10
14
(K10a
33
)
A knot diagram
1
Linearized knot diagam
8 9 6 10 1 3 2 7 4 5
Solving Sequence
1,6
5 10 4 3 7 9 2 8
c
5
c
10
c
4
c
3
c
6
c
9
c
2
c
8
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
28
− u
27
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 28 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
28
− u
27
+ · · · − 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
10
=
u
−u
3
+ u
a
4
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
u
4
− 3u
2
+ 1
u
4
− 2u
2
a
7
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
9
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
2
=
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
a
8
=
u
21
− 12u
19
+ ··· − 8u
3
+ 3u
u
21
− 11u
19
+ ··· − 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
26
+ 60u
24
− 384u
22
− 4u
21
+ 1364u
20
+ 48u
19
− 2940u
18
−
236u
17
+ 4000u
16
+ 608u
15
−3604u
14
−884u
13
+ 2428u
12
+ 784u
11
−1376u
10
−560u
9
+
576u
8
+ 384u
7
− 180u
6
− 148u
5
+ 40u
4
+ 52u
3
− 4u
2
− 16u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
28
− u
27
+ ··· + u
2
− 1
c
2
u
28
+ u
27
+ ··· − u − 2
c
3
, c
6
u
28
− 5u
27
+ ··· + 20u − 7
c
4
, c
5
, c
9
c
10
u
28
− u
27
+ ··· − 2u − 1
c
8
u
28
+ 13u
27
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
28
+ 13y
27
+ ··· − 2y + 1
c
2
y
28
− 3y
27
+ ··· − 109y + 4
c
3
, c
6
y
28
+ 17y
27
+ ··· + 118y + 49
c
4
, c
5
, c
9
c
10
y
28
− 31y
27
+ ··· − 2y + 1
c
8
y
28
+ 5y
27
+ ··· − 26y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.586405 + 0.574893I
1.11175 + 8.20859I −6.53568 − 8.40980I
u = −0.586405 − 0.574893I
1.11175 − 8.20859I −6.53568 + 8.40980I
u = 0.543996 + 0.566433I
3.04585 − 3.16640I −3.13756 + 4.02500I
u = 0.543996 − 0.566433I
3.04585 + 3.16640I −3.13756 − 4.02500I
u = 0.755212 + 0.133146I
−3.40408 − 3.35246I −13.3032 + 5.3092I
u = 0.755212 − 0.133146I
−3.40408 + 3.35246I −13.3032 − 5.3092I
u = 0.430218 + 0.577744I
3.38107 − 0.75823I −1.91828 + 3.18448I
u = 0.430218 − 0.577744I
3.38107 + 0.75823I −1.91828 − 3.18448I
u = −0.567490 + 0.434707I
−1.58402 + 1.32970I −10.44616 − 3.85928I
u = −0.567490 − 0.434707I
−1.58402 − 1.32970I −10.44616 + 3.85928I
u = −0.376046 + 0.601172I
1.72778 − 4.19313I −4.61655 + 2.23475I
u = −0.376046 − 0.601172I
1.72778 + 4.19313I −4.61655 − 2.23475I
u = −0.561801
−0.921591 −10.5330
u = 1.45325 + 0.12481I
−4.10153 + 1.71282I −8.00356 − 2.41214I
u = 1.45325 − 0.12481I
−4.10153 − 1.71282I −8.00356 + 2.41214I
u = −1.48911 + 0.14533I
−2.88101 + 3.25978I −6.00000 − 3.24223I
u = −1.48911 − 0.14533I
−2.88101 − 3.25978I −6.00000 + 3.24223I
u = −1.54219 + 0.16548I
−3.89171 + 5.80125I −6.94144 − 3.19136I
u = −1.54219 − 0.16548I
−3.89171 − 5.80125I −6.94144 + 3.19136I
u = −0.144411 + 0.424497I
−0.54493 + 1.50370I −4.95413 − 4.12502I
u = −0.144411 − 0.424497I
−0.54493 − 1.50370I −4.95413 + 4.12502I
u = 1.55614 + 0.12966I
−8.73279 − 3.39810I −13.35777 + 1.97434I
u = 1.55614 − 0.12966I
−8.73279 + 3.39810I −13.35777 − 1.97434I
u = 1.56158
−8.21476 −10.3100
u = 1.55803 + 0.17307I
−6.03932 − 10.93770I −10.01109 + 7.20566I
u = 1.55803 − 0.17307I
−6.03932 + 10.93770I −10.01109 − 7.20566I
u = −1.59109 + 0.02596I
−11.35240 + 3.87127I −14.4294 − 3.8096I
u = −1.59109 − 0.02596I
−11.35240 − 3.87127I −14.4294 + 3.8096I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
28
− u
27
+ ··· + u
2
− 1
c
2
u
28
+ u
27
+ ··· − u − 2
c
3
, c
6
u
28
− 5u
27
+ ··· + 20u − 7
c
4
, c
5
, c
9
c
10
u
28
− u
27
+ ··· − 2u − 1
c
8
u
28
+ 13u
27
+ ··· − 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
28
+ 13y
27
+ ··· − 2y + 1
c
2
y
28
− 3y
27
+ ··· − 109y + 4
c
3
, c
6
y
28
+ 17y
27
+ ··· + 118y + 49
c
4
, c
5
, c
9
c
10
y
28
− 31y
27
+ ··· − 2y + 1
c
8
y
28
+ 5y
27
+ ··· − 26y + 1
7
