11a
182
(K11a
182
)
A knot diagram
1
Linearized knot diagam
7 1 11 9 10 2 3 4 5 6 8
Solving Sequence
5,9
10 6 11 4 3 8 1 2 7
c
9
c
5
c
10
c
4
c
3
c
8
c
11
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
− u
35
+ ··· + u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 36 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
36
− u
35
+ · · · + u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
4
=
−u
u
a
3
=
u
7
− 4u
5
+ 4u
3
− 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
8
=
−u
2
+ 1
u
2
a
1
=
−u
8
+ 5u
6
− 7u
4
+ 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
− 2u
2
a
2
=
−u
25
+ 16u
23
+ ··· + 6u
3
− u
u
25
− 15u
23
+ ··· − 3u
5
+ u
a
7
=
−u
18
+ 11u
16
− 48u
14
+ 107u
12
− 133u
10
+ 95u
8
− 34u
6
+ 2u
4
+ u
2
+ 1
u
20
− 12u
18
+ 58u
16
− 144u
14
+ 193u
12
− 130u
10
+ 26u
8
+ 14u
6
− 5u
4
a
7
=
−u
18
+ 11u
16
− 48u
14
+ 107u
12
− 133u
10
+ 95u
8
− 34u
6
+ 2u
4
+ u
2
+ 1
u
20
− 12u
18
+ 58u
16
− 144u
14
+ 193u
12
− 130u
10
+ 26u
8
+ 14u
6
− 5u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes =
−4u
32
+84u
30
−780u
28
+4u
27
+4216u
26
−72u
25
−14700u
24
+560u
23
+34636u
22
−2464u
21
−
56164u
20
+6748u
19
+62536u
18
−11928u
17
−46600u
16
+13636u
15
+21736u
14
−9752u
13
−
5352u
12
+ 3984u
11
+ 364u
10
−800u
9
−32u
8
+ 168u
7
+ 60u
6
−116u
5
+ 28u
3
−4u
2
−4u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
36
+ u
35
+ ··· + u
2
− 1
c
2
u
36
+ 17u
35
+ ··· − 2u + 1
c
3
u
36
+ 5u
35
+ ··· + 38u + 5
c
4
, c
5
, c
8
c
9
, c
10
u
36
+ u
35
+ ··· + u
2
− 1
c
7
u
36
− u
35
+ ··· + 34u − 13
c
11
u
36
+ 5u
35
+ ··· − 38u − 39
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
36
+ 17y
35
+ ··· − 2y + 1
c
2
y
36
+ 5y
35
+ ··· − 6y + 1
c
3
y
36
− 7y
35
+ ··· − 1434y + 25
c
4
, c
5
, c
8
c
9
, c
10
y
36
− 47y
35
+ ··· − 2y + 1
c
7
y
36
− 7y
35
+ ··· − 3314y + 169
c
11
y
36
+ 13y
35
+ ··· + 16730y + 1521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.923130 + 0.285145I
−0.30787 − 2.25346I 5.12843 + 3.26342I
u = −0.923130 − 0.285145I
−0.30787 + 2.25346I 5.12843 − 3.26342I
u = 0.995096 + 0.286789I
4.18097 + 4.67479I 11.82536 − 4.59597I
u = 0.995096 − 0.286789I
4.18097 − 4.67479I 11.82536 + 4.59597I
u = 1.024000 + 0.199158I
5.17530 + 2.55443I 13.5240 − 4.2251I
u = 1.024000 − 0.199158I
5.17530 − 2.55443I 13.5240 + 4.2251I
u = −0.994663 + 0.317611I
2.00397 − 9.65728I 8.40249 + 8.58483I
u = −0.994663 − 0.317611I
2.00397 + 9.65728I 8.40249 − 8.58483I
u = −1.049710 + 0.138664I
3.94362 + 2.17455I 11.37017 − 2.11968I
u = −1.049710 − 0.138664I
3.94362 − 2.17455I 11.37017 + 2.11968I
u = 0.674179 + 0.268506I
−1.71251 + 3.16112I 3.99113 − 5.83038I
u = 0.674179 − 0.268506I
−1.71251 − 3.16112I 3.99113 + 5.83038I
u = −0.691311
1.07542 9.42760
u = 0.472191 + 0.368747I
−0.77973 − 3.66810I 5.58740 + 1.24735I
u = 0.472191 − 0.368747I
−0.77973 + 3.66810I 5.58740 − 1.24735I
u = 0.201428 + 0.536486I
−1.68498 + 6.75016I 2.91272 − 7.90487I
u = 0.201428 − 0.536486I
−1.68498 − 6.75016I 2.91272 + 7.90487I
u = −0.210047 + 0.484113I
0.46489 − 2.03480I 6.34842 + 4.41097I
u = −0.210047 − 0.484113I
0.46489 + 2.03480I 6.34842 − 4.41097I
u = 0.100349 + 0.504234I
−3.42760 − 0.43485I −1.35617 − 0.72368I
u = 0.100349 − 0.504234I
−3.42760 + 0.43485I −1.35617 + 0.72368I
u = −0.332629 + 0.351120I
1.029420 − 0.669064I 9.01560 + 4.71804I
u = −0.332629 − 0.351120I
1.029420 + 0.669064I 9.01560 − 4.71804I
u = −1.64665 + 0.02163I
6.41597 − 3.89056I 0
u = −1.64665 − 0.02163I
6.41597 + 3.89056I 0
u = 1.66590
9.58969 0
u = 1.70003 + 0.06962I
8.97882 + 3.61851I 0
u = 1.70003 − 0.06962I
8.97882 − 3.61851I 0
u = 1.71726 + 0.08303I
11.6119 + 11.2693I 0
u = 1.71726 − 0.08303I
11.6119 − 11.2693I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.71795 + 0.07461I
13.8143 − 6.1298I 0
u = −1.71795 − 0.07461I
13.8143 + 6.1298I 0
u = −1.72470 + 0.05141I
14.9875 − 3.5755I 0
u = −1.72470 − 0.05141I
14.9875 + 3.5755I 0
u = 1.72765 + 0.03757I
13.86510 − 1.43953I 0
u = 1.72765 − 0.03757I
13.86510 + 1.43953I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
36
+ u
35
+ ··· + u
2
− 1
c
2
u
36
+ 17u
35
+ ··· − 2u + 1
c
3
u
36
+ 5u
35
+ ··· + 38u + 5
c
4
, c
5
, c
8
c
9
, c
10
u
36
+ u
35
+ ··· + u
2
− 1
c
7
u
36
− u
35
+ ··· + 34u − 13
c
11
u
36
+ 5u
35
+ ··· − 38u − 39
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
36
+ 17y
35
+ ··· − 2y + 1
c
2
y
36
+ 5y
35
+ ··· − 6y + 1
c
3
y
36
− 7y
35
+ ··· − 1434y + 25
c
4
, c
5
, c
8
c
9
, c
10
y
36
− 47y
35
+ ··· − 2y + 1
c
7
y
36
− 7y
35
+ ··· − 3314y + 169
c
11
y
36
+ 13y
35
+ ··· + 16730y + 1521
8
