10
8
(K10a
114
)
A knot diagram
1
Linearized knot diagam
7 6 8 9 10 2 1 4 5 3
Solving Sequence
4,9
5 10 6 8 3 1 2 7
c
4
c
9
c
5
c
8
c
3
c
10
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
14
+ u
13
− 9u
12
− 8u
11
+ 30u
10
+ 23u
9
− 45u
8
− 30u
7
+ 28u
6
+ 20u
5
− 2u
4
− 6u
3
− 2u
2
+ u − 1i
* 1 irreducible components of dim
C
= 0, with total 14 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
14
+ u
13
− 9u
12
− 8u
11
+ 30u
10
+ 23u
9
− 45u
8
− 30u
7
+ 28u
6
+
20u
5
− 2u
4
− 6u
3
− 2u
2
+ u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
u
2
a
10
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
8
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
1
=
u
7
− 4u
5
+ 4u
3
− 2u
u
7
− 3u
5
+ u
a
2
=
−u
8
+ 5u
6
− 7u
4
+ 2u
2
+ 1
−u
10
+ 6u
8
− 11u
6
+ 6u
4
− u
2
a
7
=
u
13
− 8u
11
+ 23u
9
− 30u
7
+ 20u
5
− 6u
3
+ u
u
13
− 7u
11
+ 15u
9
− 8u
7
− 4u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
10
− 28u
8
+ 64u
6
+ 4u
5
− 52u
4
− 16u
3
+ 12u
2
+ 12u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
14
− u
13
+ ··· + u − 1
c
3
, c
4
, c
5
c
8
, c
9
u
14
− u
13
+ ··· − u − 1
c
10
u
14
− 5u
13
+ ··· − 9u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
14
+ 17y
13
+ ··· + 3y + 1
c
3
, c
4
, c
5
c
8
, c
9
y
14
− 19y
13
+ ··· + 3y + 1
c
10
y
14
− 11y
13
+ ··· − 873y + 121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.970951 + 0.194954I
−3.69538 + 2.85844I −9.69586 − 5.54876I
u = −0.970951 − 0.194954I
−3.69538 − 2.85844I −9.69586 + 5.54876I
u = 1.084880 + 0.290974I
−11.72400 − 4.55664I −11.05347 + 3.73465I
u = 1.084880 − 0.290974I
−11.72400 + 4.55664I −11.05347 − 3.73465I
u = 0.838105
−1.62716 −4.88720
u = −0.339787 + 0.534810I
−7.27107 + 1.74781I −6.82316 − 3.51408I
u = −0.339787 − 0.534810I
−7.27107 − 1.74781I −6.82316 + 3.51408I
u = 0.183882 + 0.352310I
−0.154017 − 0.948871I −3.14842 + 7.14990I
u = 0.183882 − 0.352310I
−0.154017 + 0.948871I −3.14842 − 7.14990I
u = −1.69593
−10.7537 −6.14500
u = 1.71487 + 0.04545I
−13.27980 − 3.79315I −10.02102 + 3.81094I
u = 1.71487 − 0.04545I
−13.27980 + 3.79315I −10.02102 − 3.81094I
u = −1.74398 + 0.07530I
17.6407 + 6.0832I −11.74201 − 2.65432I
u = −1.74398 − 0.07530I
17.6407 − 6.0832I −11.74201 + 2.65432I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
14
− u
13
+ ··· + u − 1
c
3
, c
4
, c
5
c
8
, c
9
u
14
− u
13
+ ··· − u − 1
c
10
u
14
− 5u
13
+ ··· − 9u + 11
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
14
+ 17y
13
+ ··· + 3y + 1
c
3
, c
4
, c
5
c
8
, c
9
y
14
− 19y
13
+ ··· + 3y + 1
c
10
y
14
− 11y
13
+ ··· − 873y + 121
7
