10
37
(K10a
49
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 4 10 3 8 7
Solving Sequence
3,8
9 4 10 7 1 2 6 5
c
8
c
3
c
9
c
7
c
10
c
2
c
6
c
5
c
1
, c
4
Ideals for irreducible components
2
of X
par
I
u
1
= hu
26
− u
25
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 26 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
26
− u
25
+ · · · + u + 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
2
a
7
=
u
4
− u
2
+ 1
u
4
a
1
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
2
=
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
6
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
10
+ 2u
8
− 3u
6
+ 4u
4
− u
2
a
5
=
u
15
− 2u
13
+ 6u
11
− 8u
9
+ 10u
7
− 8u
5
+ 4u
3
−u
17
+ 3u
15
− 7u
13
+ 12u
11
− 13u
9
+ 12u
7
− 6u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
25
+ 16u
23
− 4u
22
− 52u
21
+ 12u
20
+ 116u
19
− 36u
18
−
204u
17
+ 64u
16
+ 292u
15
− 96u
14
− 328u
13
+ 104u
12
+ 296u
11
− 88u
10
− 200u
9
+ 40u
8
+
88u
7
− 8u
6
− 8u
5
− 20u
4
− 8u
3
+ 12u
2
+ 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
26
+ u
25
+ ··· − u + 1
c
2
, c
4
, c
6
u
26
+ 7u
25
+ ··· + 3u + 1
c
3
, c
8
u
26
− u
25
+ ··· + u + 1
c
7
, c
9
, c
10
u
26
− 7u
25
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
y
26
− 7y
25
+ ··· − 3y + 1
c
2
, c
4
, c
6
c
7
, c
9
, c
10
y
26
+ 25y
25
+ ··· + 13y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.012160 + 0.254718I
7.03067 + 0.01867I 5.98123 − 1.03882I
u = 1.012160 − 0.254718I
7.03067 − 0.01867I 5.98123 + 1.03882I
u = −1.013780 + 0.289330I
6.82471 − 6.16497I 5.29314 + 6.39075I
u = −1.013780 − 0.289330I
6.82471 + 6.16497I 5.29314 − 6.39075I
u = −0.813977 + 0.362129I
− 3.36877I 0. + 8.60580I
u = −0.813977 − 0.362129I
3.36877I 0. − 8.60580I
u = −0.773091 + 0.826946I
− 1.11937I 0. + 2.31583I
u = −0.773091 − 0.826946I
1.11937I 0. − 2.31583I
u = 0.783473 + 0.854699I
−0.63001 − 4.85595I −1.10716 + 2.80733I
u = 0.783473 − 0.854699I
−0.63001 + 4.85595I −1.10716 − 2.80733I
u = −0.887854 + 0.783648I
−3.75047 − 2.94952I 0.57746 + 2.74210I
u = −0.887854 − 0.783648I
−3.75047 + 2.94952I 0.57746 − 2.74210I
u = 0.863693 + 0.835096I
−7.03067 − 0.01867I −5.98123 + 1.03882I
u = 0.863693 − 0.835096I
−7.03067 + 0.01867I −5.98123 − 1.03882I
u = 0.779118 + 0.130510I
1.314850 + 0.335766I 6.85384 − 0.55767I
u = 0.779118 − 0.130510I
1.314850 − 0.335766I 6.85384 + 0.55767I
u = 0.929921 + 0.812975I
−6.82471 + 6.16497I −5.29314 − 6.39075I
u = 0.929921 − 0.812975I
−6.82471 − 6.16497I −5.29314 + 6.39075I
u = −0.979820 + 0.768887I
0.63001 − 4.85595I 1.10716 + 2.80733I
u = −0.979820 − 0.768887I
0.63001 + 4.85595I 1.10716 − 2.80733I
u = 0.987090 + 0.785195I
10.9658I 0. − 7.61359I
u = 0.987090 − 0.785195I
− 10.9658I 0. + 7.61359I
u = −0.034282 + 0.657607I
3.75047 + 2.94952I −0.57746 − 2.74210I
u = −0.034282 − 0.657607I
3.75047 − 2.94952I −0.57746 + 2.74210I
u = −0.352654 + 0.410519I
−1.314850 + 0.335766I −6.85384 − 0.55767I
u = −0.352654 − 0.410519I
−1.314850 − 0.335766I −6.85384 + 0.55767I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
26
+ u
25
+ ··· − u + 1
c
2
, c
4
, c
6
u
26
+ 7u
25
+ ··· + 3u + 1
c
3
, c
8
u
26
− u
25
+ ··· + u + 1
c
7
, c
9
, c
10
u
26
− 7u
25
+ ··· − 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
y
26
− 7y
25
+ ··· − 3y + 1
c
2
, c
4
, c
6
c
7
, c
9
, c
10
y
26
+ 25y
25
+ ··· + 13y + 1
7
