11a
65
(K11a
65
)
A knot diagram
1
Linearized knot diagam
5 1 9 2 4 11 10 3 8 7 6
Solving Sequence
3,8
9 4 10 7 11 6 1 2 5
c
8
c
3
c
9
c
7
c
10
c
6
c
11
c
2
c
5
c
1
, c
4
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
+ u
28
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 29 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
29
+ u
28
+ · · · − u − 1i
(i) Arc colorings
a
3
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
4
=
u
−u
3
+ u
a
10
=
−u
2
+ 1
−u
2
a
7
=
u
4
− u
2
+ 1
u
4
a
11
=
−u
6
+ u
4
− 2u
2
+ 1
−u
6
− u
2
a
6
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
u
8
+ 2u
4
a
1
=
−u
10
+ u
8
− 4u
6
+ 3u
4
− 3u
2
+ 1
−u
10
− 3u
6
− u
2
a
2
=
u
21
− 2u
19
+ ··· − 6u
3
+ u
u
21
− u
19
+ 7u
17
− 6u
15
+ 16u
13
− 11u
11
+ 13u
9
− 6u
7
+ 3u
5
− u
3
+ u
a
5
=
u
12
− u
10
+ 5u
8
− 4u
6
+ 6u
4
− 3u
2
+ 1
−u
14
+ 2u
12
− 5u
10
+ 8u
8
− 6u
6
+ 6u
4
− u
2
a
5
=
u
12
− u
10
+ 5u
8
− 4u
6
+ 6u
4
− 3u
2
+ 1
−u
14
+ 2u
12
− 5u
10
+ 8u
8
− 6u
6
+ 6u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
27
+ 4u
26
− 8u
25
− 12u
24
+ 44u
23
+ 48u
22
− 72u
21
− 104u
20
+
184u
19
+ 208u
18
− 240u
17
− 324u
16
+ 364u
15
+ 404u
14
− 360u
13
− 440u
12
+ 340u
11
+
352u
10
− 228u
9
− 256u
8
+ 124u
7
+ 124u
6
− 32u
5
− 48u
4
+ 8u
3
+ 8u
2
+ 12u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
29
+ u
28
+ ··· + 3u − 1
c
2
, c
5
u
29
+ 11u
28
+ ··· + 3u − 1
c
3
, c
8
u
29
+ u
28
+ ··· − u − 1
c
6
, c
7
, c
9
c
10
, c
11
u
29
− 5u
28
+ ··· + 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
29
+ 11y
28
+ ··· + 3y −1
c
2
, c
5
y
29
+ 15y
28
+ ··· + 95y −1
c
3
, c
8
y
29
− 5y
28
+ ··· + 3y −1
c
6
, c
7
, c
9
c
10
, c
11
y
29
+ 39y
28
+ ··· + 15y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.662542 + 0.733995I
−2.87279 − 3.43190I 1.84331 + 2.63617I
u = 0.662542 − 0.733995I
−2.87279 + 3.43190I 1.84331 − 2.63617I
u = −0.860153 + 0.603140I
−0.92695 − 3.26280I 6.14452 + 3.98889I
u = −0.860153 − 0.603140I
−0.92695 + 3.26280I 6.14452 − 3.98889I
u = 0.800498 + 0.711356I
−6.28353 + 2.63192I −1.57742 − 3.51356I
u = 0.800498 − 0.711356I
−6.28353 − 2.63192I −1.57742 + 3.51356I
u = −0.670146 + 0.643469I
−1.53821 − 1.44300I 4.26199 + 3.33866I
u = −0.670146 − 0.643469I
−1.53821 + 1.44300I 4.26199 − 3.33866I
u = 0.897053 + 0.637489I
−2.10190 + 8.51637I 4.12248 − 8.75770I
u = 0.897053 − 0.637489I
−2.10190 − 8.51637I 4.12248 + 8.75770I
u = −0.863375 + 0.243437I
2.76289 − 4.79469I 10.76150 + 7.92652I
u = −0.863375 − 0.243437I
2.76289 + 4.79469I 10.76150 − 7.92652I
u = 0.849421 + 0.171489I
3.14251 − 0.34812I 12.60939 − 1.20059I
u = 0.849421 − 0.171489I
3.14251 + 0.34812I 12.60939 + 1.20059I
u = −0.567456 + 0.428614I
−1.16133 − 1.54019I 1.06319 + 5.77766I
u = −0.567456 − 0.428614I
−1.16133 + 1.54019I 1.06319 − 5.77766I
u = 0.925735 + 0.921889I
−10.84070 + 1.59263I 4.08077 − 2.18896I
u = 0.925735 − 0.921889I
−10.84070 − 1.59263I 4.08077 + 2.18896I
u = −0.922097 + 0.934395I
−12.57420 + 3.90608I 1.76608 − 2.34733I
u = −0.922097 − 0.934395I
−12.57420 − 3.90608I 1.76608 + 2.34733I
u = 0.955680 + 0.906089I
−10.74280 + 5.13666I 4.24719 − 2.41278I
u = 0.955680 − 0.906089I
−10.74280 − 5.13666I 4.24719 + 2.41278I
u = −0.948212 + 0.927384I
−16.7628 − 3.4088I −1.58895 + 2.29581I
u = −0.948212 − 0.927384I
−16.7628 + 3.4088I −1.58895 − 2.29581I
u = −0.966924 + 0.909523I
−12.4263 − 10.6865I 2.06858 + 6.86438I
u = −0.966924 − 0.909523I
−12.4263 + 10.6865I 2.06858 − 6.86438I
u = 0.587859
0.756056 13.9270
u = −0.086497 + 0.514422I
0.39338 + 2.26507I 2.23388 − 3.17909I
u = −0.086497 − 0.514422I
0.39338 − 2.26507I 2.23388 + 3.17909I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
u
29
+ u
28
+ ··· + 3u − 1
c
2
, c
5
u
29
+ 11u
28
+ ··· + 3u − 1
c
3
, c
8
u
29
+ u
28
+ ··· − u − 1
c
6
, c
7
, c
9
c
10
, c
11
u
29
− 5u
28
+ ··· + 3u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
29
+ 11y
28
+ ··· + 3y −1
c
2
, c
5
y
29
+ 15y
28
+ ··· + 95y −1
c
3
, c
8
y
29
− 5y
28
+ ··· + 3y −1
c
6
, c
7
, c
9
c
10
, c
11
y
29
+ 39y
28
+ ··· + 15y −1
7
