10
45
(K10a
25
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 2 3 4 5 8 7
Solving Sequence
5,9
4 8 10 3 7 1 2 6
c
4
c
8
c
9
c
3
c
7
c
10
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
44
− u
43
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 44 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
44
− u
43
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
8
=
u
u
a
10
=
u
3
u
3
+ u
a
3
=
u
8
+ u
6
+ u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
7
=
−u
3
u
5
+ u
3
+ u
a
1
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
13
+ 3u
11
+ 5u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
a
2
=
u
32
+ 7u
30
+ ··· + 2u
12
+ 1
−u
34
− 8u
32
+ ··· − 4u
6
− u
2
a
6
=
u
21
+ 4u
19
+ 9u
17
+ 12u
15
+ 12u
13
+ 10u
11
+ 9u
9
+ 6u
7
+ 3u
5
+ u
u
21
+ 5u
19
+ 13u
17
+ 20u
15
+ 20u
13
+ 13u
11
+ 7u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
43
− 4u
42
+ ··· + 12u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
44
− u
43
+ ··· − 2u + 1
c
2
u
44
+ 21u
43
+ ··· + 2u + 1
c
3
u
44
+ 5u
43
+ ··· + 82u + 13
c
4
, c
8
u
44
+ u
43
+ ··· + 2u + 1
c
6
u
44
+ u
43
+ ··· + 68u + 17
c
7
u
44
− u
43
+ ··· − 68u + 17
c
9
u
44
− 21u
43
+ ··· − 2u + 1
c
10
u
44
− 5u
43
+ ··· − 82u + 13
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
44
+ 21y
43
+ ··· + 2y + 1
c
2
, c
9
y
44
+ 5y
43
+ ··· + 6y + 1
c
3
, c
10
y
44
+ 9y
43
+ ··· + 5314y + 169
c
6
, c
7
y
44
− 11y
43
+ ··· − 4794y + 289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.219635 + 1.024160I
− 1.08070I − 60.10 + 1.298529I
u = 0.219635 − 1.024160I
1.08070I − 60.10 − 1.298529I
u = −0.651337 + 0.622116I
−3.71248 + 6.51845I −4.95829 − 6.88419I
u = −0.651337 − 0.622116I
−3.71248 − 6.51845I −4.95829 + 6.88419I
u = −0.567171 + 0.946930I
−2.75664 − 1.75570I −3.52773 + 0.85914I
u = −0.567171 − 0.946930I
−2.75664 + 1.75570I −3.52773 − 0.85914I
u = 0.525013 + 0.980467I
−0.14884 − 2.53826I 0.24501 + 3.05915I
u = 0.525013 − 0.980467I
−0.14884 + 2.53826I 0.24501 − 3.05915I
u = −0.254705 + 1.115020I
4.35508 − 1.04298I 6.65567 + 0.28795I
u = −0.254705 − 1.115020I
4.35508 + 1.04298I 6.65567 − 0.28795I
u = −0.662694 + 0.538070I
−5.06451 − 1.08737I −7.53766 + 0.51091I
u = −0.662694 − 0.538070I
−5.06451 + 1.08737I −7.53766 − 0.51091I
u = 0.603028 + 0.598100I
−1.27162 − 1.94114I −1.79245 + 3.31415I
u = 0.603028 − 0.598100I
−1.27162 + 1.94114I −1.79245 − 3.31415I
u = 0.228645 + 1.128370I
2.27286 + 5.97235I 3.25101 − 4.61402I
u = 0.228645 − 1.128370I
2.27286 − 5.97235I 3.25101 + 4.61402I
u = −0.323792 + 1.114600I
5.06451 + 1.08737I 7.53766 − 0.51091I
u = −0.323792 − 1.114600I
5.06451 − 1.08737I 7.53766 + 0.51091I
u = −0.570170 + 1.011790I
−3.67003 + 5.88530I −4.74516 − 6.36553I
u = −0.570170 − 1.011790I
−3.67003 − 5.88530I −4.74516 + 6.36553I
u = 0.764138 + 0.339961I
−2.30812 + 8.68200I −3.24304 − 6.31705I
u = 0.764138 − 0.339961I
−2.30812 − 8.68200I −3.24304 + 6.31705I
u = 0.358424 + 1.122990I
3.67003 − 5.88530I 4.74516 + 6.36553I
u = 0.358424 − 1.122990I
3.67003 + 5.88530I 4.74516 − 6.36553I
u = 0.721497 + 0.387567I
−4.35508 + 1.04298I −6.65567 − 0.28795I
u = 0.721497 − 0.387567I
−4.35508 − 1.04298I −6.65567 + 0.28795I
u = −0.737315 + 0.329710I
− 3.75579I 0. + 2.66459I
u = −0.737315 − 0.329710I
3.75579I 0. − 2.66459I
u = 0.494931 + 1.113460I
2.75664 − 1.75570I 3.52773 + 0.85914I
u = 0.494931 − 1.113460I
2.75664 + 1.75570I 3.52773 − 0.85914I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.523186 + 1.116830I
3.71248 + 6.51845I 4.95829 − 6.88419I
u = −0.523186 − 1.116830I
3.71248 − 6.51845I 4.95829 + 6.88419I
u = 0.568139 + 1.097600I
−2.27286 − 5.97235I −3.25101 + 4.61402I
u = 0.568139 − 1.097600I
−2.27286 + 5.97235I −3.25101 − 4.61402I
u = 0.326591 + 0.684448I
− 1.50871I 0. + 4.89247I
u = 0.326591 − 0.684448I
1.50871I 0. − 4.89247I
u = −0.560153 + 1.120390I
2.30812 + 8.68200I 3.24304 − 6.31705I
u = −0.560153 − 1.120390I
2.30812 − 8.68200I 3.24304 + 6.31705I
u = 0.570711 + 1.124900I
− 13.7161I 0. + 10.01278I
u = 0.570711 − 1.124900I
13.7161I 0. − 10.01278I
u = −0.663842 + 0.251119I
1.27162 − 1.94114I 1.79245 + 3.31415I
u = −0.663842 − 0.251119I
1.27162 + 1.94114I 1.79245 − 3.31415I
u = 0.633616 + 0.150714I
0.14884 − 2.53826I −0.24501 + 3.05915I
u = 0.633616 − 0.150714I
0.14884 + 2.53826I −0.24501 − 3.05915I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
44
− u
43
+ ··· − 2u + 1
c
2
u
44
+ 21u
43
+ ··· + 2u + 1
c
3
u
44
+ 5u
43
+ ··· + 82u + 13
c
4
, c
8
u
44
+ u
43
+ ··· + 2u + 1
c
6
u
44
+ u
43
+ ··· + 68u + 17
c
7
u
44
− u
43
+ ··· − 68u + 17
c
9
u
44
− 21u
43
+ ··· − 2u + 1
c
10
u
44
− 5u
43
+ ··· − 82u + 13
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
8
y
44
+ 21y
43
+ ··· + 2y + 1
c
2
, c
9
y
44
+ 5y
43
+ ··· + 6y + 1
c
3
, c
10
y
44
+ 9y
43
+ ··· + 5314y + 169
c
6
, c
7
y
44
− 11y
43
+ ··· − 4794y + 289
8
