10
7
(K10a
65
)
A knot diagram
1
Linearized knot diagam
7 8 10 9 1 2 6 5 4 3
Solving Sequence
2,7
1 6 8 3 5 9 4 10
c
1
c
6
c
7
c
2
c
5
c
8
c
4
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
21
− u
20
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 21 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= hu
21
− u
20
+ 6u
19
− 5u
18
+ 17u
17
− 13u
16
+ 28u
15
− 20u
14
+ 28u
13
−
20u
12
+ 16u
11
− 11u
10
+ 3u
9
− u
8
− 2u
7
+ 4u
6
− u
5
+ u
4
+ 2u
3
− u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
6
=
−u
u
a
8
=
−u
3
u
3
+ u
a
3
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
3
u
5
+ u
3
+ u
a
9
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
13
− 3u
11
− 5u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
4
=
u
19
+ 4u
17
+ 8u
15
+ 8u
13
+ 5u
11
+ 2u
9
+ 2u
7
+ u
3
u
20
− u
19
+ ··· + u
2
+ 1
a
10
=
u
14
+ 3u
12
+ 4u
10
+ u
8
− 2u
6
− 2u
4
+ 1
−u
14
− 4u
12
− 7u
10
− 6u
8
− 2u
6
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
19
− 4u
18
+ 20u
17
− 20u
16
+ 48u
15
− 52u
14
+ 64u
13
− 76u
12
+
48u
11
− 64u
10
+ 16u
9
− 16u
8
− 4u
7
+ 16u
6
− 8u
5
+ 16u
4
− 4u
3
− 4u
2
+ 4u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
21
+ u
20
+ ··· + u + 1
c
2
, c
5
u
21
− u
20
+ ··· + u + 5
c
3
, c
4
, c
8
c
9
, c
10
u
21
− u
20
+ ··· + u + 1
c
7
u
21
+ 11u
20
+ ··· − u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
21
+ 11y
20
+ ··· − y −1
c
2
, c
5
y
21
− 13y
20
+ ··· − 69y −25
c
3
, c
4
, c
8
c
9
, c
10
y
21
+ 27y
20
+ ··· − y −1
c
7
y
21
− y
20
+ ··· + 11y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.631235 + 0.777388I
12.97590 − 2.44340I 0.84460 + 3.15661I
u = −0.631235 − 0.777388I
12.97590 + 2.44340I 0.84460 − 3.15661I
u = 0.515219 + 0.758542I
3.44776 + 2.10610I 0.68965 − 4.22092I
u = 0.515219 − 0.758542I
3.44776 − 2.10610I 0.68965 + 4.22092I
u = 0.794642 + 0.241148I
10.29500 − 4.13640I −0.28719 + 2.17514I
u = 0.794642 − 0.241148I
10.29500 + 4.13640I −0.28719 − 2.17514I
u = −0.375476 + 1.140930I
−2.38679 − 0.77154I −6.91276 − 0.81413I
u = −0.375476 − 1.140930I
−2.38679 + 0.77154I −6.91276 + 0.81413I
u = 0.297476 + 1.182770I
5.89549 − 0.72644I −5.47305 − 0.34896I
u = 0.297476 − 1.182770I
5.89549 + 0.72644I −5.47305 + 0.34896I
u = −0.199725 + 0.739431I
−0.474299 − 1.026510I −6.88729 + 6.49406I
u = −0.199725 − 0.739431I
−0.474299 + 1.026510I −6.88729 − 6.49406I
u = 0.448707 + 1.150100I
−4.43097 + 4.04104I −10.76568 − 4.27407I
u = 0.448707 − 1.150100I
−4.43097 − 4.04104I −10.76568 + 4.27407I
u = −0.504141 + 1.153180I
−1.47889 − 7.30035I −5.16109 + 7.23595I
u = −0.504141 − 1.153180I
−1.47889 + 7.30035I −5.16109 − 7.23595I
u = −0.709616 + 0.181075I
1.31805 + 2.71325I −1.55258 − 3.99913I
u = −0.709616 − 0.181075I
1.31805 − 2.71325I −1.55258 + 3.99913I
u = 0.544516 + 1.163610I
7.57313 + 9.11591I −3.42568 − 5.67037I
u = 0.544516 − 1.163610I
7.57313 − 9.11591I −3.42568 + 5.67037I
u = 0.639263
−1.31636 −8.13790
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
21
+ u
20
+ ··· + u + 1
c
2
, c
5
u
21
− u
20
+ ··· + u + 5
c
3
, c
4
, c
8
c
9
, c
10
u
21
− u
20
+ ··· + u + 1
c
7
u
21
+ 11u
20
+ ··· − u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
21
+ 11y
20
+ ··· − y −1
c
2
, c
5
y
21
− 13y
20
+ ··· − 69y −25
c
3
, c
4
, c
8
c
9
, c
10
y
21
+ 27y
20
+ ··· − y −1
c
7
y
21
− y
20
+ ··· + 11y −1
7
