11a
154
(K11a
154
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 4 11 10 3 8 7
Solving Sequence
3,10
9 4 8 11 7 1 2 6 5
c
9
c
3
c
8
c
10
c
7
c
11
c
2
c
6
c
5
c
1
, c
4
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
+ u
32
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 33 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
33
+ u
32
+ · · · + 3u + 1i
(i) Arc colorings
a
3
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
4
=
−u
u
3
+ u
a
8
=
u
2
+ 1
−u
2
a
11
=
u
4
+ u
2
+ 1
−u
4
a
7
=
u
6
+ u
4
+ 2u
2
+ 1
−u
6
− u
2
a
1
=
u
8
+ u
6
+ 3u
4
+ 2u
2
+ 1
−u
8
− 2u
4
a
2
=
u
17
+ 2u
15
+ 7u
13
+ 10u
11
+ 15u
9
+ 14u
7
+ 10u
5
+ 4u
3
+ u
−u
17
− u
15
− 5u
13
− 4u
11
− 7u
9
− 4u
7
− 2u
5
+ u
a
6
=
u
10
+ u
8
+ 4u
6
+ 3u
4
+ 3u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 6u
6
− 3u
4
− 2u
2
a
5
=
−u
19
− 2u
17
− 8u
15
− 12u
13
− 21u
11
− 22u
9
− 20u
7
− 12u
5
− 5u
3
− 2u
u
21
+ 3u
19
+ ··· + 3u
3
+ u
a
5
=
−u
19
− 2u
17
− 8u
15
− 12u
13
− 21u
11
− 22u
9
− 20u
7
− 12u
5
− 5u
3
− 2u
u
21
+ 3u
19
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
32
−12u
30
+ 4u
29
−56u
28
+ 12u
27
−124u
26
+ 52u
25
−300u
24
+ 108u
23
−500u
22
+
240u
21
− 792u
20
+ 352u
19
− 988u
18
+ 492u
17
− 1084u
16
+ 492u
15
− 988u
14
+ 432u
13
−
736u
12
+ 264u
11
−484u
10
+ 116u
9
−232u
8
+ 44u
7
−128u
6
−48u
4
+ 12u
3
−20u
2
−8u −10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
33
+ u
32
+ ··· − u + 1
c
2
, c
4
, c
6
u
33
+ 9u
32
+ ··· + u + 1
c
3
, c
9
u
33
+ u
32
+ ··· + 3u + 1
c
7
, c
8
, c
10
c
11
u
33
− 7u
32
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
33
− 9y
32
+ ··· + y −1
c
2
, c
4
, c
6
y
33
+ 31y
32
+ ··· + 17y −1
c
3
, c
9
y
33
+ 7y
32
+ ··· + y −1
c
7
, c
8
, c
10
c
11
y
33
+ 39y
32
+ ··· + 49y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.538436 + 0.819482I
−2.15523 − 4.53843I −7.17107 + 8.79463I
u = 0.538436 − 0.819482I
−2.15523 + 4.53843I −7.17107 − 8.79463I
u = −0.450188 + 0.934775I
4.86391 + 2.09612I 0.30900 − 3.39492I
u = −0.450188 − 0.934775I
4.86391 − 2.09612I 0.30900 + 3.39492I
u = −0.015816 + 0.947822I
7.27301 + 3.05112I 4.25923 − 2.85680I
u = −0.015816 − 0.947822I
7.27301 − 3.05112I 4.25923 + 2.85680I
u = 0.477472 + 0.941151I
4.50867 − 8.17465I −0.67620 + 8.47838I
u = 0.477472 − 0.941151I
4.50867 + 8.17465I −0.67620 − 8.47838I
u = 0.581653 + 0.618567I
−2.78816 + 0.30049I −10.41364 − 0.78013I
u = 0.581653 − 0.618567I
−2.78816 − 0.30049I −10.41364 + 0.78013I
u = −0.422763 + 0.735470I
0.00215 + 1.65753I −0.44649 − 4.30187I
u = −0.422763 − 0.735470I
0.00215 − 1.65753I −0.44649 + 4.30187I
u = 0.655708 + 0.402659I
2.81758 + 3.97777I −4.79341 − 2.84216I
u = 0.655708 − 0.402659I
2.81758 − 3.97777I −4.79341 + 2.84216I
u = −0.132896 + 0.751128I
1.09758 + 1.45110I 2.34671 − 6.18390I
u = −0.132896 − 0.751128I
1.09758 − 1.45110I 2.34671 + 6.18390I
u = 0.890476 + 0.870044I
−3.73457 − 0.99486I −3.97712 + 2.18288I
u = 0.890476 − 0.870044I
−3.73457 + 0.99486I −3.97712 − 2.18288I
u = −0.903629 + 0.872248I
−4.45571 − 5.03491I −5.18044 + 2.78598I
u = −0.903629 − 0.872248I
−4.45571 + 5.03491I −5.18044 − 2.78598I
u = 0.870063 + 0.919218I
−7.65546 − 3.22231I −3.72780 + 2.45721I
u = 0.870063 − 0.919218I
−7.65546 + 3.22231I −3.72780 − 2.45721I
u = −0.895123 + 0.910482I
−11.01940 + 0.06168I −9.88848 + 1.08911I
u = −0.895123 − 0.910482I
−11.01940 − 0.06168I −9.88848 − 1.08911I
u = −0.627175 + 0.348896I
3.06985 + 1.87561I −4.30897 − 2.69437I
u = −0.627175 − 0.348896I
3.06985 − 1.87561I −4.30897 + 2.69437I
u = 0.851374 + 0.962788I
−3.44108 − 5.45030I −3.45886 + 2.65691I
u = 0.851374 − 0.962788I
−3.44108 + 5.45030I −3.45886 − 2.65691I
u = −0.880262 + 0.942385I
−10.91700 + 6.49427I −9.56969 − 5.96659I
u = −0.880262 − 0.942385I
−10.91700 − 6.49427I −9.56969 + 5.96659I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.859204 + 0.969585I
−4.14461 + 11.54620I −4.60672 − 7.46871I
u = −0.859204 − 0.969585I
−4.14461 − 11.54620I −4.60672 + 7.46871I
u = −0.356251
−0.925837 −11.3920
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
33
+ u
32
+ ··· − u + 1
c
2
, c
4
, c
6
u
33
+ 9u
32
+ ··· + u + 1
c
3
, c
9
u
33
+ u
32
+ ··· + 3u + 1
c
7
, c
8
, c
10
c
11
u
33
− 7u
32
+ ··· + u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
33
− 9y
32
+ ··· + y −1
c
2
, c
4
, c
6
y
33
+ 31y
32
+ ··· + 17y −1
c
3
, c
9
y
33
+ 7y
32
+ ··· + y −1
c
7
, c
8
, c
10
c
11
y
33
+ 39y
32
+ ··· + 49y −1
8
