10
11
(K10a
116
)
1
Arc Sequences
8 7 1 9 10 3 2 6 5 4
Solving Sequence
6,10
5 9 4 1 3 8 2 7
c
5
c
9
c
4
c
10
c
3
c
8
c
1
c
7
c
2
, c
6
Representation Ideals
I = I
u
1
I
u
1
= hu
21
u
20
+ ··· + u 1i
There are 1 irreducible components with 21 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
21
u
20
+ · · · + u 1i
(i) Arc colorings
a
6
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
9
=
u
u
3
+ u
a
4
=
u
2
+ 1
u
4
2u
2
a
1
=
u
5
+ 2u
3
u
u
7
3u
5
+ 2u
3
+ u
a
3
=
u
8
+ 3u
6
3u
4
+ 1
u
10
4u
8
+ 5u
6
3u
2
a
8
=
u
3
+ 2u
u
3
+ u
a
2
=
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
7
=
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 = 4u
18
28u
16
4u
15
+ 80u
14
+ 24u
13
104u
12
56u
11
+ 24u
10
+
52u
9
+ 88u
8
+ 8u
7
76u
6
44u
5
12u
4
+ 12u
3
+ 24u
2
+ 12u 2
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.291056 0.376139I
1.39230 6.45770I 2.54644 + 6.39068I
u = 1.291056 + 0.376139I
1.39230 + 6.45770I 2.54644 6.39068I
u = 1.281128 0.111157I
4.56809 2.45481I 8.82608 + 5.13736I
u = 1.281128 + 0.111157I
4.56809 + 2.45481I 8.82608 5.13736I
u = 1.178892 0.386444I
4.45765 + 0.58948I 5.04554 + 0.27365I
u = 1.178892 + 0.386444I
4.45765 0.58948I 5.04554 0.27365I
u = 0.430693 0.459647I
6.58253 1.66521I 5.55767 + 3.90994I
u = 0.430693 + 0.459647I
6.58253 + 1.66521I 5.55767 3.90994I
u = 0.086113 0.839589I
1.10589 5.00460I 1.84652 + 3.34739I
u = 0.086113 + 0.839589I
1.10589 + 5.00460I 1.84652 3.34739I
u = 0.027961 0.833462I
5.50220 + 2.11040I 1.91245 3.38979I
u = 0.027961 + 0.833462I
5.50220 2.11040I 1.91245 + 3.38979I
u = 0.205500 0.333164I
0.091241 + 0.864455I 2.17207 8.05526I
u = 0.205500 + 0.333164I
0.091241 0.864455I 2.17207 + 8.05526I
u = 1.18427
2.46649 1.74061
u = 1.245843 0.377074I
1.73723 + 2.23968I 1.50234 0.17506I
u = 1.245843 + 0.377074I
1.73723 2.23968I 1.50234 + 0.17506I
u = 1.328509 0.374285I
5.53903 + 9.37044I 6.11943 5.65030I
u = 1.328509 + 0.374285I
5.53903 9.37044I 6.11943 + 5.65030I
u = 1.367932 0.126822I
12.19547 + 3.59224I 10.42606 3.20950I
u = 1.367932 + 0.126822I
12.19547 3.59224I 10.42606 + 3.20950I
3
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
2
, c
6
c
7
(u
21
+ u
20
+ ··· u 1)
c
3
, c
8
, c
10
(u
21
+ 3u
20
+ ··· + 5u + 3)
c
4
, c
5
, c
9
(u
21
+ u
20
+ ··· + u + 1)
4
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
2
, c
6
c
7
(y
21
+ 23y
20
+ ··· 5y 1)
c
3
, c
8
, c
10
(y
21
+ 19y
20
+ ··· + 7y 9)
c
4
, c
5
, c
9
(y
21
17y
20
+ ··· 5y 1)
5