11a
95
(K11a
95
)
A knot diagram
1
Linearized knot diagam
5 1 9 6 2 3 11 10 4 8 7
Solving Sequence
4,10
9 3 8 11 7 1 2 6 5
c
9
c
3
c
8
c
10
c
7
c
11
c
2
c
6
c
4
c
1
, c
5
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
4
=
0
u
a
10
=
1
0
a
9
=
1
−u
2
a
3
=
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
19
+ 2u
17
− 8u
15
+ 12u
13
− 21u
11
+ 22u
9
− 20u
7
+ 12u
5
− 5u
3
+ 2u
−u
19
+ u
17
− 6u
15
+ 5u
13
− 11u
11
+ 7u
9
− 6u
7
+ 2u
5
− u
3
+ 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
21
+ 2u
19
+ ··· + 6u
3
− u
u
23
− 3u
21
+ ··· + 2u
3
+ u
a
5
=
−u
21
+ 2u
19
+ ··· + 6u
3
− u
u
23
− 3u
21
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
34
− 4u
33
+ 12u
32
+ 16u
31
− 60u
30
− 68u
29
+ 136u
28
+
180u
27
− 352u
26
− 420u
25
+ 612u
24
+ 780u
23
− 1052u
22
− 1232u
21
+ 1408u
20
+
1624u
19
− 1744u
18
− 1804u
17
+ 1796u
16
+ 1644u
15
− 1644u
14
− 1232u
13
+ 1288u
12
+
704u
11
− 852u
10
− 296u
9
+ 456u
8
+ 44u
7
− 184u
6
+ 44u
5
+ 40u
4
− 36u
3
+ 12u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
+ u
35
+ ··· − 4u − 1
c
2
, c
4
u
36
+ 11u
35
+ ··· + 6u + 1
c
3
, c
9
u
36
− u
35
+ ··· − 2u − 1
c
6
u
36
− u
35
+ ··· − 366u − 97
c
7
, c
8
, c
10
c
11
u
36
+ 7u
35
+ ··· + 6u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
36
− 11y
35
+ ··· − 6y + 1
c
2
, c
4
y
36
+ 29y
35
+ ··· − 62y + 1
c
3
, c
9
y
36
− 7y
35
+ ··· − 6y + 1
c
6
y
36
+ 17y
35
+ ··· − 13870y + 9409
c
7
, c
8
, c
10
c
11
y
36
+ 45y
35
+ ··· − 14y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.855468 + 0.478503I
−1.79064 − 4.12069I −14.4783 + 7.6804I
u = 0.855468 − 0.478503I
−1.79064 + 4.12069I −14.4783 − 7.6804I
u = −0.885209 + 0.588905I
4.26116 + 3.38021I −6.36942 − 4.06127I
u = −0.885209 − 0.588905I
4.26116 − 3.38021I −6.36942 + 4.06127I
u = 0.910885 + 0.568898I
3.52152 − 9.06176I −8.19420 + 9.30306I
u = 0.910885 − 0.568898I
3.52152 + 9.06176I −8.19420 − 9.30306I
u = −0.612613 + 0.694030I
5.14913 + 1.38552I −3.93165 − 2.60854I
u = −0.612613 − 0.694030I
5.14913 − 1.38552I −3.93165 + 2.60854I
u = −0.740711 + 0.536049I
1.42228 + 2.05301I −4.86610 − 4.82950I
u = −0.740711 − 0.536049I
1.42228 − 2.05301I −4.86610 + 4.82950I
u = 0.568507 + 0.699594I
4.63406 + 4.35057I −4.96741 − 3.00405I
u = 0.568507 − 0.699594I
4.63406 − 4.35057I −4.96741 + 3.00405I
u = −0.882589 + 0.153471I
−0.44906 + 4.79281I −14.2901 − 6.9019I
u = −0.882589 − 0.153471I
−0.44906 − 4.79281I −14.2901 + 6.9019I
u = 0.835861 + 0.225802I
−0.001943 + 0.306901I −12.89345 + 1.58755I
u = 0.835861 − 0.225802I
−0.001943 − 0.306901I −12.89345 − 1.58755I
u = −0.854609
−4.25142 −21.1240
u = −0.905500 + 0.888140I
6.73510 + 0.05242I −9.91031 + 1.11538I
u = −0.905500 − 0.888140I
6.73510 − 0.05242I −9.91031 − 1.11538I
u = −0.942056 + 0.872713I
6.61933 + 6.45885I −10.23279 − 5.88059I
u = −0.942056 − 0.872713I
6.61933 − 6.45885I −10.23279 + 5.88059I
u = 0.929633 + 0.892365I
10.03410 − 3.29411I −3.98637 + 2.43304I
u = 0.929633 − 0.892365I
10.03410 + 3.29411I −3.98637 − 2.43304I
u = −0.901015 + 0.922180I
13.3053 − 5.0936I −5.21713 + 2.79441I
u = −0.901015 − 0.922180I
13.3053 + 5.0936I −5.21713 − 2.79441I
u = 0.909275 + 0.920439I
14.07570 − 0.94615I −3.96028 + 2.12397I
u = 0.909275 − 0.920439I
14.07570 + 0.94615I −3.96028 − 2.12397I
u = 0.962084 + 0.893022I
13.9035 − 5.7329I −4.26372 + 2.53612I
u = 0.962084 − 0.893022I
13.9035 + 5.7329I −4.26372 − 2.53612I
u = −0.967629 + 0.887890I
13.0885 + 11.7607I −5.64793 − 7.43079I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.967629 − 0.887890I
13.0885 − 11.7607I −5.64793 + 7.43079I
u = 0.484510 + 0.469460I
−0.731880 + 0.351895I −10.65376 − 0.66893I
u = 0.484510 − 0.469460I
−0.731880 − 0.351895I −10.65376 + 0.66893I
u = 0.043246 + 0.549053I
2.46542 − 2.71564I −4.42006 + 3.22989I
u = 0.043246 − 0.549053I
2.46542 + 2.71564I −4.42006 − 3.22989I
u = 0.530314
−0.709168 −14.3100
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
+ u
35
+ ··· − 4u − 1
c
2
, c
4
u
36
+ 11u
35
+ ··· + 6u + 1
c
3
, c
9
u
36
− u
35
+ ··· − 2u − 1
c
6
u
36
− u
35
+ ··· − 366u − 97
c
7
, c
8
, c
10
c
11
u
36
+ 7u
35
+ ··· + 6u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
36
− 11y
35
+ ··· − 6y + 1
c
2
, c
4
y
36
+ 29y
35
+ ··· − 62y + 1
c
3
, c
9
y
36
− 7y
35
+ ··· − 6y + 1
c
6
y
36
+ 17y
35
+ ··· − 13870y + 9409
c
7
, c
8
, c
10
c
11
y
36
+ 45y
35
+ ··· − 14y + 1
8
