11a
195
(K11a
195
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 3 6 5 4 8
Solving Sequence
5,10
4 11 3 9 6 8 1 2 7
c
4
c
10
c
3
c
9
c
5
c
8
c
11
c
2
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
26
+ u
25
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 26 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
26
+ u
25
+ · · · + u + 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
6
=
u
2
+ 1
−u
2
a
8
=
−u
3
− 2u
u
3
+ u
a
1
=
−u
9
− 6u
7
− 11u
5
− 6u
3
+ u
u
9
+ 5u
7
+ 7u
5
+ 4u
3
+ u
a
2
=
u
22
+ 15u
20
+ ··· + 3u
4
+ 1
−u
22
− 14u
20
+ ··· − 6u
4
+ u
2
a
7
=
u
9
+ 6u
7
+ 11u
5
+ 6u
3
− u
u
11
+ 7u
9
+ 16u
7
+ 13u
5
+ 3u
3
+ u
a
7
=
u
9
+ 6u
7
+ 11u
5
+ 6u
3
− u
u
11
+ 7u
9
+ 16u
7
+ 13u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
24
− 4u
23
− 72u
22
− 68u
21
− 556u
20
− 492u
19
− 2408u
18
−
1976u
17
− 6420u
16
− 4820u
15
− 10888u
14
− 7348u
13
− 11724u
12
− 6960u
11
− 7772u
10
−
3996u
9
− 3012u
8
− 1416u
7
− 688u
6
− 388u
5
− 124u
4
− 84u
3
− 12u
2
− 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
26
+ u
25
+ ··· + u + 1
c
2
u
26
+ 13u
25
+ ··· + u + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
26
+ u
25
+ ··· + u + 1
c
7
u
26
− u
25
+ ··· − 15u + 13
c
11
u
26
+ 5u
25
+ ··· + 13u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
26
+ 13y
25
+ ··· + y + 1
c
2
y
26
+ y
25
+ ··· + 13y + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
26
+ 37y
25
+ ··· + y + 1
c
7
y
26
− 11y
25
+ ··· − 771y + 169
c
11
y
26
− 7y
25
+ ··· + 209y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.077128 + 1.053710I
−3.09394 + 2.15610I 1.13399 − 4.05651I
u = 0.077128 − 1.053710I
−3.09394 − 2.15610I 1.13399 + 4.05651I
u = 0.161363 + 1.198920I
−5.09746 + 3.38991I 0.31521 − 3.08376I
u = 0.161363 − 1.198920I
−5.09746 − 3.38991I 0.31521 + 3.08376I
u = −0.197878 + 1.227700I
−7.64978 − 8.20022I −2.78707 + 6.68979I
u = −0.197878 − 1.227700I
−7.64978 + 8.20022I −2.78707 − 6.68979I
u = −0.110529 + 1.259790I
−9.26319 − 0.26212I −5.31196 − 0.01260I
u = −0.110529 − 1.259790I
−9.26319 + 0.26212I −5.31196 + 0.01260I
u = −0.244565 + 0.622723I
−3.16465 + 0.96048I −3.09934 + 0.95175I
u = −0.244565 − 0.622723I
−3.16465 − 0.96048I −3.09934 − 0.95175I
u = −0.408899 + 0.513910I
−2.03162 − 6.10006I 0.39307 + 8.69218I
u = −0.408899 − 0.513910I
−2.03162 + 6.10006I 0.39307 − 8.69218I
u = 0.348180 + 0.441188I
0.20618 + 1.65739I 4.39967 − 5.42760I
u = 0.348180 − 0.441188I
0.20618 − 1.65739I 4.39967 + 5.42760I
u = −0.456797 + 0.108055I
−0.84040 + 3.21915I 4.62809 − 2.59939I
u = −0.456797 − 0.108055I
−0.84040 − 3.21915I 4.62809 + 2.59939I
u = 0.358117 + 0.227225I
0.833642 + 0.761088I 8.16561 − 5.13707I
u = 0.358117 − 0.227225I
0.833642 − 0.761088I 8.16561 + 5.13707I
u = 0.01146 + 1.75714I
−13.35510 + 2.46006I 0. − 3.10858I
u = 0.01146 − 1.75714I
−13.35510 − 2.46006I 0. + 3.10858I
u = 0.04046 + 1.78541I
−16.0177 + 4.2821I 0. − 2.02711I
u = 0.04046 − 1.78541I
−16.0177 − 4.2821I 0. + 2.02711I
u = −0.05012 + 1.79182I
−18.6999 − 9.3134I −3.16767 + 5.53584I
u = −0.05012 − 1.79182I
−18.6999 + 9.3134I −3.16767 − 5.53584I
u = −0.02793 + 1.79884I
18.9562 − 0.8960I −5.38672 + 0.I
u = −0.02793 − 1.79884I
18.9562 + 0.8960I −5.38672 + 0.I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
26
+ u
25
+ ··· + u + 1
c
2
u
26
+ 13u
25
+ ··· + u + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
u
26
+ u
25
+ ··· + u + 1
c
7
u
26
− u
25
+ ··· − 15u + 13
c
11
u
26
+ 5u
25
+ ··· + 13u + 7
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
26
+ 13y
25
+ ··· + y + 1
c
2
y
26
+ y
25
+ ··· + 13y + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
y
26
+ 37y
25
+ ··· + y + 1
c
7
y
26
− 11y
25
+ ··· − 771y + 169
c
11
y
26
− 7y
25
+ ··· + 209y + 49
7
