11a
13
(K11a
13
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 3 11 10 4 8 7 6
Solving Sequence
4,8
9 10 3 7 11 6 1 2 5
c
8
c
9
c
3
c
7
c
10
c
6
c
11
c
2
c
5
c
1
, c
4
Ideals for irreducible components
2
of X
par
I
u
1
= hu
30
+ u
29
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 30 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
30
+ u
29
+ · · · + u + 1i
(i) Arc colorings
a
4
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
10
=
u
2
+ 1
−u
2
a
3
=
−u
u
3
+ u
a
7
=
u
4
+ u
2
+ 1
−u
4
a
11
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
6
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
8
− 2u
4
a
1
=
u
10
+ u
8
+ 4u
6
+ 3u
4
+ 3u
2
+ 1
−u
10
− 3u
6
− u
2
a
2
=
u
23
+ 2u
21
+ ··· + 18u
5
+ 6u
3
−u
23
− u
21
+ ··· − 3u
5
+ u
a
5
=
u
12
+ u
10
+ 5u
8
+ 4u
6
+ 6u
4
+ 3u
2
+ 1
−u
14
− 2u
12
− 5u
10
− 8u
8
− 6u
6
− 6u
4
− u
2
a
5
=
u
12
+ u
10
+ 5u
8
+ 4u
6
+ 6u
4
+ 3u
2
+ 1
−u
14
− 2u
12
− 5u
10
− 8u
8
− 6u
6
− 6u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
28
−4u
27
−12u
26
−8u
25
−56u
24
−44u
23
−120u
22
−72u
21
−
288u
20
− 184u
19
− 448u
18
− 240u
17
− 688u
16
− 372u
15
− 772u
14
− 376u
13
− 784u
12
−
392u
11
−616u
10
−300u
9
−392u
8
−220u
7
−196u
6
−112u
5
−64u
4
−52u
3
−16u
2
−12u −6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
30
+ u
29
+ ··· + 3u + 1
c
2
u
30
+ 13u
29
+ ··· + 3u + 1
c
3
, c
8
u
30
+ u
29
+ ··· + u + 1
c
5
u
30
− u
29
+ ··· − 9u + 1
c
6
, c
7
, c
9
c
10
, c
11
u
30
+ 5u
29
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
+ 13y
29
+ ··· + 3y + 1
c
2
y
30
+ 9y
29
+ ··· + 23y + 1
c
3
, c
8
y
30
+ 5y
29
+ ··· + 3y + 1
c
5
y
30
+ 5y
29
+ ··· − 29y + 1
c
6
, c
7
, c
9
c
10
, c
11
y
30
+ 41y
29
+ ··· + 15y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.576972 + 0.788172I
0.12621 + 2.18606I −3.44242 − 4.00116I
u = 0.576972 − 0.788172I
0.12621 − 2.18606I −3.44242 + 4.00116I
u = 0.753269 + 0.693656I
3.64770 − 3.48747I 1.74738 + 2.61442I
u = 0.753269 − 0.693656I
3.64770 + 3.48747I 1.74738 − 2.61442I
u = −0.734724 + 0.748106I
5.14265 − 1.49049I 4.17557 + 2.85810I
u = −0.734724 − 0.748106I
5.14265 + 1.49049I 4.17557 − 2.85810I
u = −0.685664 + 0.853521I
4.78950 − 3.76974I 3.14381 + 3.88461I
u = −0.685664 − 0.853521I
4.78950 + 3.76974I 3.14381 − 3.88461I
u = −0.287305 + 0.847959I
−2.28263 − 5.27377I −6.56092 + 8.94909I
u = −0.287305 − 0.847959I
−2.28263 + 5.27377I −6.56092 − 8.94909I
u = 0.664026 + 0.894813I
2.98040 + 8.73007I −0.24401 − 8.71246I
u = 0.664026 − 0.894813I
2.98040 − 8.73007I −0.24401 + 8.71246I
u = −0.115414 + 0.820064I
−3.15838 + 1.07159I −10.31816 − 0.17759I
u = −0.115414 − 0.820064I
−3.15838 − 1.07159I −10.31816 + 0.17759I
u = 0.290049 + 0.709988I
−0.316552 + 1.365600I −2.18848 − 5.41625I
u = 0.290049 − 0.709988I
−0.316552 − 1.365600I −2.18848 + 5.41625I
u = −0.911746 + 0.940114I
9.51868 − 3.35799I −1.73657 + 2.30059I
u = −0.911746 − 0.940114I
9.51868 + 3.35799I −1.73657 − 2.30059I
u = −0.939027 + 0.928155I
13.7360 + 3.9165I 1.75197 − 2.34228I
u = −0.939027 − 0.928155I
13.7360 − 3.9165I 1.75197 + 2.34228I
u = 0.935072 + 0.937925I
15.4906 + 1.5996I 4.05928 − 2.15774I
u = 0.935072 − 0.937925I
15.4906 − 1.5996I 4.05928 + 2.15774I
u = 0.922373 + 0.959915I
15.4175 + 5.2269I 3.92816 − 2.38623I
u = 0.922373 − 0.959915I
15.4175 − 5.2269I 3.92816 + 2.38623I
u = −0.916401 + 0.967754I
13.6047 − 10.7354I 1.48227 + 6.83107I
u = −0.916401 − 0.967754I
13.6047 + 10.7354I 1.48227 − 6.83107I
u = 0.459289 + 0.421277I
0.49693 + 1.38708I 2.54940 − 4.49142I
u = 0.459289 − 0.421277I
0.49693 − 1.38708I 2.54940 + 4.49142I
u = −0.510769 + 0.183576I
−0.23650 + 2.48738I 1.65273 − 3.25175I
u = −0.510769 − 0.183576I
−0.23650 − 2.48738I 1.65273 + 3.25175I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
30
+ u
29
+ ··· + 3u + 1
c
2
u
30
+ 13u
29
+ ··· + 3u + 1
c
3
, c
8
u
30
+ u
29
+ ··· + u + 1
c
5
u
30
− u
29
+ ··· − 9u + 1
c
6
, c
7
, c
9
c
10
, c
11
u
30
+ 5u
29
+ ··· + 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
30
+ 13y
29
+ ··· + 3y + 1
c
2
y
30
+ 9y
29
+ ··· + 23y + 1
c
3
, c
8
y
30
+ 5y
29
+ ··· + 3y + 1
c
5
y
30
+ 5y
29
+ ··· − 29y + 1
c
6
, c
7
, c
9
c
10
, c
11
y
30
+ 41y
29
+ ··· + 15y + 1
7
