11a
235
(K11a
235
)
A knot diagram
1
Linearized knot diagam
7 1 9 11 10 8 2 3 4 5 6
Solving Sequence
4,11
5 10 6 1 9 3 2 8 7
c
4
c
10
c
5
c
11
c
9
c
3
c
2
c
8
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
− u
34
+ ··· − 4u + 1i
* 1 irreducible components of dim
C
= 0, with total 35 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
35
− u
34
+ · · · − 4u + 1i
(i) Arc colorings
a
4
=
1
0
a
11
=
0
u
a
5
=
1
u
2
a
10
=
u
u
3
+ u
a
6
=
u
2
+ 1
u
4
+ 2u
2
a
1
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
9
=
u
3
+ 2u
u
3
+ u
a
3
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
6
− 2u
4
− u
2
a
2
=
u
18
+ 7u
16
+ 20u
14
+ 27u
12
+ 11u
10
− 13u
8
− 16u
6
− 6u
4
− u
2
+ 1
u
20
+ 8u
18
+ 26u
16
+ 40u
14
+ 19u
12
− 24u
10
− 30u
8
− 2u
6
+ 5u
4
− 2u
2
a
8
=
−u
9
− 4u
7
− 5u
5
+ 3u
−u
9
− 3u
7
− 3u
5
+ u
a
7
=
−u
22
− 9u
20
+ ··· + 4u
2
+ 1
−u
22
− 8u
20
+ ··· − 4u
4
+ 3u
2
a
7
=
−u
22
− 9u
20
+ ··· + 4u
2
+ 1
−u
22
− 8u
20
+ ··· − 4u
4
+ 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
34
− 4u
33
+ 52u
32
− 48u
31
+ 300u
30
− 256u
29
+ 980u
28
− 772u
27
+ 1868u
26
−
1352u
25
+ 1680u
24
− 1100u
23
− 756u
22
+ 500u
21
− 3692u
20
+ 2060u
19
− 3200u
18
+
1536u
17
+ 804u
16
−428u
15
+ 3104u
14
−1136u
13
+ 1216u
12
−208u
11
−976u
10
+ 368u
9
−
704u
8
+ 64u
7
+ 136u
6
− 128u
5
+ 128u
4
− 24u
3
− 28u
2
+ 20u − 22
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
35
+ u
34
+ ··· − 2u − 1
c
2
, c
6
u
35
+ 13u
34
+ ··· + 10u + 1
c
3
, c
8
, c
9
c
11
u
35
− u
34
+ ··· − 8u − 1
c
4
, c
5
, c
10
u
35
+ u
34
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
35
− 13y
34
+ ··· + 10y −1
c
2
, c
6
y
35
+ 19y
34
+ ··· + 26y −1
c
3
, c
8
, c
9
c
11
y
35
− 41y
34
+ ··· + 26y −1
c
4
, c
5
, c
10
y
35
+ 27y
34
+ ··· + 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.154678 + 1.010450I
1.47757 − 2.06754I −12.18012 + 2.63820I
u = −0.154678 − 1.010450I
1.47757 + 2.06754I −12.18012 − 2.63820I
u = 0.908910
−13.2599 −19.8870
u = 0.902196 + 0.033304I
−9.04332 − 7.10158I −16.2339 + 4.8820I
u = 0.902196 − 0.033304I
−9.04332 + 7.10158I −16.2339 − 4.8820I
u = −0.889066 + 0.023250I
−7.40598 + 1.64045I −14.07012 − 0.25947I
u = −0.889066 − 0.023250I
−7.40598 − 1.64045I −14.07012 + 0.25947I
u = 0.126515 + 1.195620I
2.79133 − 1.62971I −6.97786 + 4.00042I
u = 0.126515 − 1.195620I
2.79133 + 1.62971I −6.97786 − 4.00042I
u = −0.253657 + 1.196640I
−0.75414 + 3.23838I −15.3127 − 4.6996I
u = −0.253657 − 1.196640I
−0.75414 − 3.23838I −15.3127 + 4.6996I
u = 0.198838 + 1.295440I
4.68045 − 2.80636I −6.46642 + 3.03616I
u = 0.198838 − 1.295440I
4.68045 + 2.80636I −6.46642 − 3.03616I
u = 0.016865 + 1.315770I
6.80865 − 2.68270I −3.85369 + 3.32127I
u = 0.016865 − 1.315770I
6.80865 + 2.68270I −3.85369 − 3.32127I
u = −0.229253 + 1.304350I
3.85759 + 8.16795I −8.47769 − 8.32654I
u = −0.229253 − 1.304350I
3.85759 − 8.16795I −8.47769 + 8.32654I
u = 0.441243 + 1.254100I
−5.26665 + 2.30484I −13.10183 − 1.73912I
u = 0.441243 − 1.254100I
−5.26665 − 2.30484I −13.10183 + 1.73912I
u = −0.426047 + 1.260090I
−3.57477 + 3.06228I −10.68806 − 2.96548I
u = −0.426047 − 1.260090I
−3.57477 − 3.06228I −10.68806 + 2.96548I
u = 0.437322 + 1.284290I
−9.27089 − 4.80858I −16.4615 + 3.1101I
u = 0.437322 − 1.284290I
−9.27089 + 4.80858I −16.4615 − 3.1101I
u = −0.638167
−4.33695 −20.8200
u = −0.610512 + 0.184495I
−0.75413 + 5.18051I −14.8353 − 7.3100I
u = −0.610512 − 0.184495I
−0.75413 − 5.18051I −14.8353 + 7.3100I
u = −0.416900 + 1.297630I
−3.29192 + 6.31527I −10.32852 − 3.15989I
u = −0.416900 − 1.297630I
−3.29192 − 6.31527I −10.32852 + 3.15989I
u = 0.423822 + 1.307190I
−4.86404 − 11.84450I −12.4530 + 7.6430I
u = 0.423822 − 1.307190I
−4.86404 + 11.84450I −12.4530 − 7.6430I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.520978 + 0.193769I
0.117264 − 0.215670I −13.04627 + 2.21794I
u = 0.520978 − 0.193769I
0.117264 + 0.215670I −13.04627 − 2.21794I
u = 0.123574 + 0.525438I
1.48613 − 2.36443I −8.99438 + 4.59259I
u = 0.123574 − 0.525438I
1.48613 + 2.36443I −8.99438 − 4.59259I
u = 0.306778
−0.541818 −18.3300
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
u
35
+ u
34
+ ··· − 2u − 1
c
2
, c
6
u
35
+ 13u
34
+ ··· + 10u + 1
c
3
, c
8
, c
9
c
11
u
35
− u
34
+ ··· − 8u − 1
c
4
, c
5
, c
10
u
35
+ u
34
+ ··· − 4u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
35
− 13y
34
+ ··· + 10y −1
c
2
, c
6
y
35
+ 19y
34
+ ··· + 26y −1
c
3
, c
8
, c
9
c
11
y
35
− 41y
34
+ ··· + 26y −1
c
4
, c
5
, c
10
y
35
+ 27y
34
+ ··· + 10y −1
8
