11a
335
(K11a
335
)
A knot diagram
1
Linearized knot diagam
7 8 1 11 10 9 2 3 4 5 6
Solving Sequence
2,7
8 3 9 1 4 10 6 5 11
c
7
c
2
c
8
c
1
c
3
c
9
c
6
c
5
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
37
+ u
36
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 37 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
37
+ u
36
+ · · · − u − 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
u
a
4
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
a
10
=
u
14
− 7u
12
+ 16u
10
− 11u
8
− 2u
6
− 2u
2
+ 1
u
14
− 8u
12
+ 23u
10
− 28u
8
+ 14u
6
− 6u
4
+ 3u
2
a
6
=
−u
6
+ 3u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
5
=
−u
36
+ 19u
34
+ ··· − 5u
2
+ 1
−u
36
+ 20u
34
+ ··· + 46u
6
− 13u
4
a
11
=
−u
15
+ 8u
13
− 24u
11
+ 34u
9
− 26u
7
+ 14u
5
− 4u
3
+ 2u
−u
17
+ 9u
15
− 31u
13
+ 50u
11
− 37u
9
+ 12u
7
− 4u
5
+ u
a
11
=
−u
15
+ 8u
13
− 24u
11
+ 34u
9
− 26u
7
+ 14u
5
− 4u
3
+ 2u
−u
17
+ 9u
15
− 31u
13
+ 50u
11
− 37u
9
+ 12u
7
− 4u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
34
+ 76u
32
− 640u
30
+ 4u
29
+ 3140u
28
− 64u
27
− 9936u
26
+
444u
25
+ 21272u
24
− 1744u
23
− 31696u
22
+ 4260u
21
+ 33924u
20
− 6752u
19
− 27600u
18
+
7232u
17
+ 18308u
16
− 5760u
15
− 9996u
14
+ 3932u
13
+ 4396u
12
− 2240u
11
− 1720u
10
+
976u
9
+ 536u
8
− 448u
7
− 124u
6
+ 140u
5
+ 24u
4
− 36u
3
+ 20u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
37
+ u
36
+ ··· − u − 1
c
3
, c
6
u
37
− 7u
36
+ ··· + u − 7
c
4
, c
5
, c
10
u
37
+ u
36
+ ··· − 3u − 1
c
9
, c
11
u
37
− u
36
+ ··· − 3u − 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
37
− 41y
36
+ ··· + 11y −1
c
3
, c
6
y
37
+ 19y
36
+ ··· + 239y −49
c
4
, c
5
, c
10
y
37
+ 31y
36
+ ··· + 11y −1
c
9
, c
11
y
37
− 21y
36
+ ··· + 41y −4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.602666 + 0.566356I
3.41113 − 9.03749I −9.15046 + 8.29355I
u = 0.602666 − 0.566356I
3.41113 + 9.03749I −9.15046 − 8.29355I
u = −0.801510 + 0.100864I
−0.75596 + 3.77593I −14.9240 − 4.3419I
u = −0.801510 − 0.100864I
−0.75596 − 3.77593I −14.9240 + 4.3419I
u = −0.601221 + 0.535743I
−1.30987 + 5.10979I −14.0141 − 6.9625I
u = −0.601221 − 0.535743I
−1.30987 − 5.10979I −14.0141 + 6.9625I
u = 0.798272
−4.65627 −19.8710
u = −0.487866 + 0.583035I
7.89022 + 1.99397I −4.51029 − 3.60908I
u = −0.487866 − 0.583035I
7.89022 − 1.99397I −4.51029 + 3.60908I
u = 0.593447 + 0.468250I
1.51106 − 1.30299I −11.08606 + 3.41779I
u = 0.593447 − 0.468250I
1.51106 + 1.30299I −11.08606 − 3.41779I
u = 0.349527 + 0.599396I
4.15088 + 5.05582I −6.99986 − 2.20493I
u = 0.349527 − 0.599396I
4.15088 − 5.05582I −6.99986 + 2.20493I
u = 0.475022 + 0.478306I
1.72361 − 1.67469I −8.06184 + 5.20256I
u = 0.475022 − 0.478306I
1.72361 + 1.67469I −8.06184 − 5.20256I
u = −0.330514 + 0.550465I
−0.53120 − 1.35599I −11.83231 + 0.62165I
u = −0.330514 − 0.550465I
−0.53120 + 1.35599I −11.83231 − 0.62165I
u = −1.43981 + 0.10188I
−1.46648 − 2.68282I −10.45967 + 0.I
u = −1.43981 − 0.10188I
−1.46648 + 2.68282I −10.45967 + 0.I
u = 0.202017 + 0.475850I
2.54473 − 1.90283I −7.07864 + 3.49708I
u = 0.202017 − 0.475850I
2.54473 + 1.90283I −7.07864 − 3.49708I
u = 1.48943 + 0.07957I
−6.30817 − 0.50143I −15.7929 + 0.I
u = 1.48943 − 0.07957I
−6.30817 + 0.50143I −15.7929 + 0.I
u = 1.51213 + 0.16185I
1.30989 − 4.63234I 0
u = 1.51213 − 0.16185I
1.30989 + 4.63234I 0
u = −1.52555 + 0.12217I
−4.95014 + 3.74741I 0
u = −1.52555 − 0.12217I
−4.95014 − 3.74741I 0
u = −1.56321 + 0.13997I
−5.73875 + 3.53679I 0
u = −1.56321 − 0.13997I
−5.73875 − 3.53679I 0
u = 1.56555 + 0.15892I
−8.57063 − 7.64850I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.56555 − 0.15892I
−8.57063 + 7.64850I 0
u = −1.56495 + 0.17025I
−3.83357 + 11.73380I 0
u = −1.56495 − 0.17025I
−3.83357 − 11.73380I 0
u = −1.60055
−12.7836 0
u = 1.60063 + 0.01829I
−8.89081 − 4.15452I 0
u = 1.60063 − 0.01829I
−8.89081 + 4.15452I 0
u = −0.349317
−0.504726 −19.7380
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
c
8
u
37
+ u
36
+ ··· − u − 1
c
3
, c
6
u
37
− 7u
36
+ ··· + u − 7
c
4
, c
5
, c
10
u
37
+ u
36
+ ··· − 3u − 1
c
9
, c
11
u
37
− u
36
+ ··· − 3u − 2
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
37
− 41y
36
+ ··· + 11y −1
c
3
, c
6
y
37
+ 19y
36
+ ··· + 239y −49
c
4
, c
5
, c
10
y
37
+ 31y
36
+ ··· + 11y −1
c
9
, c
11
y
37
− 21y
36
+ ··· + 41y −4
8
