11a
334
(K11a
334
)
A knot diagram
1
Linearized knot diagam
7 8 1 10 11 9 2 3 4 5 6
Solving Sequence
5,10
11 6 1 4 3 9 7 2 8
c
10
c
5
c
11
c
4
c
3
c
9
c
6
c
1
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
24
− u
23
+ ··· + 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 24 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
24
− u
23
+ · · · + 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
10
=
1
0
a
11
=
1
u
2
a
6
=
−u
−u
3
+ u
a
1
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
u
u
a
3
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
9
=
−u
2
+ 1
−u
2
a
7
=
u
7
− 4u
5
+ 4u
3
− 2u
u
7
− 3u
5
+ u
a
2
=
u
18
− 11u
16
+ 48u
14
− 107u
12
+ 133u
10
− 95u
8
+ 34u
6
− 2u
4
− 3u
2
+ 1
u
18
− 10u
16
+ 37u
14
− 60u
12
+ 35u
10
+ 8u
8
− 16u
6
+ 2u
4
+ 3u
2
a
8
=
u
18
− 11u
16
+ 48u
14
− 107u
12
+ 133u
10
− 95u
8
+ 34u
6
− 2u
4
− 3u
2
+ 1
u
20
− 12u
18
+ ··· − 5u
4
− 2u
2
a
8
=
u
18
− 11u
16
+ 48u
14
− 107u
12
+ 133u
10
− 95u
8
+ 34u
6
− 2u
4
− 3u
2
+ 1
u
20
− 12u
18
+ ··· − 5u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
20
+ 52u
18
− 276u
16
+ 4u
15
+ 768u
14
− 40u
13
− 1200u
12
+
152u
11
+ 1048u
10
− 272u
9
− 456u
8
+ 232u
7
+ 16u
6
− 84u
5
+ 64u
4
− 16u
2
+ 4u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
24
+ u
23
+ ··· + 2u + 1
c
3
, c
6
u
24
− 5u
23
+ ··· + 8u + 1
c
4
, c
5
, c
9
c
10
, c
11
u
24
− u
23
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
24
− 27y
23
+ ··· − 12y + 1
c
3
, c
6
y
24
+ 9y
23
+ ··· − 52y + 1
c
4
, c
5
, c
9
c
10
, c
11
y
24
− 31y
23
+ ··· − 12y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.950752 + 0.350160I
−8.25724 + 7.03301I −18.3094 − 5.9376I
u = −0.950752 − 0.350160I
−8.25724 − 7.03301I −18.3094 + 5.9376I
u = 0.889313 + 0.320048I
−1.05294 − 4.61822I −15.0731 + 7.6448I
u = 0.889313 − 0.320048I
−1.05294 + 4.61822I −15.0731 − 7.6448I
u = 0.931166
−4.16199 −21.6480
u = −1.08787
−11.9871 −21.6380
u = −0.791765 + 0.276135I
−0.346278 + 1.021000I −12.74843 − 0.89701I
u = −0.791765 − 0.276135I
−0.346278 − 1.021000I −12.74843 + 0.89701I
u = 0.603718 + 0.367833I
−6.35060 + 0.70363I −16.4740 + 1.9101I
u = 0.603718 − 0.367833I
−6.35060 − 0.70363I −16.4740 − 1.9101I
u = 0.139902 + 0.569572I
−4.91541 − 3.91207I −12.94617 + 4.09440I
u = 0.139902 − 0.569572I
−4.91541 + 3.91207I −12.94617 − 4.09440I
u = −0.055351 + 0.524042I
1.82022 + 1.73926I −8.19189 − 4.76160I
u = −0.055351 − 0.524042I
1.82022 − 1.73926I −8.19189 + 4.76160I
u = −1.63181
−13.8397 −18.0490
u = 1.66882 + 0.06009I
−9.03688 − 2.20767I −14.13375 − 0.08900I
u = 1.66882 − 0.06009I
−9.03688 + 2.20767I −14.13375 + 0.08900I
u = −1.68602 + 0.08006I
−10.10980 + 6.14857I −16.6878 − 5.7012I
u = −1.68602 − 0.08006I
−10.10980 − 6.14857I −16.6878 + 5.7012I
u = −1.68905
−13.4393 −20.4550
u = 1.70217 + 0.09194I
−17.5954 − 8.7809I −19.5765 + 4.4157I
u = 1.70217 − 0.09194I
−17.5954 + 8.7809I −19.5765 − 4.4157I
u = −0.291508
−0.498247 −19.9340
u = 1.72899
17.4406 −21.9940
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
24
+ u
23
+ ··· + 2u + 1
c
3
, c
6
u
24
− 5u
23
+ ··· + 8u + 1
c
4
, c
5
, c
9
c
10
, c
11
u
24
− u
23
+ ··· + 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
24
− 27y
23
+ ··· − 12y + 1
c
3
, c
6
y
24
+ 9y
23
+ ··· − 52y + 1
c
4
, c
5
, c
9
c
10
, c
11
y
24
− 31y
23
+ ··· − 12y + 1
7
