11a
192
(K11a
192
)
A knot diagram
1
Linearized knot diagam
6 1 10 9 7 2 3 11 4 5 8
Solving Sequence
5,9
4 10 11 3 8 1 2 7 6
c
4
c
9
c
10
c
3
c
8
c
11
c
2
c
7
c
5
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
+ u
47
+ ··· − 4u − 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
+ u
47
+ · · · − 4u − 1i
(i) Arc colorings
a
5
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
−u
u
3
+ u
a
11
=
−u
3
− 2u
u
3
+ u
a
3
=
u
2
+ 1
−u
4
− 2u
2
a
8
=
u
7
+ 4u
5
+ 4u
3
−u
7
− 3u
5
− 2u
3
+ u
a
1
=
−u
11
− 6u
9
− 12u
7
− 8u
5
− u
3
− 2u
u
11
+ 5u
9
+ 8u
7
+ 3u
5
− u
3
+ u
a
2
=
−u
26
− 13u
24
+ ··· + 3u
2
+ 1
u
26
+ 12u
24
+ ··· + 4u
4
− 3u
2
a
7
=
u
13
+ 6u
11
+ 13u
9
+ 12u
7
+ 6u
5
+ 4u
3
+ u
−u
15
− 7u
13
− 18u
11
− 19u
9
− 6u
7
− 2u
5
− 4u
3
+ u
a
6
=
−u
28
− 13u
26
+ ··· + u
2
+ 1
u
30
+ 14u
28
+ ··· − 8u
4
+ u
2
a
6
=
−u
28
− 13u
26
+ ··· + u
2
+ 1
u
30
+ 14u
28
+ ··· − 8u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
47
+ 4u
46
+ ··· − 24u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
− u
47
+ ··· + 4u
2
− 1
c
2
, c
5
u
48
+ 15u
47
+ ··· + 8u + 1
c
3
, c
4
, c
9
u
48
+ u
47
+ ··· − 4u − 1
c
7
u
48
+ u
47
+ ··· − 282u − 61
c
8
, c
11
u
48
− 7u
47
+ ··· − 16u + 1
c
10
u
48
− u
47
+ ··· − 198u − 37
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
− 15y
47
+ ··· − 8y + 1
c
2
, c
5
y
48
+ 37y
47
+ ··· − 40y + 1
c
3
, c
4
, c
9
y
48
+ 45y
47
+ ··· − 8y + 1
c
7
y
48
+ 13y
47
+ ··· − 22428y + 3721
c
8
, c
11
y
48
+ 41y
47
+ ··· + 200y + 1
c
10
y
48
+ 17y
47
+ ··· + 24140y + 1369
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.068968 + 1.151590I
2.32852 + 2.32135I −10.38591 + 0.I
u = 0.068968 − 1.151590I
2.32852 − 2.32135I −10.38591 + 0.I
u = −0.683357 + 0.405926I
5.21260 + 9.77857I −8.26482 − 8.48475I
u = −0.683357 − 0.405926I
5.21260 − 9.77857I −8.26482 + 8.48475I
u = 0.673489 + 0.415868I
6.02949 − 3.89902I −6.63992 + 3.50313I
u = 0.673489 − 0.415868I
6.02949 + 3.89902I −6.63992 − 3.50313I
u = −0.576773 + 0.522352I
5.67693 − 5.57732I −6.94459 + 2.40000I
u = −0.576773 − 0.522352I
5.67693 + 5.57732I −6.94459 − 2.40000I
u = 0.589475 + 0.506546I
6.39491 − 0.29411I −5.62712 + 2.80614I
u = 0.589475 − 0.506546I
6.39491 + 0.29411I −5.62712 − 2.80614I
u = 0.173044 + 1.237190I
−0.64228 − 2.86520I 0
u = 0.173044 − 1.237190I
−0.64228 + 2.86520I 0
u = −0.640543 + 0.369715I
−0.68024 + 4.58900I −13.6527 − 7.1281I
u = −0.640543 − 0.369715I
