11a
207
(K11a
207
)
A knot diagram
1
Linearized knot diagam
7 1 9 11 10 2 6 3 4 5 8
Solving Sequence
4,11
5 10 6 9 3 8 1 2 7
c
4
c
10
c
5
c
9
c
3
c
8
c
11
c
2
c
7
c
1
, c
6
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
4
=
1
0
a
11
=
0
u
a
5
=
1
−u
2
a
10
=
−u
u
3
+ u
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
9
=
−u
3
− 2u
u
3
+ u
a
3
=
−u
6
− 3u
4
− 2u
2
+ 1
u
6
+ 2u
4
+ u
2
a
8
=
u
9
+ 4u
7
+ 5u
5
− 3u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
19
+ 8u
17
+ 26u
15
+ 40u
13
+ 19u
11
− 24u
9
− 30u
7
+ 9u
3
−u
19
− 7u
17
− 20u
15
− 27u
13
− 11u
11
+ 13u
9
+ 14u
7
− 3u
3
+ u
a
2
=
−u
32
− 13u
30
+ ··· − 2u
2
+ 1
u
32
+ 12u
30
+ ··· − 8u
6
+ 10u
4
a
7
=
u
15
+ 6u
13
+ 14u
11
+ 14u
9
+ 2u
7
− 6u
5
− 4u
3
− 2u
−u
17
− 7u
15
− 19u
13
− 22u
11
− 3u
9
+ 14u
7
+ 6u
5
− 2u
3
+ u
a
7
=
u
15
+ 6u
13
+ 14u
11
+ 14u
9
+ 2u
7
− 6u
5
− 4u
3
− 2u
−u
17
− 7u
15
− 19u
13
− 22u
11
− 3u
9
+ 14u
7
+ 6u
5
− 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
41
− 4u
40
+ ··· − 16u + 10
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
, c
7
u
42
+ 13u
41
+ ··· − 7u + 1
c
3
, c
8
, c
9
u
42
+ u
41
+ ··· − 7u − 1
c
4
, c
5
, c
10
u
42
− u
41
+ ··· + u − 1
c
11
u
42
− 5u
41
+ ··· + 536u − 112
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
+ 13y
41
+ ··· − 7y + 1
c
2
, c
7
y
42
+ 33y
41
+ ··· − 83y + 1
c
3
, c
8
, c
9
y
42
− 43y
41
+ ··· + 9y + 1
c
4
, c
5
, c
10
y
42
+ 33y
41
+ ··· − 7y + 1
c
11
y
42
− 15y
41
+ ··· − 104736y + 12544
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.084866 + 0.923766I
1.35453 − 2.76686I 9.42200 + 3.38146I
u = −0.084866 − 0.923766I
1.35453 + 2.76686I 9.42200 − 3.38146I
u = 0.880691 + 0.040826I
10.66200 + 2.16328I 14.13258 − 0.47169I
u = 0.880691 − 0.040826I
10.66200 − 2.16328I 14.13258 + 0.47169I
u = −0.879079 + 0.051740I
9.88329 − 8.13672I 12.75687 + 5.51016I
u = −0.879079 − 0.051740I
9.88329 + 8.13672I 12.75687 − 5.51016I
u = 0.855130
6.83608 14.4990
u = −0.836220 + 0.033472I
3.58400 − 3.03568I 8.16735 + 3.88704I
u = −0.836220 − 0.033472I
3.58400 + 3.03568I 8.16735 − 3.88704I
u = −0.098348 + 1.233710I
−3.04850 − 1.58009I 6.29997 + 4.16737I
u = −0.098348 − 1.233710I
−3.04850 + 1.58009I 6.29997 − 4.16737I
u = −0.376057 + 1.243220I
−0.153213 − 1.320920I 4.68472 + 0.I
u = −0.376057 − 1.243220I
−0.153213 + 1.320920I 4.68472 + 0.I
u = −0.425057 + 1.229040I
6.25079 + 3.47148I 9.66765 + 0.I
u = −0.425057 − 1.229040I
6.25079 − 3.47148I 9.66765 + 0.I
u = 0.424115 + 1.240230I
6.95625 + 2.50407I 10.88098 + 0.I
u = 0.424115 − 1.240230I
6.95625 − 2.50407I 10.88098 + 0.I
u = −0.195205 + 1.297820I
−1.39593 − 2.80686I 6.44866 + 0.I
u = −0.195205 − 1.297820I
−1.39593 + 2.80686I 6.44866 + 0.I
u = 0.035155 + 1.315210I
−4.04030 − 2.27723I 0
u = 0.035155 − 1.315210I
−4.04030 + 2.27723I 0
u = 0.122930 + 1.316230I
−6.86790 + 2.94706I 0
u = 0.122930 − 1.316230I
−6.86790 − 2.94706I 0
u = 0.394311 + 1.273400I
2.88132 + 4.48173I 10.66614 + 0.I
u = 0.394311 − 1.273400I
2.88132 − 4.48173I 10.66614 + 0.I
u = 0.186816 + 1.325010I
−2.22914 + 8.22632I 0
u = 0.186816 − 1.325010I
−2.22914 − 8.22632I 0
u = −0.379309 + 1.296770I
−0.56467 − 7.40547I 0
u = −0.379309 − 1.296770I
−0.56467 + 7.40547I 0
u = 0.407279 + 1.306890I
6.45725 + 6.77734I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.407279 − 1.306890I
6.45725 − 6.77734I 0
u = −0.404155 + 1.314050I
5.61722 − 12.73560I 0
u = −0.404155 − 1.314050I
5.61722 + 12.73560I 0
u = 0.551129 + 0.261557I
2.69787 + 5.64894I 10.88515 − 7.96618I
u = 0.551129 − 0.261557I
2.69787 − 5.64894I 10.88515 + 7.96618I
u = 0.118650 + 0.596465I
1.34684 − 2.67555I 7.55600 + 2.24740I
u = 0.118650 − 0.596465I
1.34684 + 2.67555I 7.55600 − 2.24740I
u = −0.560874 + 0.207268I
3.23539 − 0.14490I 12.69254 + 2.12339I
u = −0.560874 − 0.207268I
3.23539 + 0.14490I 12.69254 − 2.12339I
u = 0.366568 + 0.310618I
−1.92633 + 1.23641I 3.06440 − 5.84978I
u = 0.366568 − 0.310618I
−1.92633 − 1.23641I 3.06440 + 5.84978I
u = −0.352081
0.588838 16.8680
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
42
+ u
41
+ ··· + u − 1
c
2
, c
7
u
42
+ 13u
41
+ ··· − 7u + 1
c
3
, c
8
, c
9
u
42
+ u
41
+ ··· − 7u − 1
c
4
, c
5
, c
10
u
42
− u
41
+ ··· + u − 1
c
11
u
42
− 5u
41
+ ··· + 536u − 112
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
42
+ 13y
41
+ ··· − 7y + 1
c
2
, c
7
y
42
+ 33y
41
+ ··· − 83y + 1
c
3
, c
8
, c
9
y
42
− 43y
41
+ ··· + 9y + 1
c
4
, c
5
, c
10
y
42
+ 33y
41
+ ··· − 7y + 1
c
11
y
42
− 15y
41
+ ··· − 104736y + 12544
8
