10
9
(K10a
110
)
A knot diagram
1
Linearized knot diagam
7 9 8 2 10 1 3 4 5 6
Solving Sequence
6,10
1 7 2 5 4 9 3 8
c
10
c
6
c
1
c
5
c
4
c
9
c
2
c
8
c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
− 2u
17
+ ··· − u + 1i
I
u
2
= hu + 1i
* 2 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
18
− 2u
17
− 10u
16
+ 21u
15
+ 37u
14
− 85u
13
− 59u
12
+ 166u
11
+
27u
10
− 160u
9
+ 30u
8
+ 65u
7
− 39u
6
+ 5u
5
+ 9u
4
− 7u
3
+ 2u
2
− u + 1i
(i) Arc colorings
a
6
=
0
u
a
10
=
1
0
a
1
=
1
u
2
a
7
=
−u
−u
3
+ u
a
2
=
−u
2
+ 1
−u
4
+ 2u
2
a
5
=
u
u
a
4
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
9
=
−u
2
+ 1
−u
2
a
3
=
−u
8
+ 5u
6
− 7u
4
+ 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
+ 2u
2
a
8
=
−2u
17
+ u
16
+ ··· − u + 2
−3u
17
+ u
16
+ ··· + 3u
2
+ 2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
15
+40u
13
−152u
11
+4u
10
+272u
9
−28u
8
−232u
7
+64u
6
+84u
5
−52u
4
+12u
2
−4u−2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
, c
10
u
18
− 2u
17
+ ··· − u + 1
c
2
u
18
− 3u
17
+ ··· + 3u − 3
c
3
, c
7
, c
8
u
18
− 8u
16
+ ··· − u + 1
c
4
u
18
− 4u
17
+ ··· − 5u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
, c
10
y
18
− 24y
17
+ ··· + 3y + 1
c
2
y
18
+ 3y
17
+ ··· − 39y + 9
c
3
, c
7
, c
8
y
18
− 16y
17
+ ··· + 3y + 1
c
4
y
18
+ 22y
16
+ ··· − 65y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972680 + 0.237177I
−3.70552 − 3.19755I −8.61366 + 5.32391I
u = 0.972680 − 0.237177I
−3.70552 + 3.19755I −8.61366 − 5.32391I
u = −0.965445 + 0.329507I
1.32984 + 6.64718I −3.24506 − 6.19689I
u = −0.965445 − 0.329507I
1.32984 − 6.64718I −3.24506 + 6.19689I
u = −0.884294
−1.71487 −4.98730
u = 0.572262 + 0.347341I
3.49531 + 0.56492I −0.70794 + 1.84066I
u = 0.572262 − 0.347341I
3.49531 − 0.56492I −0.70794 − 1.84066I
u = 0.158501 + 0.549521I
4.78286 − 3.66002I 2.48971 + 4.64953I
u = 0.158501 − 0.549521I
4.78286 + 3.66002I 2.48971 − 4.64953I
u = −0.184698 + 0.383796I
−0.150453 + 1.027520I −2.68106 − 6.45577I
u = −0.184698 − 0.383796I
−0.150453 − 1.027520I −2.68106 + 6.45577I
u = −1.62858
−3.96483 −2.02740
u = 1.70718 + 0.02414I
−11.15470 − 0.27346I −6.21894 − 1.07083I
u = 1.70718 − 0.02414I
−11.15470 + 0.27346I −6.21894 + 1.07083I
u = 1.70822 + 0.08549I
−8.11334 − 8.29410I −4.53964 + 4.66449I
u = 1.70822 − 0.08549I
−8.11334 + 8.29410I −4.53964 − 4.66449I
u = −1.71227 + 0.06112I
−13.25300 + 4.38839I −8.97609 − 3.55329I
u = −1.71227 − 0.06112I
−13.25300 − 4.38839I −8.97609 + 3.55329I
5
II. I
u
2
= hu + 1i
(i) Arc colorings
a
6
=
0
−1
a
10
=
1
0
a
1
=
1
1
a
7
=
1
0
a
2
=
0
1
a
5
=
−1
−1
a
4
=
−1
0
a
9
=
0
−1
a
3
=
0
1
a
8
=
1
−1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −6
6
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
c
6
, c
7
, c
8
c
9
, c
10
u + 1
c
2
u
c
4
u − 1
7
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
y −1
c
2
y
8
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
−1.64493 −6.00000
9
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
9
, c
10
(u + 1)(u
18
− 2u
17
+ ··· − u + 1)
c
2
u(u
18
− 3u
17
+ ··· + 3u − 3)
c
3
, c
7
, c
8
(u + 1)(u
18
− 8u
16
+ ··· − u + 1)
c
4
(u − 1)(u
18
− 4u
17
+ ··· − 5u − 1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
9
, c
10
(y −1)(y
18
− 24y
17
+ ··· + 3y + 1)
c
2
y(y
18
+ 3y
17
+ ··· − 39y + 9)
c
3
, c
7
, c
8
(y −1)(y
18
− 16y
17
+ ··· + 3y + 1)
c
4
(y −1)(y
18
+ 22y
16
+ ··· − 65y + 1)
11
