10
4
(K10a
113
)
A knot diagram
1
Linearized knot diagam
7 6 10 9 8 1 2 5 4 3
Solving Sequence
4,9
5 10 3 1 8 6 2 7
c
4
c
9
c
3
c
10
c
8
c
5
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
13
+ u
12
+ 10u
11
+ 9u
10
+ 37u
9
+ 29u
8
+ 62u
7
+ 40u
6
+ 46u
5
+ 22u
4
+ 12u
3
+ 3u
2
+ u + 1i
* 1 irreducible components of dim
C
= 0, with total 13 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
13
+ u
12
+ 10u
11
+ 9u
10
+ 37u
9
+ 29u
8
+ 62u
7
+ 40u
6
+ 46u
5
+
22u
4
+ 12u
3
+ 3u
2
+ u + 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
u
a
3
=
u
2
+ 1
−u
2
a
1
=
−u
3
− 2u
u
3
+ u
a
8
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
u
8
+ 5u
6
+ 7u
4
+ 4u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 6u
4
− u
2
a
7
=
u
10
+ 7u
8
+ 16u
6
+ 13u
4
+ 3u
2
+ 1
−u
10
− 6u
8
− 11u
6
− 6u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
11
+ 4u
10
+ 36u
9
+ 32u
8
+ 116u
7
+ 88u
6
+ 160u
5
+ 96u
4
+ 88u
3
+ 36u
2
+ 12u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u
13
+ u
12
+ ··· + u − 1
c
2
u
13
− 3u
12
+ ··· − 15u + 8
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
13
− u
12
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
y
13
− 13y
12
+ ··· − 5y −1
c
2
y
13
− 9y
12
+ ··· + 65y −64
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
13
+ 19y
12
+ ··· − 5y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083038 + 1.167020I
4.84943 − 1.92579I 3.99878 + 3.82169I
u = 0.083038 − 1.167020I
4.84943 + 1.92579I 3.99878 − 3.82169I
u = −0.179330 + 1.269600I
10.92570 + 4.78537I 7.34460 − 3.59229I
u = −0.179330 − 1.269600I
10.92570 − 4.78537I 7.34460 + 3.59229I
u = −0.379427 + 0.590112I
4.88223 + 2.83275I 4.99682 − 5.17990I
u = −0.379427 − 0.590112I
4.88223 − 2.83275I 4.99682 + 5.17990I
u = −0.485085
3.11610 0.0828820
u = 0.245118 + 0.346982I
−0.059028 − 0.886909I −1.30388 + 7.82576I
u = 0.245118 − 0.346982I
−0.059028 + 0.886909I −1.30388 − 7.82576I
u = 0.01838 + 1.78025I
15.6533 − 2.3518I 4.35700 + 2.76650I
u = 0.01838 − 1.78025I
15.6533 + 2.3518I 4.35700 − 2.76650I
u = −0.04523 + 1.80316I
−17.2479 + 5.8171I 7.56524 − 2.75393I
u = −0.04523 − 1.80316I
−17.2479 − 5.8171I 7.56524 + 2.75393I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
7
u
13
+ u
12
+ ··· + u − 1
c
2
u
13
− 3u
12
+ ··· − 15u + 8
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
13
− u
12
+ ··· + u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
7
y
13
− 13y
12
+ ··· − 5y −1
c
2
y
13
− 9y
12
+ ··· + 65y −64
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
13
+ 19y
12
+ ··· − 5y −1
7