−0.68024 − 4.58900I −13.6527 + 7.1281I
u = 0.603013 + 0.419142I
2.62424 − 1.94253I −5.82906 + 3.77516I
u = 0.603013 − 0.419142I
2.62424 + 1.94253I −5.82906 − 3.77516I
u = −0.090373 + 1.285590I
3.24763 + 1.60907I 0
u = −0.090373 − 1.285590I
3.24763 − 1.60907I 0
u = 0.218506 + 1.294790I
3.84600 − 8.17225I 0
u = 0.218506 − 1.294790I
3.84600 + 8.17225I 0
u = −0.505212 + 0.440988I
−0.223689 − 0.846659I −12.11040 + 0.46472I
u = −0.505212 − 0.440988I
−0.223689 + 0.846659I −12.11040 − 0.46472I
u = −0.196581 + 1.315430I
4.69521 + 2.82559I 0
u = −0.196581 − 1.315430I
4.69521 − 2.82559I 0
u = 0.627758 + 0.108061I
−0.50327 − 5.09371I −14.3561 + 6.8355I
u = 0.627758 − 0.108061I
−0.50327 + 5.09371I −14.3561 − 6.8355I
u = 0.609769
−4.36789 −20.8280
u = −0.582317 + 0.152321I
0.1388920 − 0.0056976I −12.76408 − 1.77198I
u = −0.582317 − 0.152321I
0.1388920 + 0.0056976I −12.76408 + 1.77198I
u = −0.012644 + 1.408660I
7.96823 + 2.83806I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.012644 − 1.408660I
7.96823 − 2.83806I 0
u = −0.074086 + 0.558977I
2.01219 + 2.59814I −6.70685 − 3.63850I
u = −0.074086 − 0.558977I
2.01219 − 2.59814I −6.70685 + 3.63850I
u = −0.20167 + 1.44404I
5.75150 + 1.80433I 0
u = −0.20167 − 1.44404I
5.75150 − 1.80433I 0
u = −0.24122 + 1.44657I
5.16114 + 7.81947I 0
u = −0.24122 − 1.44657I
5.16114 − 7.81947I 0
u = 0.22417 + 1.45752I
8.65974 − 4.98357I 0
u = 0.22417 − 1.45752I
8.65974 + 4.98357I 0
u = −0.25363 + 1.46457I
11.2407 + 13.2008I 0
u = −0.25363 − 1.46457I
11.2407 − 13.2008I 0
u = 0.24833 + 1.46680I
12.09980 − 7.26678I 0
u = 0.24833 − 1.46680I
12.09980 + 7.26678I 0
u = −0.19351 + 1.48062I
12.14030 − 2.80062I 0
u = −0.19351 − 1.48062I
12.14030 + 2.80062I 0
u = 0.20123 + 1.47969I
12.80670 − 3.15758I 0
u = 0.20123 − 1.47969I
12.80670 + 3.15758I 0
u = −0.361931
−0.601903 −16.4760
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
48
− u
47
+ ··· + 4u
2
− 1
c
2
, c
5
u
48
+ 15u
47
+ ··· + 8u + 1
c
3
, c
4
, c
9
u
48
+ u
47
+ ··· − 4u − 1
c
7
u
48
+ u
47
+ ··· − 282u − 61
c
8
, c
11
u
48
− 7u
47
+ ··· − 16u + 1
c
10
u
48
− u
47
+ ··· − 198u − 37
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
48
− 15y
47
+ ··· − 8y + 1
c
2
, c
5
y
48
+ 37y
47
+ ··· − 40y + 1
c
3
, c
4
, c
9
y
48
+ 45y
47
+ ··· − 8y + 1
c
7
y
48
+ 13y
47
+ ··· − 22428y + 3721
c
8
, c
11
y
48
+ 41y
47
+ ··· + 200y + 1
c
10
y
48
+ 17y
47
+ ··· + 24140y + 1369
8
