11a
185
(K11a
185
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 3 4 5 8 6
Solving Sequence
2,6
7 1 3 8 11 4 9 5 10
c
6
c
1
c
2
c
7
c
11
c
3
c
8
c
5
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
54
+ u
53
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 54 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
54
+ u
53
+ · · · + u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
−u
3
u
5
+ u
3
+ u
a
8
=
−u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
a
11
=
u
3
u
3
+ u
a
4
=
−u
11
− 2u
9
− 2u
7
− u
3
−u
11
− 3u
9
− 4u
7
− u
5
+ u
3
+ u
a
9
=
u
30
+ 7u
28
+ ··· − 2u
12
+ 1
u
30
+ 8u
28
+ ··· + 4u
6
− u
2
a
5
=
−u
47
− 12u
45
+ ··· − 20u
9
− 8u
7
u
49
+ 13u
47
+ ··· − 2u
5
+ u
a
10
=
−u
17
− 4u
15
− 7u
13
− 4u
11
+ 3u
9
+ 6u
7
+ 2u
5
− u
u
19
+ 5u
17
+ 12u
15
+ 15u
13
+ 9u
11
− u
9
− 4u
7
− 2u
5
+ u
3
+ u
a
10
=
−u
17
− 4u
15
− 7u
13
− 4u
11
+ 3u
9
+ 6u
7
+ 2u
5
− u
u
19
+ 5u
17
+ 12u
15
+ 15u
13
+ 9u
11
− u
9
− 4u
7
− 2u
5
+ u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
52
− 4u
51
+ ··· + 4u
2
− 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
54
+ u
53
+ ··· + u + 1
c
2
u
54
+ 29u
53
+ ··· − u + 1
c
3
u
54
− 7u
53
+ ··· − 47u + 5
c
4
, c
5
, c
9
u
54
− u
53
+ ··· − u + 1
c
7
, c
11
u
54
− u
53
+ ··· + u + 1
c
8
u
54
+ u
53
+ ··· + 11u + 1
c
10
u
54
+ 11u
53
+ ··· + 1951u + 187
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
54
+ 29y
53
+ ··· − y + 1
c
2
y
54
− 7y
53
+ ··· − 5y + 1
c
3
y
54
− 3y
53
+ ··· + 631y + 25
c
4
, c
5
, c
9
y
54
+ 49y
53
+ ··· − y + 1
c
7
, c
11
y
54
− 43y
53
+ ··· − 97y + 1
c
8
y
54
+ 5y
53
+ ··· − 49y + 1
c
10
y
54
+ 21y
53
+ ··· + 184179y + 34969
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526458 + 0.850149I
1.84506 − 5.20730I 6.07211 + 8.44255I
u = −0.526458 − 0.850149I
1.84506 + 5.20730I 6.07211 − 8.44255I
u = 0.063963 + 0.969473I
−2.01199 + 1.57241I −2.93647 − 4.70910I
u = 0.063963 − 0.969473I
−2.01199 − 1.57241I −2.93647 + 4.70910I
u = 0.542026 + 0.876210I
−3.38874 + 8.60756I 0.88746 − 8.62489I
u = 0.542026 − 0.876210I
−3.38874 − 8.60756I 0.88746 + 8.62489I
u = −0.068795 + 1.043570I
−7.55344 − 4.33327I −6.71453 + 3.78697I
u = −0.068795 − 1.043570I
−7.55344 + 4.33327I −6.71453 − 3.78697I
u = −0.404606 + 0.965250I
−5.19453 − 0.85164I −2.69916 + 2.79194I
u = −0.404606 − 0.965250I
−5.19453 + 0.85164I −2.69916 − 2.79194I
u = 0.459955 + 0.798537I
0.23556 + 1.92632I 2.54464 − 3.58852I
u = 0.459955 − 0.798537I
0.23556 − 1.92632I 2.54464 + 3.58852I
u = 0.514528 + 0.758613I
0.15792 + 2.10554I 4.75076 − 4.16265I
u = 0.514528 − 0.758613I
0.15792 − 2.10554I 4.75076 + 4.16265I
u = −0.521169 + 0.661679I
2.37968 + 0.93113I 8.32580 − 1.37232I
u = −0.521169 − 0.661679I
2.37968 − 0.93113I 8.32580 + 1.37232I
