11a
190
(K11a
190
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 11 2 3 5 4 8 7
Solving Sequence
2,7
6 1 3 8 11 5 9 4 10
c
6
c
1
c
2
c
7
c
11
c
5
c
8
c
4
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
42
− u
41
+ ··· − u + 1i
* 1 irreducible components of dim
C
= 0, with total 42 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
42
− u
41
+ · · · − u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
8
=
u
8
− u
6
+ u
4
+ 1
−u
10
+ 2u
8
− 3u
6
+ 2u
4
− u
2
a
11
=
u
3
−u
3
+ u
a
5
=
u
8
− u
6
+ u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
9
=
u
26
− 5u
24
+ ··· + u
2
+ 1
−u
26
+ 6u
24
+ ··· + 2u
4
− u
2
a
4
=
−u
39
+ 8u
37
+ ··· + 6u
5
− 2u
3
u
41
− 9u
39
+ ··· − 3u
5
+ u
a
10
=
−u
21
+ 4u
19
+ ··· + 2u
3
− u
u
23
− 5u
21
+ ··· − 3u
5
+ u
a
10
=
−u
21
+ 4u
19
+ ··· + 2u
3
− u
u
23
− 5u
21
+ ··· − 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
40
−36u
38
+ 4u
37
+ 168u
36
−32u
35
−516u
34
+ 136u
33
+ 1152u
32
−384u
31
−1972u
30
+
796u
29
+ 2700u
28
− 1276u
27
− 3092u
26
+ 1648u
25
+ 3116u
24
− 1780u
23
− 2872u
22
+
1668u
21
+ 2424u
20
−1388u
19
−1832u
18
+ 1020u
17
+ 1244u
16
−640u
15
−796u
14
+ 324u
13
+
484u
12
− 124u
11
− 256u
10
+ 28u
9
+ 112u
8
+ 8u
7
− 48u
6
− 20u
5
+ 24u
4
+ 16u
3
− 8u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
42
− u
41
+ ··· − u + 1
c
2
u
42
+ 19u
41
+ ··· − u + 1
c
3
, c
4
, c
8
c
9
u
42
+ u
41
+ ··· + 3u + 1
c
5
, c
7
u
42
+ u
41
+ ··· − 12u + 4
c
10
u
42
+ 13u
41
+ ··· + 2109u + 283
c
11
u
42
− 3u
41
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
− 19y
41
+ ··· + y + 1
c
2
y
42
+ 9y
41
+ ··· − 11y + 1
c
3
, c
4
, c
8
c
9
y
42
+ 49y
41
+ ··· + y + 1
c
5
, c
7
y
42
− 35y
41
+ ··· − 328y + 16
c
10
y
42
− 19y
41
+ ··· − 701527y + 80089
c
11
y
42
+ y
41
+ ··· + 37y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.958451 + 0.182027I
−1.50976 + 0.22408I −7.80723 − 0.81667I
u = −0.958451 − 0.182027I
−1.50976 − 0.22408I −7.80723 + 0.81667I
u = −0.794065 + 0.558308I
8.84617 + 2.25274I 4.58162 − 3.46798I
u = −0.794065 − 0.558308I
8.84617 − 2.25274I 4.58162 + 3.46798I
u = 1.059210 + 0.106332I
0.18706 + 2.88066I −2.91592 − 4.70329I
u = 1.059210 − 0.106332I
0.18706 − 2.88066I −2.91592 + 4.70329I
u = 0.534293 + 0.761914I
13.9445 − 3.9233I 5.91216 + 2.83813I
u = 0.534293 − 0.761914I
13.9445 + 3.9233I 5.91216 − 2.83813I
u = 0.814354 + 0.428559I
1.05337 − 1.87068I 3.39079 + 4.68483I
u = 0.814354 − 0.428559I
1.05337 + 1.87068I 3.39079 − 4.68483I
u = 0.437218 + 0.793916I
13.4042 + 6.9529I 5.22220 − 3.15637I
u = 0.437218 − 0.793916I
