10
34
(K10a
19
)
A knot diagram
1
Linearized knot diagam
4 8 5 2 1 10 9 3 7 6
Solving Sequence
1,4
2 5 6 3 10 7 9 8
c
1
c
4
c
5
c
3
c
10
c
6
c
9
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
− u
17
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 18 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
18
− u
17
− 5u
16
+ 6u
15
+ 10u
14
− 15u
13
− 5u
12
+ 16u
11
− 11u
10
+
u
9
+ 17u
8
− 18u
7
− 2u
6
+ 12u
5
− 8u
4
+ 2u
3
+ 3u
2
− 3u + 1i
(i) Arc colorings
a
1
=
1
0
a
4
=
0
u
a
2
=
1
u
2
a
5
=
−u
−u
3
+ u
a
6
=
−u
3
−u
3
+ u
a
3
=
u
3
u
5
− u
3
+ u
a
10
=
u
6
− u
4
+ 1
u
6
− 2u
4
+ u
2
a
7
=
−u
9
+ 2u
7
− u
5
− 2u
3
+ u
−u
9
+ 3u
7
− 3u
5
+ u
a
9
=
u
12
− 3u
10
+ 3u
8
+ 2u
6
− 4u
4
+ u
2
+ 1
u
12
− 4u
10
+ 6u
8
− 2u
6
− 3u
4
+ 2u
2
a
8
=
−u
15
+ 4u
13
− 6u
11
+ 8u
7
− 6u
5
− 2u
3
+ 2u
−u
15
+ 5u
13
− 10u
11
+ 7u
9
+ 4u
7
− 8u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
16
− 20u
14
+ 4u
13
+ 44u
12
− 16u
11
− 36u
10
+ 28u
9
− 16u
8
−
12u
7
+ 56u
6
− 16u
5
− 24u
4
+ 24u
3
− 8u
2
+ 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
18
− u
17
+ ··· − 3u + 1
c
2
, c
8
u
18
+ u
17
+ ··· + u + 1
c
3
u
18
+ 11u
17
+ ··· + 3u + 1
c
5
, c
6
, c
7
c
9
, c
10
u
18
− 3u
17
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
18
− 11y
17
+ ··· − 3y + 1
c
2
, c
8
y
18
− 3y
17
+ ··· − 3y + 1
c
3
y
18
− 7y
17
+ ··· + y + 1
c
5
, c
6
, c
7
c
9
, c
10
y
18
+ 25y
17
+ ··· + 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.909285 + 0.387234I
0.00395 − 3.50386I 4.01768 + 8.20647I
u = 0.909285 − 0.387234I
0.00395 + 3.50386I 4.01768 − 8.20647I
u = −0.949796 + 0.161768I
−1.67574 + 0.60080I −4.05524 − 0.52802I
u = −0.949796 − 0.161768I
−1.67574 − 0.60080I −4.05524 + 0.52802I
u = 0.012693 + 0.930781I
−12.31670 + 3.38380I 0.20360 − 2.27447I
u = 0.012693 − 0.930781I
−12.31670 − 3.38380I 0.20360 + 2.27447I
u = −1.166330 + 0.369488I
−5.99819 + 1.29789I −3.32252 − 0.68135I
u = −1.166330 − 0.369488I
−5.99819 − 1.29789I −3.32252 + 0.68135I
u = 1.143080 + 0.442338I
−5.44176 − 6.61296I −1.60438 + 7.00860I
u = 1.143080 − 0.442338I
−5.44176 + 6.61296I −1.60438 − 7.00860I
u = 0.082055 + 0.692654I
−2.41237 + 2.42038I 1.45127 − 3.59982I
u = 0.082055 − 0.692654I
−2.41237 − 2.42038I 1.45127 + 3.59982I
u = 1.279130 + 0.484277I
−16.2022 − 8.4223I −2.83851 + 5.16445I
u = 1.279130 − 0.484277I
−16.2022 + 8.4223I −2.83851 − 5.16445I
u = −1.285130 + 0.469694I
−16.3133 + 1.5857I −3.06627 − 0.65832I
u = −1.285130 − 0.469694I
−16.3133 − 1.5857I −3.06627 + 0.65832I
u = 0.475010 + 0.326439I
1.138660 + 0.137643I 9.21435 − 0.51404I
u = 0.475010 − 0.326439I
1.138660 − 0.137643I 9.21435 + 0.51404I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
18
− u
17
+ ··· − 3u + 1
c
2
, c
8
u
18
+ u
17
+ ··· + u + 1
c
3
u
18
+ 11u
17
+ ··· + 3u + 1
c
5
, c
6
, c
7
c
9
, c
10
u
18
− 3u
17
+ ··· − 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
18
− 11y
17
+ ··· − 3y + 1
c
2
, c
8
y
18
− 3y
17
+ ··· − 3y + 1
c
3
y
18
− 7y
17
+ ··· + y + 1
c
5
, c
6
, c
7
c
9
, c
10
y
18
+ 25y
17
+ ··· + 9y + 1
7
