10
35
(K10a
23
)
A knot diagram
1
Linearized knot diagam
6 10 2 8 7 1 5 4 3 9
Solving Sequence
1,7
6 2 5 8 4 9 3 10
c
6
c
1
c
5
c
7
c
4
c
8
c
3
c
10
c
2
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
+ u
23
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 24 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
24
+ u
23
+ · · · + 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
2
=
−u
u
3
+ u
a
5
=
u
2
+ 1
−u
2
a
8
=
u
4
+ u
2
+ 1
−u
4
a
4
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
9
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
8
− 2u
4
a
3
=
u
10
+ u
8
+ 4u
6
+ 3u
4
+ 3u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 6u
6
− 3u
4
− 2u
2
a
10
=
u
17
+ 2u
15
+ 7u
13
+ 10u
11
+ 15u
9
+ 14u
7
+ 10u
5
+ 4u
3
+ u
−u
17
− u
15
− 5u
13
− 4u
11
− 7u
9
− 4u
7
− 2u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
23
− 8u
21
+ 4u
20
− 36u
19
+ 8u
18
− 56u
17
+ 32u
16
− 116u
15
+ 44u
14
− 136u
13
+
80u
12
− 160u
11
+ 68u
10
− 132u
9
+ 64u
8
− 84u
7
+ 20u
6
− 48u
5
+ 4u
4
− 8u
3
− 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
24
+ u
23
+ ··· + 2u + 1
c
2
, c
9
u
24
+ u
23
+ ··· − 2u + 1
c
3
, c
10
u
24
+ 9u
23
+ ··· + 4u + 1
c
4
, c
5
, c
7
c
8
u
24
− 5u
23
+ ··· − 4u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
24
+ 5y
23
+ ··· + 4y + 1
c
2
, c
9
y
24
+ 9y
23
+ ··· + 4y + 1
c
3
, c
10
y
24
+ 13y
23
+ ··· + 44y + 1
c
4
, c
5
, c
7
c
8
y
24
+ 29y
23
+ ··· + 20y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.438618 + 0.887955I
1.66329 + 2.08350I 4.24893 − 3.59251I
u = −0.438618 − 0.887955I
1.66329 − 2.08350I 4.24893 + 3.59251I
u = 0.500467 + 0.918869I
0.78944 − 7.34378I 2.03585 + 8.70536I
u = 0.500467 − 0.918869I
0.78944 + 7.34378I 2.03585 − 8.70536I
u = 0.598969 + 0.738905I
−3.49325 − 2.24409I −5.16388 + 4.25877I
u = 0.598969 − 0.738905I
−3.49325 + 2.24409I −5.16388 − 4.25877I
u = −0.039909 + 0.910777I
3.76737 + 2.61939I 8.11481 − 3.60921I
u = −0.039909 − 0.910777I
3.76737 − 2.61939I 8.11481 + 3.60921I
u = 0.638378 + 0.466853I
−0.63403 + 3.08008I −2.04297 − 2.82964I
u = 0.638378 − 0.466853I
−0.63403 − 3.08008I −2.04297 + 2.82964I
u = 0.883157 + 0.890417I
−6.63583 − 1.57218I 0.12166 + 2.29522I
u = 0.883157 − 0.890417I
−6.63583 + 1.57218I 0.12166 − 2.29522I
u = −0.906724 + 0.884305I
−8.32116 − 3.84160I −2.22402 + 2.38554I
u = −0.906724 − 0.884305I
−8.32116 + 3.84160I −2.22402 − 2.38554I
u = 0.859271 + 0.947484I
−6.45491 − 4.87894I 0.44407 + 2.58342I
u = 0.859271 − 0.947484I
−6.45491 + 4.87894I 0.44407 − 2.58342I
u = −0.895419 + 0.930518I
−12.40930 + 3.30322I −5.60088 − 2.43434I
u = −0.895419 − 0.930518I
−12.40930 − 3.30322I −5.60088 + 2.43434I
u = −0.868488 + 0.965452I
−8.06054 + 10.39450I −1.68269 − 7.07233I
u = −0.868488 − 0.965452I
−8.06054 − 10.39450I −1.68269 + 7.07233I
u = −0.320922 + 0.618972I
0.204139 + 1.110190I 3.08627 − 5.87957I
u = −0.320922 − 0.618972I
0.204139 − 1.110190I 3.08627 + 5.87957I
u = −0.510161 + 0.301021I
0.10636 + 1.48443I −1.33713 − 3.68159I
u = −0.510161 − 0.301021I
0.10636 − 1.48443I −1.33713 + 3.68159I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
24
+ u
23
+ ··· + 2u + 1
c
2
, c
9
u
24
+ u
23
+ ··· − 2u + 1
c
3
, c
10
u
24
+ 9u
23
+ ··· + 4u + 1
c
4
, c
5
, c
7
c
8
u
24
− 5u
23
+ ··· − 4u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
24
+ 5y
23
+ ··· + 4y + 1
c
2
, c
9
y
24
+ 9y
23
+ ··· + 4y + 1
c
3
, c
10
y
24
+ 13y
23
+ ··· + 44y + 1
c
4
, c
5
, c
7
c
8
y
24
+ 29y
23
+ ··· + 20y + 1
7
