10
13
(K10a
54
)
A knot diagram
1
Linearized knot diagam
9 4 7 1 10 8 3 2 6 5
Solving Sequence
6,9
10 5 1 2 4 8 7 3
c
9
c
5
c
10
c
1
c
4
c
8
c
6
c
3
c
2
, c
7
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
6
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
2
=
u
4
+ 3u
2
+ 1
u
4
+ 2u
2
a
4
=
u
3
+ 2u
u
5
+ 3u
3
+ u
a
8
=
u
8
+ 5u
6
+ 7u
4
+ 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
7
=
−u
17
− 10u
15
− 39u
13
− 74u
11
− 71u
9
− 38u
7
− 18u
5
− 4u
3
− u
−u
17
− 9u
15
− 31u
13
− 50u
11
− 37u
9
− 12u
7
− 4u
5
+ u
a
3
=
u
12
+ 7u
10
+ 17u
8
+ 16u
6
+ 6u
4
+ 5u
2
+ 1
u
14
+ 8u
12
+ 23u
10
+ 28u
8
+ 14u
6
+ 6u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
24
+ 4u
23
+ 56u
22
+ 52u
21
+ 332u
20
+ 284u
19
+ 1080u
18
+
844u
17
+ 2096u
16
+ 1484u
15
+ 2508u
14
+ 1596u
13
+ 1940u
12
+ 1096u
11
+ 1112u
10
+
540u
9
+ 504u
8
+ 212u
7
+ 132u
6
+ 60u
5
+ 48u
4
+ 12u
3
+ 16u
2
+ 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
26
+ 5u
25
+ ··· + 5u + 3
c
2
, c
6
u
26
+ 9u
25
+ ··· + 5u + 1
c
3
, c
7
u
26
− u
25
+ ··· − u + 1
c
4
, c
5
, c
9
c
10
u
26
− u
25
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
26
+ 13y
25
+ ··· + 161y + 9
c
2
, c
6
y
26
+ 17y
25
+ ··· + 29y + 1
c
3
, c
7
y
26
+ 9y
25
+ ··· + 5y + 1
c
4
, c
5
, c
9
c
10
y
26
+ 29y
25
+ ··· + 5y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.557205 + 0.605601I
−0.14856 + 7.92757I −1.52051 − 8.33110I
u = −0.557205 − 0.605601I
−0.14856 − 7.92757I −1.52051 + 8.33110I
u = 0.063283 + 0.808616I
3.72335 − 2.64715I 4.54618 + 3.67555I
u = 0.063283 − 0.808616I
3.72335 + 2.64715I 4.54618 − 3.67555I
u = 0.506771 + 0.602442I
0.97512 − 2.50037I 0.62782 + 3.68649I
u = 0.506771 − 0.602442I
0.97512 + 2.50037I 0.62782 − 3.68649I
u = −0.565256 + 0.486664I
−4.58704 + 1.94179I −7.39486 − 3.84898I
u = −0.565256 − 0.486664I
−4.58704 − 1.94179I −7.39486 + 3.84898I
u = −0.588033 + 0.339866I
−0.92248 − 4.00629I −3.77829 + 2.28167I
u = −0.588033 − 0.339866I
−0.92248 + 4.00629I −3.77829 − 2.28167I
u = 0.489623 + 0.284759I
0.114247 − 1.005510I −2.42231 + 3.62739I
u = 0.489623 − 0.284759I
0.114247 + 1.005510I −2.42231 − 3.62739I
u = −0.08778 + 1.44888I
4.66701 − 1.77746I −0.37085 + 2.67865I
u = −0.08778 − 1.44888I
4.66701 + 1.77746I −0.37085 − 2.67865I
u = 0.304550 + 0.390095I
−0.062024 − 0.992541I −1.03716 + 6.67512I
u = 0.304550 − 0.390095I
−0.062024 + 0.992541I −1.03716 − 6.67512I
u = −0.15393 + 1.51610I
2.02080 + 4.47678I −3.30340 − 3.58620I
u = −0.15393 − 1.51610I
2.02080 − 4.47678I −3.30340 + 3.58620I
u = 0.09394 + 1.52190I
6.42783 − 2.46970I 3.58807 + 2.77943I
u = 0.09394 − 1.52190I
6.42783 + 2.46970I 3.58807 − 2.77943I
u = 0.14965 + 1.56671I
8.26058 − 4.90123I 3.70149 + 2.20839I
u = 0.14965 − 1.56671I
8.26058 + 4.90123I 3.70149 − 2.20839I
u = −0.16684 + 1.56649I
7.11908 + 10.57850I 1.76076 − 6.94484I
u = −0.16684 − 1.56649I
7.11908 − 10.57850I 1.76076 + 6.94484I
u = 0.01123 + 1.60251I
11.89050 − 2.88146I 5.60306 + 2.87824I
u = 0.01123 − 1.60251I
11.89050 + 2.88146I 5.60306 − 2.87824I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
26
+ 5u
25
+ ··· + 5u + 3
c
2
, c
6
u
26
+ 9u
25
+ ··· + 5u + 1
c
3
, c
7
u
26
− u
25
+ ··· − u + 1
c
4
, c
5
, c
9
c
10
u
26
− u
25
+ ··· + u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
26
+ 13y
25
+ ··· + 161y + 9
c
2
, c
6
y
26
+ 17y
25
+ ··· + 29y + 1
c
3
, c
7
y
26
+ 9y
25
+ ··· + 5y + 1
c
4
, c
5
, c
9
c
10
y
26
+ 29y
25
+ ··· + 5y + 1
7
