11a
360
(K11a
360
)
A knot diagram
1
Linearized knot diagam
9 8 7 1 11 10 2 3 4 6 5
Solving Sequence
5,11
6 1 4 10 7 3 9 2 8
c
5
c
11
c
4
c
10
c
6
c
3
c
9
c
1
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
28
− u
27
+ ··· + 4u − 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
+ · · · + 4u − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
u
2
a
1
=
−u
u
a
4
=
u
2
+ 1
−u
2
a
10
=
u
u
3
+ u
a
7
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
8
− 5u
6
− 7u
4
− 2u
2
+ 1
−u
10
− 6u
8
− 11u
6
− 6u
4
− u
2
a
9
=
u
7
+ 4u
5
+ 4u
3
+ 2u
−u
7
− 3u
5
+ u
a
2
=
−u
13
− 8u
11
− 23u
9
− 30u
7
− 20u
5
− 6u
3
− u
u
13
+ 7u
11
+ 15u
9
+ 8u
7
− 4u
5
− 3u
3
+ u
a
8
=
−u
25
− 16u
23
+ ··· + 2u
3
+ 3u
−u
27
− 17u
25
+ ··· − u
3
+ u
a
8
=
−u
25
− 16u
23
+ ··· + 2u
3
+ 3u
−u
27
− 17u
25
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
27
+ 4u
26
− 76u
25
+ 72u
24
− 628u
23
+ 556u
22
− 2956u
21
+ 2404u
20
− 8720u
19
+
6372u
18
−16704u
17
+ 10652u
16
−20788u
15
+ 11088u
14
−16232u
13
+ 6688u
12
−7212u
11
+
1772u
10
− 1372u
9
− 168u
8
− 32u
7
− 140u
6
− 68u
5
+ 8u
4
− 20u
3
− 16u
2
+ 16u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
u
28
+ 3u
27
+ ··· + 29u + 8
c
2
, c
7
, c
8
u
28
− u
27
+ ··· − 2u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
28
+ u
27
+ ··· − 4u − 1
c
9
u
28
+ u
27
+ ··· − 100u − 61
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
28
+ 21y
27
+ ··· − 793y + 64
c
2
, c
7
, c
8
y
28
− 23y
27
+ ··· − 10y + 1
c
4
, c
5
, c
6
c
10
, c
11
y
28
+ 37y
27
+ ··· − 10y + 1
c
9
y
28
+ 13y
27
+ ··· − 3534y + 3721
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.304139 + 1.027830I
2.34823 − 8.20316I −7.50942 + 6.87147I
u = 0.304139 − 1.027830I
2.34823 + 8.20316I −7.50942 − 6.87147I
u = −0.265481 + 1.044260I
6.76083 + 4.04685I −2.74550 − 4.44082I
u = −0.265481 − 1.044260I
6.76083 − 4.04685I −2.74550 + 4.44082I
u = 0.208386 + 1.064510I
3.42392 + 0.10107I −5.90157 + 0.38033I
u = 0.208386 − 1.064510I
3.42392 − 0.10107I −5.90157 − 0.38033I
u = 0.100569 + 0.877295I
2.08521 − 1.33119I −6.23078 + 5.40479I
u = 0.100569 − 0.877295I
2.08521 + 1.33119I −6.23078 − 5.40479I
u = −0.265641 + 0.799341I
−3.12024 + 2.65179I −11.98850 − 4.74580I
u = −0.265641 − 0.799341I
−3.12024 − 2.65179I −11.98850 + 4.74580I
u = 0.526451 + 0.252550I
−1.61862 − 5.37366I −12.50162 + 6.60941I
u = 0.526451 − 0.252550I
−1.61862 + 5.37366I −12.50162 − 6.60941I
u = 0.430028 + 0.394667I
−1.11578 + 2.20453I −10.78929 + 0.67162I
u = 0.430028 − 0.394667I
−1.11578 − 2.20453I −10.78929 − 0.67162I
u = −0.473056 + 0.300840I
2.59067 + 1.52781I −7.09485 − 4.38679I
u = −0.473056 − 0.300840I
2.59067 − 1.52781I −7.09485 + 4.38679I
u = −0.499593
−5.51225 −18.3880
u = −0.04326 + 1.66904I
5.56370 + 3.66754I −10.51538 + 0.I
u = −0.04326 − 1.66904I
5.56370 − 3.66754I −10.51538 + 0.I
u = 0.01768 + 1.69715I
11.29630 − 1.73601I −5.59144 + 0.I
u = 0.01768 − 1.69715I
11.29630 + 1.73601I −5.59144 + 0.I
u = 0.290753
−0.512208 −19.3960
u = 0.07952 + 1.72739I
12.1446 − 9.7685I 0
u = 0.07952 − 1.72739I
12.1446 + 9.7685I 0
u = −0.06882 + 1.73175I
16.6638 + 5.4189I 0
u = −0.06882 − 1.73175I
16.6638 − 5.4189I 0
u = 0.05390 + 1.73452I
13.43200 − 0.98282I 0
u = 0.05390 − 1.73452I
13.43200 + 0.98282I 0
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
3
u
28
+ 3u
27
+ ··· + 29u + 8
c
2
, c
7
, c
8
u
28
− u
27
+ ··· − 2u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
28
+ u
27
+ ··· − 4u − 1
c
9
u
28
+ u
27
+ ··· − 100u − 61
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
y
28
+ 21y
27
+ ··· − 793y + 64
c
2
, c
7
, c
8
y
28
− 23y
27
+ ··· − 10y + 1
c
4
, c
5
, c
6
c
10
, c
11
y
28
+ 37y
27
+ ··· − 10y + 1
c
9
y
28
+ 13y
27
+ ··· − 3534y + 3721
7
