9
21
(K9a
21
)
A knot diagram
1
Linearized knot diagam
4 7 8 6 9 3 2 1 5
Solving Sequence
2,8
7 3 4 1 9 6 5
c
7
c
2
c
3
c
1
c
8
c
6
c
5
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
21
+ u
20
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 21 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
21
+ u
20
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
7
− 4u
5
− 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
9
=
u
14
+ 7u
12
+ 18u
10
+ 19u
8
+ 4u
6
− 4u
4
+ 1
u
14
+ 6u
12
+ 13u
10
+ 10u
8
− 2u
6
− 4u
4
+ u
2
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
5
=
u
9
+ 4u
7
+ 5u
5
+ 2u
3
+ u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
a
5
=
u
9
+ 4u
7
+ 5u
5
+ 2u
3
+ u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
19
+ 4u
18
+ 36u
17
+ 32u
16
+ 132u
15
+ 100u
14
+ 244u
13
+
140u
12
+ 216u
11
+ 52u
10
+ 40u
9
− 68u
8
− 56u
7
− 52u
6
+ 12u
4
+ 36u
3
+ 12u
2
+ 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
21
+ 5u
20
+ ··· − 11u − 3
c
2
, c
6
, c
7
u
21
+ u
20
+ ··· − u − 1
c
3
u
21
− u
20
+ ··· − 3u − 1
c
4
, c
8
u
21
+ 7u
20
+ ··· + 3u − 1
c
5
, c
9
u
21
− u
20
+ ··· + u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 3y
20
+ ··· − 41y −9
c
2
, c
6
, c
7
y
21
+ 19y
20
+ ··· + 3y −1
c
3
y
21
− y
20
+ ··· + 3y −1
c
4
, c
8
y
21
+ 15y
20
+ ··· + 27y −1
c
5
, c
9
y
21
+ 7y
20
+ ··· + 3y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.199184 + 0.953331I
1.36988 + 2.68588I 5.85070 − 3.67518I
u = 0.199184 − 0.953331I
1.36988 − 2.68588I 5.85070 + 3.67518I
u = −0.268883 + 0.739769I
1.15989 + 2.73152I 4.80842 − 2.00184I
u = −0.268883 − 0.739769I
1.15989 − 2.73152I 4.80842 + 2.00184I
u = −0.721828 + 0.253446I
2.90434 − 6.51836I 7.49661 + 6.69162I
u = −0.721828 − 0.253446I
2.90434 + 6.51836I 7.49661 − 6.69162I
u = 0.708881 + 0.196468I
3.65968 + 0.90110I 9.44354 − 1.25880I
u = 0.708881 − 0.196468I
3.65968 − 0.90110I 9.44354 + 1.25880I
u = 0.161237 + 1.327480I
−3.39772 + 2.26276I 4.12423 − 3.11409I
u = 0.161237 − 1.327480I
−3.39772 − 2.26276I 4.12423 + 3.11409I
u = −0.520195 + 0.340511I
−2.02154 − 1.59690I 0.86726 + 4.73829I
u = −0.520195 − 0.340511I
−2.02154 + 1.59690I 0.86726 − 4.73829I
u = 0.280467 + 1.374360I
−1.32092 + 4.48385I 4.56586 − 2.47352I
u = 0.280467 − 1.374360I
−1.32092 − 4.48385I 4.56586 + 2.47352I
u = −0.085311 + 1.403890I
−5.14411 + 1.80763I −0.25907 − 2.73625I
u = −0.085311 − 1.403890I
−5.14411 − 1.80763I −0.25907 + 2.73625I
u = −0.20569 + 1.41170I
−7.58755 − 4.29720I −2.75143 + 3.93304I
u = −0.20569 − 1.41170I
−7.58755 + 4.29720I −2.75143 − 3.93304I
u = −0.28719 + 1.40273I
−2.37086 − 10.18330I 2.74618 + 7.21296I
u = −0.28719 − 1.40273I
−2.37086 + 10.18330I 2.74618 − 7.21296I
u = 0.478663
0.823807 12.2150
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
21
+ 5u
20
+ ··· − 11u − 3
c
2
, c
6
, c
7
u
21
+ u
20
+ ··· − u − 1
c
3
u
21
− u
20
+ ··· − 3u − 1
c
4
, c
8
u
21
+ 7u
20
+ ··· + 3u − 1
c
5
, c
9
u
21
− u
20
+ ··· + u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
21
+ 3y
20
+ ··· − 41y −9
c
2
, c
6
, c
7
y
21
+ 19y
20
+ ··· + 3y −1
c
3
y
21
− y
20
+ ··· + 3y −1
c
4
, c
8
y
21
+ 15y
20
+ ··· + 27y −1
c
5
, c
9
y
21
+ 7y
20
+ ··· + 3y −1
7
