10
22
(K10a
112
)
A knot diagram
1
Linearized knot diagam
6 9 8 7 1 10 3 4 2 5
Solving Sequence
4,9
8 3 2 10 7 5 6 1
c
8
c
3
c
2
c
9
c
7
c
4
c
6
c
1
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
− u
23
+ ··· + 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 24 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
24
− u
23
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
8
=
1
−u
2
a
3
=
u
−u
3
+ u
a
2
=
−u
3
+ 2u
−u
3
+ u
a
10
=
u
6
− 3u
4
+ 2u
2
+ 1
u
6
− 2u
4
+ u
2
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
5
+ 2u
3
− u
u
7
− 3u
5
+ 2u
3
+ u
a
6
=
−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
1
=
u
18
− 7u
16
+ 20u
14
− 27u
12
+ 11u
10
+ 13u
8
− 14u
6
+ 3u
2
+ 1
−u
20
+ 8u
18
− 26u
16
+ 40u
14
− 19u
12
− 24u
10
+ 30u
8
− 9u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
21
+ 32u
19
+ 4u
18
− 108u
17
− 28u
16
+ 180u
15
+ 80u
14
− 104u
13
− 104u
12
−
120u
11
+ 24u
10
+ 216u
9
+ 88u
8
− 56u
7
− 76u
6
− 80u
5
− 12u
4
+ 36u
3
+ 24u
2
+ 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
u
24
+ u
23
+ ··· + 2u
2
+ 1
c
2
, c
4
, c
9
u
24
− 3u
23
+ ··· − 8u + 1
c
3
, c
7
, c
8
u
24
+ u
23
+ ··· + 2u
2
+ 1
c
6
u
24
− 3u
23
+ ··· + 20u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
y
24
− 23y
23
+ ··· + 4y + 1
c
2
, c
4
, c
9
y
24
+ 25y
23
+ ··· − 20y + 1
c
3
, c
7
, c
8
y
24
− 19y
23
+ ··· + 4y + 1
c
6
y
24
− 11y
23
+ ··· − 904y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.047552 + 0.882738I
12.21820 + 5.35992I 5.68286 − 3.17670I
u = −0.047552 − 0.882738I
12.21820 − 5.35992I 5.68286 + 3.17670I
u = 0.023946 + 0.850260I
5.90820 − 2.14805I 2.49248 + 3.24690I
u = 0.023946 − 0.850260I
5.90820 + 2.14805I 2.49248 − 3.24690I
u = −0.832524
3.20914 1.52540
u = 1.20293
−2.53343 −1.89060
u = −1.293390 + 0.128068I
−4.64383 + 2.66216I −8.07524 − 4.83074I
u = −1.293390 − 0.128068I
−4.64383 − 2.66216I −8.07524 + 4.83074I
u = −1.234200 + 0.427679I
8.55472 − 0.67393I 2.54072 − 0.18139I
u = −1.234200 − 0.427679I
8.55472 + 0.67393I 2.54072 + 0.18139I
u = −0.691969
3.21354 0.806220
u = 1.30821
−2.22926 −4.75390
u = 1.252440 + 0.391136I
2.10558 − 2.30642I −0.925091 + 0.098908I
u = 1.252440 − 0.391136I
2.10558 + 2.30642I −0.925091 − 0.098908I
u = 1.317160 + 0.196052I
−0.01480 − 5.67994I −2.05445 + 5.89837I
u = 1.317160 − 0.196052I
−0.01480 + 5.67994I −2.05445 − 5.89837I
u = −1.291330 + 0.388939I
1.81113 + 6.59660I −1.74384 − 6.15928I
u = −1.291330 − 0.388939I
1.81113 − 6.59660I −1.74384 + 6.15928I
u = 1.311950 + 0.407404I
7.97363 − 9.98187I 1.73153 + 5.91019I
u = 1.311950 − 0.407404I
7.97363 + 9.98187I 1.73153 − 5.91019I
u = −0.240904 + 0.566295I
4.81497 + 3.00632I 4.21158 − 5.20782I
u = −0.240904 − 0.566295I
4.81497 − 3.00632I 4.21158 + 5.20782I
u = 0.208545 + 0.356460I
−0.079333 − 0.910145I −1.70410 + 7.59691I
u = 0.208545 − 0.356460I
−0.079333 + 0.910145I −1.70410 − 7.59691I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
10
u
24
+ u
23
+ ··· + 2u
2
+ 1
c
2
, c
4
, c
9
u
24
− 3u
23
+ ··· − 8u + 1
c
3
, c
7
, c
8
u
24
+ u
23
+ ··· + 2u
2
+ 1
c
6
u
24
− 3u
23
+ ··· + 20u − 7
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
10
y
24
− 23y
23
+ ··· + 4y + 1
c
2
, c
4
, c
9
y
24
+ 25y
23
+ ··· − 20y + 1
c
3
, c
7
, c
8
y
24
− 19y
23
+ ··· + 4y + 1
c
6
y
24
− 11y
23
+ ··· − 904y + 49
7
