = 0.608900 0.346466I
b = 1.97849 0.94868I
4.11625 + 4.48763I 9.60010 6.67821I
u = 1.53445 0.45405I
a = 0.249494 0.583595I
b = 0.273191 0.464394I
4.48635 + 0.55125I 10.94303 0.19758I
u = 1.53445 + 0.45405I
a = 0.249494 + 0.583595I
b = 0.273191 + 0.464394I
4.48635 0.55125I 10.94303 + 0.19758I
5
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
29
+ 5u
28
+ ··· + u + 1)
c
2
, c
5
(u
29
+ u
28
+ ··· + 5u 1)
c
3
(u
29
+ u
28
+ ··· u + 19)
c
4
(u
29
+ u
28
+ ··· + 21u 11)
c
6
, c
9
(u
29
+ u
28
+ ··· + 3u 1)
c
7
(u
29
+ 3u
28
+ ··· + u + 1)
c
8
(u
29
+ 11u
28
+ ··· + 3u 1)
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
29
+ 3y
28
+ ··· 5y 1)
c
2
, c
5
(y
29
21y
28
+ ··· 5y 1)
c
3
(y
29
+ 15y
28
+ ··· + 1103y 361)
c
4
(y
29
+ 31y
28
+ ··· 1869y 121)
c
6
, c
9
(y
29
+ 11y
28
+ ··· + 3y 1)
c
7
(y
29
5y
28
+ ··· + 3y 1)
c
8
(y
29
+ 15y
28
+ ··· + 175y 1)
7