11a
234
(K11a
234
)
A knot diagram
1
Linearized knot diagam
7 1 9 10 11 8 2 3 4 5 6
Solving Sequence
4,10
5 11 6 1 9 3 2 8 7
c
4
c
10
c
5
c
11
c
9
c
3
c
2
c
8
c
6
c
1
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
− u
17
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 18 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
18
− u
17
− 13u
16
+ 12u
15
+ 68u
14
− 57u
13
− 183u
12
+ 136u
11
+
269u
10
− 169u
9
− 213u
8
+ 98u
7
+ 88u
6
− 14u
5
− 20u
4
− 6u
3
− u
2
+ 3u + 1i
(i) Arc colorings
a
4
=
1
0
a
10
=
0
u
a
5
=
1
u
2
a
11
=
−u
−u
3
+ u
a
6
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
3
− 2u
u
5
− 3u
3
+ u
a
9
=
u
u
a
3
=
−u
2
+ 1
−u
2
a
2
=
u
10
− 7u
8
+ 16u
6
− 13u
4
+ u
2
+ 1
u
12
− 8u
10
+ 22u
8
− 24u
6
+ 9u
4
− 2u
2
a
8
=
−u
3
+ 2u
−u
3
+ u
a
7
=
u
10
− 7u
8
+ 16u
6
− 13u
4
+ u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 8u
4
+ 3u
2
a
7
=
u
10
− 7u
8
+ 16u
6
− 13u
4
+ u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 8u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
14
+ 44u
12
−184u
10
+ 364u
8
+ 4u
7
−344u
6
−24u
5
+ 136u
4
+ 40u
3
−16u
2
−16u −22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
18
+ u
17
+ ··· + 3u + 1
c
2
, c
6
u
18
+ 7u
17
+ ··· + 11u + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
c
11
u
18
− u
17
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
18
− 7y
17
+ ··· − 11y + 1
c
2
, c
6
y
18
+ 9y
17
+ ··· − 47y + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
c
11
y
18
− 27y
17
+ ··· − 11y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.802264
−4.07451 −21.8940
u = 0.682462 + 0.319779I
−0.72908 − 4.95076I −15.7381 + 7.5517I
u = 0.682462 − 0.319779I
−0.72908 + 4.95076I −15.7381 − 7.5517I
u = 1.293990 + 0.094892I
−5.94680 − 1.32320I −15.7100 + 0.4777I
u = 1.293990 − 0.094892I
−5.94680 + 1.32320I −15.7100 − 0.4777I
u = −1.345790 + 0.141741I
−7.44415 + 6.58593I −17.8634 − 5.4114I
u = −1.345790 − 0.141741I
−7.44415 − 6.58593I −17.8634 + 5.4114I
u = −0.540515 + 0.292466I
0.102284 + 0.099203I −13.71777 − 2.29447I
u = −0.540515 − 0.292466I
0.102284 − 0.099203I −13.71777 + 2.29447I
u = −1.39228
−11.4338 −21.8520
u = −0.061930 + 0.448593I
1.53103 + 2.40291I −8.85929 − 4.25520I
u = −0.061930 − 0.448593I
1.53103 − 2.40291I −8.85929 + 4.25520I
u = −0.325737
−0.531842 −18.6180
u = −1.81666 + 0.02246I
−17.5190 + 1.8647I −15.9411 − 0.0828I
u = −1.81666 − 0.02246I
−17.5190 − 1.8647I −15.9411 + 0.0828I
u = 1.82734 + 0.03524I
−19.2732 − 7.4400I −18.1912 + 4.5032I
u = 1.82734 − 0.03524I
−19.2732 + 7.4400I −18.1912 − 4.5032I
u = 1.83796
15.9019 −21.5940
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
18
+ u
17
+ ··· + 3u + 1
c
2
, c
6
u
18
+ 7u
17
+ ··· + 11u + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
c
11
u
18
− u
17
+ ··· + 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
18
− 7y
17
+ ··· − 11y + 1
c
2
, c
6
y
18
+ 9y
17
+ ··· − 47y + 1
c
3
, c
4
, c
5
c
8
, c
9
, c
10
c
11
y
18
− 27y
17
+ ··· − 11y + 1
7
