9
15
(K9a
10
)
A knot diagram
1
Linearized knot diagam
5 4 8 2 7 9 3 1 6
Solving Sequence
4,8
3 2 5 1 9 7 6
c
3
c
2
c
4
c
1
c
8
c
7
c
6
c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
19
+ u
18
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 19 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
19
+ u
18
− 2u
17
− 3u
16
+ 6u
15
+ 8u
14
− 8u
13
− 13u
12
+ 11u
11
+
17u
10
− 10u
9
− 15u
8
+ 8u
7
+ 10u
6
− 4u
5
− 2u
4
+ 3u
3
− u
2
+ 1i
(i) Arc colorings
a
4
=
1
0
a
8
=
0
u
a
3
=
1
u
2
a
2
=
−u
2
+ 1
u
2
a
5
=
u
4
− u
2
+ 1
−u
4
a
1
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
9
=
−u
13
+ 2u
11
− 5u
9
+ 6u
7
− 6u
5
+ 4u
3
− u
u
13
− u
11
+ 3u
9
− 2u
7
+ 2u
5
− u
3
+ u
a
7
=
−u
−u
3
+ u
a
6
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
u
10
− 2u
8
+ 3u
6
− 4u
4
+ u
2
a
6
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
u
10
− 2u
8
+ 3u
6
− 4u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
18
− 12u
16
− 4u
15
+ 32u
14
+ 8u
13
− 56u
12
− 20u
11
+ 72u
10
+
24u
9
− 76u
8
− 24u
7
+ 52u
6
+ 12u
5
− 24u
4
− 4u
3
+ 4u
2
− 8u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
19
− 5u
18
+ ··· + 2u − 1
c
3
, c
7
u
19
− u
18
+ ··· + u
2
− 1
c
5
, c
8
u
19
+ 7u
18
+ ··· + 2u − 1
c
6
, c
9
u
19
+ u
18
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
19
+ 19y
18
+ ··· + 10y −1
c
3
, c
7
y
19
− 5y
18
+ ··· + 2y −1
c
5
, c
8
y
19
+ 11y
18
+ ··· + 42y −1
c
6
, c
9
y
19
+ 7y
18
+ ··· + 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.964317 + 0.230449I
3.62212 − 0.16816I 10.16829 + 0.91431I
u = −0.964317 − 0.230449I
3.62212 + 0.16816I 10.16829 − 0.91431I
u = 0.978202 + 0.313897I
3.12958 + 5.52702I 8.42794 − 7.00248I
u = 0.978202 − 0.313897I
3.12958 − 5.52702I 8.42794 + 7.00248I
u = 0.820272 + 0.802988I
−2.83381 + 1.53005I 4.20605 − 2.54963I
u = 0.820272 − 0.802988I
−2.83381 − 1.53005I 4.20605 + 2.54963I
u = −0.809650 + 0.858173I
−4.41408 + 3.71612I 1.80100 − 2.45937I
u = −0.809650 − 0.858173I
−4.41408 − 3.71612I 1.80100 + 2.45937I
u = 0.635698 + 0.450549I
−1.41106 + 1.72326I 0.18035 − 5.18112I
u = 0.635698 − 0.450549I
−1.41106 − 1.72326I 0.18035 + 5.18112I
u = 0.949254 + 0.773576I
−2.43770 + 4.39903I 4.93348 − 2.80289I
u = 0.949254 − 0.773576I
−2.43770 − 4.39903I 4.93348 + 2.80289I
u = −0.903405 + 0.838368I
−8.30762 − 3.11880I −1.58624 + 2.69239I
u = −0.903405 − 0.838368I
−8.30762 + 3.11880I −1.58624 − 2.69239I
u = −0.975971 + 0.799116I
−3.89635 − 9.88550I 2.86128 + 7.31129I
u = −0.975971 − 0.799116I
−3.89635 + 9.88550I 2.86128 − 7.31129I
u = −0.667698
0.907373 11.4720
u = 0.103765 + 0.589022I
0.46836 − 2.32534I 2.27174 + 3.09456I
u = 0.103765 − 0.589022I
0.46836 + 2.32534I 2.27174 − 3.09456I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
u
19
− 5u
18
+ ··· + 2u − 1
c
3
, c
7
u
19
− u
18
+ ··· + u
2
− 1
c
5
, c
8
u
19
+ 7u
18
+ ··· + 2u − 1
c
6
, c
9
u
19
+ u
18
+ ··· + 2u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
y
19
+ 19y
18
+ ··· + 10y −1
c
3
, c
7
y
19
− 5y
18
+ ··· + 2y −1
c
5
, c
8
y
19
+ 11y
18
+ ··· + 42y −1
c
6
, c
9
y
19
+ 7y
18
+ ··· + 2y −1
7
