11a
144
(K11a
144
)
A knot diagram
1
Linearized knot diagam
6 1 9 10 2 5 11 3 4 8 7
Solving Sequence
3,8
9 4 10 5 11 7 1 2 6
c
8
c
3
c
9
c
4
c
10
c
7
c
11
c
2
c
6
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
+ u
35
+ ··· + 3u
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
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
11
=
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
1
=
u
12
− 7u
10
+ 17u
8
− 16u
6
+ 6u
4
− 5u
2
+ 1
u
12
− 6u
10
+ 12u
8
− 8u
6
+ u
4
− 2u
2
a
2
=
u
25
− 14u
23
+ ··· − 10u
3
+ u
u
25
− 13u
23
+ ··· − 2u
3
+ u
a
6
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
−u
18
+ 10u
16
− 39u
14
+ 74u
12
− 71u
10
+ 40u
8
− 26u
6
+ 12u
4
− u
2
a
6
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
−u
18
+ 10u
16
− 39u
14
+ 74u
12
− 71u
10
+ 40u
8
− 26u
6
+ 12u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
34
− 76u
32
+ 640u
30
− 4u
29
− 3140u
28
+ 64u
27
+ 9940u
26
−
444u
25
− 21336u
24
+ 1744u
23
+ 32132u
22
− 4260u
21
− 35572u
20
+ 6752u
19
+ 31380u
18
−
7232u
17
− 23756u
16
+ 5760u
15
+ 15076u
14
− 3928u
13
− 7748u
12
+ 2204u
11
+ 3552u
10
−
860u
9
− 1320u
8
+ 288u
7
+ 336u
6
− 52u
5
− 64u
4
+ 4u
2
+ 16u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
− u
35
+ ··· + 2u − 1
c
2
, c
6
u
36
+ 13u
35
+ ··· − 6u + 1
c
3
, c
4
, c
8
c
9
u
36
+ u
35
+ ··· + 3u
2
− 1
c
7
, c
10
, c
11
u
36
+ 5u
35
+ ··· − 28u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
36
+ 13y
35
+ ··· − 6y + 1
c
2
, c
6
y
36
+ 21y
35
+ ··· − 126y + 1
c
3
, c
4
, c
8
c
9
y
36
− 39y
35
+ ··· − 6y + 1
c
7
, c
10
, c
11
y
36
+ 33y
35
+ ··· − 406y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.551237 + 0.623942I
−3.83553 + 8.85264I 5.15779 − 8.13246I
u = 0.551237 − 0.623942I
−3.83553 − 8.85264I 5.15779 + 8.13246I
u = 0.500204 + 0.638390I
−8.13948 + 2.15908I 0.61666 − 3.24444I
u = 0.500204 − 0.638390I
−8.13948 − 2.15908I 0.61666 + 3.24444I
u = −0.538088 + 0.602358I
−2.39341 − 3.42442I 7.19469 + 3.59924I
u = −0.538088 − 0.602358I
−2.39341 + 3.42442I 7.19469 − 3.59924I
u = 0.442037 + 0.642214I
−4.15822 − 4.56725I 4.13742 + 2.02324I
u = 0.442037 − 0.642214I
−4.15822 + 4.56725I 4.13742 − 2.02324I
u = −0.450189 + 0.609743I
−2.65222 − 0.70366I 6.36717 + 3.04538I
u = −0.450189 − 0.609743I
−2.65222 + 0.70366I 6.36717 − 3.04538I
u = −0.667436 + 0.296361I
2.57098 − 4.98460I 11.29661 + 8.23770I
u = −0.667436 − 0.296361I
2.57098 + 4.98460I 11.29661 − 8.23770I
u = 0.678355 + 0.217774I
3.00630 − 0.23147I 13.24902 − 1.70066I
u = 0.678355 − 0.217774I
3.00630 + 0.23147I 13.24902 + 1.70066I
u = −0.395417 + 0.368366I
−1.48090 − 1.31158I 2.04069 + 6.11196I
u = −0.395417 − 0.368366I
−1.48090 + 1.31158I 2.04069 − 6.11196I
u = 1.48018 + 0.05647I
4.63881 + 2.63367I 0
u = 1.48018 − 0.05647I
4.63881 − 2.63367I 0
u = −1.47649 + 0.18272I
2.05877 + 1.63752I 0
u = −1.47649 − 0.18272I
2.05877 − 1.63752I 0
u = 1.49536 + 0.16633I
3.69893 + 3.42946I 0
u = 1.49536 − 0.16633I
3.69893 − 3.42946I 0
u = −1.51977
7.24314 14.1450
u = −1.51236 + 0.19447I
−1.54097 − 5.15567I 0
u = −1.51236 − 0.19447I
−1.54097 + 5.15567I 0
u = −0.056671 + 0.454706I
0.72337 + 2.40081I 4.52745 − 2.97125I
u = −0.056671 − 0.454706I
0.72337 − 2.40081I 4.52745 + 2.97125I
u = 1.53594 + 0.18267I
4.47120 + 6.26474I 0
u = 1.53594 − 0.18267I
4.47120 − 6.26474I 0
u = −1.53983 + 0.19295I
3.07837 − 11.82290I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.53983 − 0.19295I
3.07837 + 11.82290I 0
u = −1.56923 + 0.05302I
10.58170 − 0.71346I 0
u = −1.56923 − 0.05302I
10.58170 + 0.71346I 0
u = 1.56931 + 0.07118I
10.11540 + 6.26287I 0
u = 1.56931 − 0.07118I
10.11540 − 6.26287I 0
u = 0.425953
0.618616 16.2520
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
− u
35
+ ··· + 2u − 1
c
2
, c
6
u
36
+ 13u
35
+ ··· − 6u + 1
c
3
, c
4
, c
8
c
9
u
36
+ u
35
+ ··· + 3u
2
− 1
c
7
, c
10
, c
11
u
36
+ 5u
35
+ ··· − 28u − 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
36
+ 13y
35
+ ··· − 6y + 1
c
2
, c
6
y
36
+ 21y
35
+ ··· − 126y + 1
c
3
, c
4
, c
8
c
9
y
36
− 39y
35
+ ··· − 6y + 1
c
7
, c
10
, c
11
y
36
+ 33y
35
+ ··· − 406y + 49
8
