8
17
(K8a
14
)
1
Arc Sequences
7 5 1 2 8 3 4 6
Solving Sequence
2,5 3,7
1 4 8 6
c
2
c
1
c
4
c
7
c
6
c
3
, c
5
, c
8
Representation Ideals
I = I
u
1
I
u
1
= hu
18
u
17
+ ··· 3u + 1, 54800u
17
38000u
16
+ ··· + 654509b 54084,
59564u
17
+ 3084u
16
+ ··· + 654509a + 2126652i
There are 1 irreducible components with 18 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
18
u
17
+ · · · 3u + 1, 54800u
17
38000u
16
+ · · · + 654509b
54084, 5.96 × 10
4
u
17
+ 3084u
16
+ · · · + 6.55 × 10
5
a + 2.13 × 10
6
i
(i) Arc colorings
a
2
=
1
0
a
5
=
0
u
a
3
=
1
u
2
a
7
=
0.0910056u
17
0.00471193u
16
+ ··· + 1.29187u 3.24923
0.0837269u
17
+ 0.0580588u
16
+ ··· + 1.59307u + 0.0826329
a
1
=
0.830548u
17
0.000715040u
16
+ ··· 3.82730u + 0.113930
0.831263u
17
0.591022u
16
+ ··· + 2.37771u 0.830548
a
4
=
u
u
a
8
=
0.816945u
17
0.800072u
16
+ ··· + 1.11727u 3.18861
0.809666u
17
+ 0.853418u
16
+ ··· + 1.76767u + 0.0220073
a
6
=
0.732219u
17
0.799714u
16
+ ··· 0.469078u 3.24557
0.737310u
17
+ 0.628062u
16
+ ··· + 2.69565u 0.0711556
(ii) Obstruction class = 1
(iii) Cusp Shapes =
2081176
654509
u
17
+
1538700
654509
u
16
+ ··· +
3609404
654509
u
2997870
654509
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.342096 0.135496I
a = 0.963587 + 0.156714I
b = 0.674472 + 0.071072I
2.59619 + 0.05903I 5.04488 + 1.45254I
u = 1.342096 + 0.135496I
a = 0.963587 0.156714I
b = 0.674472 0.071072I
2.59619 0.05903I 5.04488 1.45254I
u = 1.168299 0.720176I
a = 0.544039 0.375065I
b = 0.754095 0.312835I
1.46999 + 3.11720I 3.21326 6.66243I
u = 1.168299 + 0.720176I
a = 0.544039 + 0.375065I
b = 0.754095 + 0.312835I
1.46999 3.11720I 3.21326 + 6.66243I
u = 0.950168 0.130449I
a = 0.74897 + 2.21234I
b = 0.245889 + 0.448672I
0.520528I 13.0168I
u = 0.950168 + 0.130449I
a = 0.74897 2.21234I
b = 0.245889 0.448672I
0.520528I 13.0168I
u = 0.081063 0.532154I
a = 0.580215 0.167271I
b = 0.519308 0.647363I
1.47534I 4.20317I
u = 0.081063 + 0.532154I
a = 0.580215 + 0.167271I
b = 0.519308 + 0.647363I
1.47534I 4.20317I
u = 0.167072 1.125402I
a = 0.0930237 0.0911235I
b = 0.754282 + 0.760835I
3.57267 + 4.95181I 3.31278 5.61624I
u = 0.167072 + 1.125402I
a = 0.0930237 + 0.0911235I
b = 0.754282 0.760835I
3.57267 4.95181I 3.31278 + 5.61624I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.470709 0.243089I
a = 2.88627 0.66769I
b = 1.040627 0.285497I
2.59619 + 0.05903I 5.04488 + 1.45254I
u = 0.470709 + 0.243089I
a = 2.88627 + 0.66769I
b = 1.040627 + 0.285497I
2.59619 0.05903I 5.04488 1.45254I
u = 0.912810 0.341070I
a = 0.459093 0.966672I
b = 0.68103 + 1.36209I
1.46999 3.11720I 3.21326 + 6.66243I
u = 0.912810 + 0.341070I
a = 0.459093 + 0.966672I
b = 0.68103 1.36209I
1.46999 + 3.11720I 3.21326 6.66243I
u = 1.190057 0.368733I
a = 1.72448 0.04974I
b = 1.29997 + 0.94483I
3.57267 4.95181I 3.31278 + 5.61624I
u = 1.190057 + 0.368733I
a = 1.72448 + 0.04974I
b = 1.29997 0.94483I
3.57267 + 4.95181I 3.31278 5.61624I
u = 1.30098 0.59320I
a = 1.53530 0.15585I
b = 1.16885 0.94542I
10.9859I 7.09338I
u = 1.30098 + 0.59320I
a = 1.53530 + 0.15585I
b = 1.16885 + 0.94542I
10.9859I 7.09338I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
3
(u
18
+ 3u
17
+ ··· + u + 1)
c
2
, c
4
, c
5
c
8
(u
18
+ u
17
+ ··· + 3u + 1)
c
6
, c
7
(u
18
+ u
17
+ ··· 5u + 1)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
(y
18
3y
17
+ ··· 3y + 1)
c
2
, c
4
, c
5
c
8
(y
18
11y
17
+ ··· 3y + 1)
c
6
, c
7
(y
18
+ 13y
17
+ ··· 3y + 1)
6