10
11
(K10a
116
)
A knot diagram
1
Linearized knot diagam
8 7 1 9 10 3 2 6 5 4
Solving Sequence
4,9
5 10 6 1 3 7 2 8
c
4
c
9
c
5
c
10
c
3
c
6
c
2
c
8
c
1
, c
7
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
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
1
=
u
3
− 2u
−u
3
+ u
a
3
=
u
6
− 3u
4
+ 2u
2
+ 1
−u
6
+ 2u
4
− u
2
a
7
=
−u
16
+ 7u
14
− 19u
12
+ 22u
10
− 3u
8
− 14u
6
+ 6u
4
+ 2u
2
+ 1
u
16
− 6u
14
+ 14u
12
− 14u
10
+ 2u
8
+ 6u
6
− 4u
4
+ 2u
2
a
2
=
−u
15
+ 6u
13
− 14u
11
+ 14u
9
− 2u
7
− 6u
5
+ 4u
3
− 2u
−u
17
+ 7u
15
− 19u
13
+ 22u
11
− 3u
9
− 14u
7
+ 6u
5
+ 2u
3
+ u
a
8
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
18
− 28u
16
+ 4u
15
+ 80u
14
− 24u
13
− 104u
12
+ 56u
11
+ 24u
10
−
52u
9
+ 88u
8
− 8u
7
− 76u
6
+ 44u
5
− 12u
4
− 12u
3
+ 24u
2
− 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
21
− u
20
+ ··· − u + 1
c
3
, c
8
, c
10
u
21
− 3u
20
+ ··· + 5u − 3
c
4
, 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
, c
2
, c
6
c
7
y
21
+ 23y
20
+ ··· − 5y −1
c
3
, c
8
, c
10
y
21
+ 19y
20
+ ··· + 7y −9
c
4
, c
5
, c
9
y
21
− 17y
20
+ ··· − 5y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.086113 + 0.839589I
−1.10589 − 5.00460I −1.84652 + 3.34739I
u = 0.086113 − 0.839589I
−1.10589 + 5.00460I −1.84652 − 3.34739I
u = −0.027961 + 0.833462I
5.50220 + 2.11040I 1.91245 − 3.38979I
u = −0.027961 − 0.833462I
5.50220 − 2.11040I 1.91245 + 3.38979I
u = −1.18427
−2.46649 −1.74060
u = 1.178890 + 0.386444I
−4.45765 + 0.58948I −5.04554 + 0.27365I
u = 1.178890 − 0.386444I
−4.45765 − 0.58948I −5.04554 − 0.27365I
u = 1.281130 + 0.111157I
−4.56809 − 2.45481I −8.82608 + 5.13736I
u = 1.281130 − 0.111157I
−4.56809 + 2.45481I −8.82608 − 5.13736I
u = −1.245840 + 0.377074I
1.73723 + 2.23968I −1.50234 − 0.17506I
u = −1.245840 − 0.377074I
1.73723 − 2.23968I −1.50234 + 0.17506I
u = 1.291060 + 0.376139I
1.39230 − 6.45770I −2.54644 + 6.39068I
u = 1.291060 − 0.376139I
1.39230 + 6.45770I −2.54644 − 6.39068I
u = 0.430693 + 0.459647I
−6.58253 − 1.66521I −5.55767 + 3.90994I
u = 0.430693 − 0.459647I
−6.58253 + 1.66521I −5.55767 − 3.90994I
u = −1.367930 + 0.126822I
−12.19550 + 3.59224I −10.42606 − 3.20950I
u = −1.367930 − 0.126822I
−12.19550 − 3.59224I −10.42606 + 3.20950I
u = −1.328510 + 0.374285I
−5.53903 + 9.37044I −6.11943 − 5.65030I
u = −1.328510 − 0.374285I
−5.53903 − 9.37044I −6.11943 + 5.65030I
u = −0.205500 + 0.333164I
−0.091241 + 0.864455I −2.17207 − 8.05526I
u = −0.205500 − 0.333164I
−0.091241 − 0.864455I −2.17207 + 8.05526I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
7
u
21
− u
20
+ ··· − u + 1
c
3
, c
8
, c
10
u
21
− 3u
20
+ ··· + 5u − 3
c
4
, c
5
, c
9
u
21
+ u
20
+ ··· + u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
6
c
7
y
21
+ 23y
20
+ ··· − 5y −1
c
3
, c
8
, c
10
y
21
+ 19y
20
+ ··· + 7y −9
c
4
, c
5
, c
9
y
21
− 17y
20
+ ··· − 5y −1
7
