11a
210
(K11a
210
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 8 2 6 3 5 4 9
Solving Sequence
5,10
4 11 3 9 1 2 8 6 7
c
4
c
10
c
3
c
9
c
11
c
2
c
8
c
5
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
− u
35
+ ··· − 2u + 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
+ · · · − 2u + 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
11
=
u
u
3
+ u
a
3
=
u
2
+ 1
u
4
+ 2u
2
a
9
=
−u
u
a
1
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
2
=
u
14
+ 7u
12
+ 16u
10
+ 11u
8
− 2u
6
+ 1
−u
14
− 8u
12
− 23u
10
− 28u
8
− 14u
6
− 4u
4
+ u
2
a
8
=
u
7
+ 4u
5
+ 4u
3
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
6
=
u
16
+ 9u
14
+ 31u
12
+ 50u
10
+ 37u
8
+ 12u
6
+ 4u
4
+ 1
u
18
+ 10u
16
+ 39u
14
+ 74u
12
+ 71u
10
+ 38u
8
+ 18u
6
+ 4u
4
+ u
2
a
7
=
u
25
+ 14u
23
+ ··· + 6u
3
+ u
u
27
+ 15u
25
+ ··· + 3u
3
+ u
a
7
=
u
25
+ 14u
23
+ ··· + 6u
3
+ u
u
27
+ 15u
25
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
34
+ 4u
33
− 80u
32
+ 76u
31
− 712u
30
+ 640u
29
− 3712u
28
+ 3144u
27
− 12568u
26
+
9996u
25
− 29012u
24
+ 21652u
23
− 46856u
22
+ 33008u
21
− 53996u
20
+ 36580u
19
−
45668u
18
+30752u
17
−29624u
16
+20396u
15
−15384u
14
+10740u
13
−6764u
12
+4600u
11
−
2980u
10
+ 1824u
9
− 1312u
8
+ 688u
7
− 460u
6
+ 268u
5
− 128u
4
+ 92u
3
− 20u
2
+ 12u − 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
, c
5
, c
7
u
36
+ 9u
35
+ ··· + 2u + 1
c
3
, c
4
, c
9
c
10
u
36
+ u
35
+ ··· + 2u + 1
c
8
u
36
+ u
35
+ ··· + 24u + 5
c
11
u
36
− 9u
35
+ ··· + 8u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
36
+ 9y
35
+ ··· + 2y + 1
c
2
, c
5
, c
7
y
36
+ 37y
35
+ ··· + 18y + 1
c
3
, c
4
, c
9
c
10
y
36
+ 41y
35
+ ··· + 2y + 1
c
8
y
36
− 3y
35
+ ··· − 6y + 25
c
11
y
36
+ y
35
+ ··· − 30y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.039758 + 0.866938I
2.43227 − 2.98822I −1.17573 + 2.50595I
u = 0.039758 − 0.866938I
2.43227 + 2.98822I −1.17573 − 2.50595I
u = 0.528849 + 0.662164I
5.28964 + 8.99184I 2.24371 − 8.34910I
u = 0.528849 − 0.662164I
5.28964 − 8.99184I 2.24371 + 8.34910I
u = −0.529498 + 0.643326I
5.68597 − 2.74218I 3.17354 + 3.44962I
u = −0.529498 − 0.643326I
5.68597 + 2.74218I 3.17354 − 3.44962I
u = 0.434530 + 0.674620I
−2.03776 + 5.19435I −3.33716 − 9.21025I
u = 0.434530 − 0.674620I
−2.03776 − 5.19435I −3.33716 + 9.21025I
u = 0.279015 + 0.697032I
−3.00780 + 0.17019I −7.29367 − 0.75206I
u = 0.279015 − 0.697032I
−3.00780 − 0.17019I −7.29367 + 0.75206I
u = −0.401351 + 0.583059I
0.07417 − 1.89235I 3.15479 + 4.52320I
u = −0.401351 − 0.583059I
0.07417 + 1.89235I 3.15479 − 4.52320I
u = −0.588252 + 0.276624I
6.75859 − 1.08065I 5.91547 + 2.62482I
u = −0.588252 − 0.276624I
6.75859 + 1.08065I 5.91547 − 2.62482I
u = 0.596249 + 0.252176I
6.48998 − 5.15115I 5.34177 + 2.63886I
u = 0.596249 − 0.252176I
6.48998 + 5.15115I 5.34177 − 2.63886I
u = −0.014393 + 1.396600I
1.85163 − 3.15004I 0. + 2.61659I
u = −0.014393 − 1.396600I
1.85163 + 3.15004I 0. − 2.61659I
u = −0.383996 + 0.360002I
0.721812 − 0.963189I 5.72873 + 5.37633I
u = −0.383996 − 0.360002I
0.721812 + 0.963189I 5.72873 − 5.37633I
u = 0.469156 + 0.145748I
−0.55346 − 2.03006I 1.12004 + 4.04451I
u = 0.469156 − 0.145748I
−0.55346 + 2.03006I 1.12004 − 4.04451I
u = −0.04789 + 1.52934I
−5.61681 − 2.13861I 0
u = −0.04789 − 1.52934I
−5.61681 + 2.13861I 0
u = −0.11001 + 1.57378I
−7.26818 − 3.72706I 0
u = −0.11001 − 1.57378I
−7.26818 + 3.72706I 0
u = −0.15462 + 1.58238I
−1.80521 − 5.25682I 0
u = −0.15462 − 1.58238I
−1.80521 + 5.25682I 0
u = 0.15565 + 1.58986I
−2.30348 + 11.52240I 0
u = 0.15565 − 1.58986I
−2.30348 − 11.52240I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.08438 + 1.59811I
−10.84150 + 1.55360I 0
u = 0.08438 − 1.59811I
−10.84150 − 1.55360I 0
u = 0.12378 + 1.59576I
−9.75368 + 7.25706I 0
u = 0.12378 − 1.59576I
−9.75368 − 7.25706I 0
u = 0.01864 + 1.60315I
−5.85535 − 2.75781I 0
u = 0.01864 − 1.60315I
−5.85535 + 2.75781I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
36
+ u
35
+ ··· + u
2
+ 1
c
2
, c
5
, c
7
u
36
+ 9u
35
+ ··· + 2u + 1
c
3
, c
4
, c
9
c
10
u
36
+ u
35
+ ··· + 2u + 1
c
8
u
36
+ u
35
+ ··· + 24u + 5
c
11
u
36
− 9u
35
+ ··· + 8u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
36
+ 9y
35
+ ··· + 2y + 1
c
2
, c
5
, c
7
y
36
+ 37y
35
+ ··· + 18y + 1
c
3
, c
4
, c
9
c
10
y
36
+ 41y
35
+ ··· + 2y + 1
c
8
y
36
− 3y
35
+ ··· − 6y + 25
c
11
y
36
+ y
35
+ ··· − 30y + 1
8