u = 0.555404 + 0.618983I
−2.66786 − 4.19841I 2.85328 + 2.26313I
u = 0.555404 − 0.618983I
−2.66786 + 4.19841I 2.85328 − 2.26313I
u = −0.812471 + 0.137850I
−6.92259 + 9.00910I −0.82614 − 5.72677I
u = −0.812471 − 0.137850I
−6.92259 − 9.00910I −0.82614 + 5.72677I
u = −0.409939 + 1.110810I
−5.37080 − 0.77260I 0
u = −0.409939 − 1.110810I
−5.37080 + 0.77260I 0
u = 0.803336 + 0.074667I
−8.69949 + 0.21899I −3.12382 − 0.07866I
u = 0.803336 − 0.074667I
−8.69949 − 0.21899I −3.12382 + 0.07866I
u = 0.793006 + 0.135744I
−1.35714 − 5.52569I 3.45218 + 5.82582I
u = 0.793006 − 0.135744I
−1.35714 + 5.52569I 3.45218 − 5.82582I
u = 0.465718 + 1.132140I
−1.40488 + 3.87836I 0
u = 0.465718 − 1.132140I
−1.40488 − 3.87836I 0
u = −0.768273 + 0.105402I
−2.42732 + 1.73641I 0.699777 + 0.008860I
u = −0.768273 − 0.105402I
−2.42732 − 1.73641I 0.699777 − 0.008860I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.492150 + 1.152340I
−4.72150 − 7.14315I 0
u = −0.492150 − 1.152340I
−4.72150 + 7.14315I 0
u = −0.403427 + 1.196670I
−6.22025 − 2.29095I 0
u = −0.403427 − 1.196670I
−6.22025 + 2.29095I 0
u = 0.382721 + 1.204180I
−5.34368 − 1.56137I 0
u = 0.382721 − 1.204180I
−5.34368 + 1.56137I 0
u = −0.378306 + 1.216650I
−11.00630 + 4.98743I 0
u = −0.378306 − 1.216650I
−11.00630 − 4.98743I 0
u = 0.415619 + 1.215680I
−12.53210 + 4.46314I 0
u = 0.415619 − 1.215680I
−12.53210 − 4.46314I 0
u = −0.494467 + 1.187320I
−5.57287 − 6.38943I 0
u = −0.494467 − 1.187320I
−5.57287 + 6.38943I 0
u = −0.688011 + 0.172752I
−1.90661 + 2.65629I 2.99397 − 3.57576I
u = −0.688011 − 0.172752I
−1.90661 − 2.65629I 2.99397 + 3.57576I
u = 0.508429 + 1.190650I
−4.45647 + 10.31740I 0
u = 0.508429 − 1.190650I
−4.45647 − 10.31740I 0
u = 0.486868 + 1.204310I
−12.02490 + 4.47153I 0
u = 0.486868 − 1.204310I
−12.02490 − 4.47153I 0
u = −0.513281 + 1.197090I
−10.0524 − 13.8722I 0
u = −0.513281 − 1.197090I
−10.0524 + 13.8722I 0
u = −0.553091 + 0.375407I
−3.44062 − 3.02821I 2.33743 + 2.90410I
u = −0.553091 − 0.375407I
−3.44062 + 3.02821I 2.33743 − 2.90410I
u = 0.542871 + 0.222612I
1.223040 + 0.207996I 8.65252 − 1.10768I
u = 0.542871 − 0.222612I
1.223040 − 0.207996I 8.65252 + 1.10768I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
54
+ u
53
+ ··· + u + 1
c
2
u
54
+ 29u
53
+ ··· − u + 1
c
3
u
54
− 7u
53
+ ··· − 47u + 5
c
4
, c
5
, c
9
u
54
− u
53
+ ··· − u + 1
c
7
, c
11
u
54
− u
53
+ ··· + u + 1
c
8
u
54
+ u
53
+ ··· + 11u + 1
c
10
u
54
+ 11u
53
+ ··· + 1951u + 187
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
54
+ 29y
53
+ ··· − y + 1
c
2
y
54
− 7y
53
+ ··· − 5y + 1
c
3
y
54
− 3y
53
+ ··· + 631y + 25
c
4
, c
5
, c
9
y
54
+ 49y
53
+ ··· − y + 1
c
7
, c
11
y
54
− 43y
53
+ ··· − 97y + 1
c
8
y
54
+ 5y
53
+ ··· − 49y + 1
c
10
y
54
+ 21y
53
+ ··· + 184179y + 34969
8