13.4042 − 6.9529I 5.22220 + 3.15637I
u = −0.510362 + 0.737623I
5.58647 + 2.00252I 4.43798 − 4.06646I
u = −0.510362 − 0.737623I
5.58647 − 2.00252I 4.43798 + 4.06646I
u = −1.109120 + 0.092741I
8.15110 − 4.89812I −0.84749 + 2.79086I
u = −1.109120 − 0.092741I
8.15110 + 4.89812I −0.84749 − 2.79086I
u = −0.440224 + 0.767604I
5.20119 − 4.76095I 3.47757 + 4.70504I
u = −0.440224 − 0.767604I
5.20119 + 4.76095I 3.47757 − 4.70504I
u = −1.052970 + 0.403941I
−2.94816 + 1.84155I −7.97014 − 0.12089I
u = −1.052970 − 0.403941I
−2.94816 − 1.84155I −7.97014 + 0.12089I
u = 1.079910 + 0.334044I
3.19579 − 0.38496I −4.05769 + 0.70837I
u = 1.079910 − 0.334044I
3.19579 + 0.38496I −4.05769 − 0.70837I
u = 0.460288 + 0.731314I
3.06576 + 1.25733I −0.386808 − 0.265317I
u = 0.460288 − 0.731314I
3.06576 − 1.25733I −0.386808 + 0.265317I
u = 1.069990 + 0.454007I
−2.58903 − 5.04565I −5.96481 + 8.68441I
u = 1.069990 − 0.454007I
−2.58903 + 5.04565I −5.96481 − 8.68441I
u = −1.096730 + 0.488278I
4.21047 + 6.88158I −1.95632 − 6.72572I
u = −1.096730 − 0.488278I
4.21047 − 6.88158I −1.95632 + 6.72572I
u = −1.049770 + 0.605621I
3.98383 + 3.11596I 2.01311 − 1.17218I
u = −1.049770 − 0.605621I
3.98383 − 3.11596I 2.01311 + 1.17218I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.042540 + 0.627034I
12.43060 − 1.33379I 3.69918 + 2.21003I
u = 1.042540 − 0.627034I
12.43060 + 1.33379I 3.69918 − 2.21003I
u = 1.074510 + 0.592401I
1.24809 − 6.31321I −3.41953 + 4.87109I
u = 1.074510 − 0.592401I
1.24809 + 6.31321I −3.41953 − 4.87109I
u = −1.091090 + 0.602467I
3.27056 + 9.94153I 0.33743 − 9.11948I
u = −1.091090 − 0.602467I
3.27056 − 9.94153I 0.33743 + 9.11948I
u = 1.100260 + 0.611942I
11.4291 − 12.2349I 2.31503 + 7.47393I
u = 1.100260 − 0.611942I
11.4291 + 12.2349I 2.31503 − 7.47393I
u = −0.194284 + 0.626683I
6.70392 − 2.62174I 1.89600 + 2.88322I
u = −0.194284 − 0.626683I
6.70392 + 2.62174I 1.89600 − 2.88322I
u = 0.124492 + 0.489748I
−0.169198 + 1.278750I −1.95713 − 5.54449I
u = 0.124492 − 0.489748I
−0.169198 − 1.278750I −1.95713 + 5.54449I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
42
− u
41
+ ··· − u + 1
c
2
u
42
+ 19u
41
+ ··· − u + 1
c
3
, c
4
, c
8
c
9
u
42
+ u
41
+ ··· + 3u + 1
c
5
, c
7
u
42
+ u
41
+ ··· − 12u + 4
c
10
u
42
+ 13u
41
+ ··· + 2109u + 283
c
11
u
42
− 3u
41
+ ··· − u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
− 19y
41
+ ··· + y + 1
c
2
y
42
+ 9y
41
+ ··· − 11y + 1
c
3
, c
4
, c
8
c
9
y
42
+ 49y
41
+ ··· + y + 1
c
5
, c
7
y
42
− 35y
41
+ ··· − 328y + 16
c
10
y
42
− 19y
41
+ ··· − 701527y + 80089
c
11
y
42
+ y
41
+ ··· + 37y + 1
8
