11a
59
(K11a
59
)
A knot diagram
1
Linearized knot diagam
4 1 8 2 11 10 9 3 7 6 5
Solving Sequence
2,5
4 1 3 11 6 10 7 9 8
c
4
c
1
c
2
c
11
c
5
c
10
c
6
c
9
c
8
c
3
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
21
+ u
20
+ ··· − 3u − 1i
* 1 irreducible components of dim
C
= 0, with total 21 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
21
+ u
20
+ · · · − 3u − 1i
(i) Arc colorings
a
2
=
0
u
a
5
=
1
0
a
4
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
6
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
7
=
u
12
− 3u
10
+ 3u
8
+ 2u
6
− 4u
4
+ u
2
+ 1
−u
12
+ 4u
10
− 6u
8
+ 2u
6
+ 3u
4
− 2u
2
a
9
=
u
15
− 4u
13
+ 6u
11
− 8u
7
+ 6u
5
+ 2u
3
− 2u
−u
15
+ 5u
13
− 10u
11
+ 7u
9
+ 4u
7
− 8u
5
+ 2u
3
+ u
a
8
=
u
18
− 5u
16
+ 10u
14
− 5u
12
− 11u
10
+ 17u
8
− 2u
6
− 8u
4
+ 3u
2
+ 1
−u
18
+ 6u
16
− 15u
14
+ 16u
12
+ u
10
− 18u
8
+ 12u
6
+ 2u
4
− 3u
2
a
8
=
u
18
− 5u
16
+ 10u
14
− 5u
12
− 11u
10
+ 17u
8
− 2u
6
− 8u
4
+ 3u
2
+ 1
−u
18
+ 6u
16
− 15u
14
+ 16u
12
+ u
10
− 18u
8
+ 12u
6
+ 2u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
19
+ 24u
17
+ 4u
16
− 64u
15
− 20u
14
+ 76u
13
+ 44u
12
− 4u
11
−
36u
10
− 100u
9
− 16u
8
+ 92u
7
+ 56u
6
− 24u
4
− 44u
3
− 8u
2
+ 8u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
21
− u
20
+ ··· − 3u + 1
c
2
u
21
+ 13u
20
+ ··· − u + 1
c
3
, c
8
u
21
− u
20
+ ··· + u + 1
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
21
− 3u
20
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 13y
20
+ ··· − y −1
c
2
y
21
− 9y
20
+ ··· + 3y −1
c
3
, c
8
y
21
+ 3y
20
+ ··· − y −1
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
21
+ 31y
20
+ ··· + 19y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.007758 + 0.949268I
−16.7890 − 3.4594I −3.86074 + 2.19983I
u = −0.007758 − 0.949268I
−16.7890 + 3.4594I −3.86074 − 2.19983I
u = 1.052520 + 0.258621I
−2.94174 − 0.96273I −7.66565 + 0.63893I
u = 1.052520 − 0.258621I
−2.94174 + 0.96273I −7.66565 − 0.63893I
u = −1.014220 + 0.391763I
−1.91084 + 4.81660I −2.93817 − 8.87119I
u = −1.014220 − 0.391763I
−1.91084 − 4.81660I −2.93817 + 8.87119I
u = 0.887361
−1.29680 −8.38840
u = −0.742095 + 0.310540I
0.91477 + 1.54422I 4.91782 − 5.70348I
u = −0.742095 − 0.310540I
0.91477 − 1.54422I 4.91782 + 5.70348I
u = −0.042739 + 0.780467I
−5.48993 − 2.78640I −3.21012 + 3.06333I
u = −0.042739 − 0.780467I
−5.48993 + 2.78640I −3.21012 − 3.06333I
u = −1.190720 + 0.447677I
−8.87843 + 7.21776I −6.27845 − 6.45593I
u = −1.190720 − 0.447677I
−8.87843 − 7.21776I −6.27845 + 6.45593I
u = 1.208770 + 0.404400I
−9.21675 − 1.40322I −7.22383 + 0.67485I
u = 1.208770 − 0.404400I
−9.21675 + 1.40322I −7.22383 − 0.67485I
u = −1.290770 + 0.486469I
18.7348 + 8.5672I −6.90755 − 5.03550I
u = −1.290770 − 0.486469I
18.7348 − 8.5672I −6.90755 + 5.03550I
u = 1.295050 + 0.477383I
18.6641 − 1.6077I −7.04859 + 0.65486I
u = 1.295050 − 0.477383I
18.6641 + 1.6077I −7.04859 − 0.65486I
u = −0.211725 + 0.440665I
0.159228 − 1.336100I 1.40948 + 5.21346I
u = −0.211725 − 0.440665I
0.159228 + 1.336100I 1.40948 − 5.21346I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
21
− u
20
+ ··· − 3u + 1
c
2
u
21
+ 13u
20
+ ··· − u + 1
c
3
, c
8
u
21
− u
20
+ ··· + u + 1
c
5
, c
6
, c
7
c
9
, c
10
, c
11
u
21
− 3u
20
+ ··· − u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
21
− 13y
20
+ ··· − y −1
c
2
y
21
− 9y
20
+ ··· + 3y −1
c
3
, c
8
y
21
+ 3y
20
+ ··· − y −1
c
5
, c
6
, c
7
c
9
, c
10
, c
11
y
21
+ 31y
20
+ ··· + 19y −1
7
