11a
140
(K11a
140
)
A knot diagram
1
Linearized knot diagam
5 1 9 8 2 11 10 3 4 7 6
Solving Sequence
2,6
5 1 3 11 7 10 8 9 4
c
5
c
1
c
2
c
11
c
6
c
10
c
7
c
8
c
4
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
32
+ u
31
+ ··· − 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 32 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
32
+ u
31
+ · · · − 2u − 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
1
=
u
−u
3
+ u
a
3
=
−u
3
u
5
− u
3
+ u
a
11
=
u
3
−u
3
+ u
a
7
=
u
6
− u
4
+ 1
−u
6
+ 2u
4
− u
2
a
10
=
u
9
− 2u
7
+ u
5
+ 2u
3
− u
−u
9
+ 3u
7
− 3u
5
+ u
a
8
=
u
12
− 3u
10
+ 3u
8
+ 2u
6
− 4u
4
+ u
2
+ 1
−u
12
+ 4u
10
− 6u
8
+ 2u
6
+ 3u
4
− 2u
2
a
9
=
−u
20
+ 5u
18
− 11u
16
+ 10u
14
+ 2u
12
− 13u
10
+ 9u
8
+ 2u
6
− 5u
4
+ u
2
+ 1
u
22
− 6u
20
+ 17u
18
− 26u
16
+ 20u
14
− 13u
10
+ 10u
8
− 3u
6
+ 2u
4
− u
2
a
4
=
−u
26
+ 7u
24
+ ··· + u
2
+ 1
u
26
− 8u
24
+ ··· − 2u
4
− u
2
a
4
=
−u
26
+ 7u
24
+ ··· + u
2
+ 1
u
26
− 8u
24
+ ··· − 2u
4
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
31
−40u
29
−4u
28
+ 184u
27
+ 36u
26
−484u
25
−148u
24
+ 728u
23
+ 340u
22
−420u
21
−
420u
20
− 556u
19
+ 116u
18
+ 1316u
17
+ 444u
16
− 872u
15
− 652u
14
− 292u
13
+ 236u
12
+
772u
11
+ 244u
10
−316u
9
−260u
8
−124u
7
+ 36u
6
+ 116u
5
+ 44u
4
−4u
3
−12u
2
−12u −14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
32
+ u
31
+ ··· − 2u − 1
c
2
u
32
+ 19u
31
+ ··· − 8u
2
+ 1
c
3
, c
8
, c
9
u
32
− u
31
+ ··· − 2u − 1
c
4
u
32
+ 3u
31
+ ··· + 202u + 77
c
6
, c
7
, c
10
c
11
u
32
+ 3u
31
+ ··· + 16u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
32
− 19y
31
+ ··· − 8y
2
+ 1
c
2
y
32
− 11y
31
+ ··· − 16y + 1
c
3
, c
8
, c
9
y
32
− 31y
31
+ ··· − 16y
2
+ 1
c
4
y
32
− 19y
31
+ ··· − 95320y + 5929
c
6
, c
7
, c
10
c
11
y
32
+ 41y
31
+ ··· − 112y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.868634 + 0.432115I
−3.34862 + 4.04370I −6.04453 − 7.13519I
u = −0.868634 − 0.432115I
−3.34862 − 4.04370I −6.04453 + 7.13519I
u = 1.04533
−6.54630 −13.9220
u = −0.026700 + 0.917936I
−14.7670 − 5.6087I −9.35181 + 2.83991I
u = −0.026700 − 0.917936I
−14.7670 + 5.6087I −9.35181 − 2.83991I
u = 0.012118 + 0.901786I
−8.30499 + 2.26267I −6.08064 − 2.91656I
u = 0.012118 − 0.901786I
−8.30499 − 2.26267I −6.08064 + 2.91656I
u = −1.083140 + 0.341712I
−3.37831 + 1.66824I −9.56243 − 0.35146I
u = −1.083140 − 0.341712I
−3.37831 − 1.66824I −9.56243 + 0.35146I
u = 1.076920 + 0.423315I
−2.77345 − 5.10982I −6.71803 + 8.18202I
u = 1.076920 − 0.423315I
−2.77345 + 5.10982I −6.71803 − 8.18202I
u = 0.756512 + 0.350926I
0.83897 − 1.64134I 1.45053 + 5.73960I
u = 0.756512 − 0.350926I
0.83897 + 1.64134I 1.45053 − 5.73960I
u = −0.804096
−1.07276 −10.5910
u = 1.157410 + 0.314330I
−9.45578 + 0.50238I −13.25888 + 0.22265I
u = 1.157410 − 0.314330I
−9.45578 − 0.50238I −13.25888 − 0.22265I
u = −1.110460 + 0.463462I
−8.33031 + 8.05747I −10.74797 − 7.46464I
u = −1.110460 − 0.463462I
−8.33031 − 8.05747I −10.74797 + 7.46464I
u = −0.163704 + 0.669811I
−5.64755 − 3.79286I −7.65510 + 3.79891I
u = −0.163704 − 0.669811I
−5.64755 + 3.79286I −7.65510 − 3.79891I
u = −0.522402 + 0.426932I
−2.44365 − 0.31845I −3.24811 − 0.20471I
u = −0.522402 − 0.426932I
−2.44365 + 0.31845I −3.24811 + 0.20471I
u = −1.267860 + 0.464164I
−12.21500 + 2.58352I −9.43681 − 0.14752I
u = −1.267860 − 0.464164I
−12.21500 − 2.58352I −9.43681 + 0.14752I
u = 1.263650 + 0.477439I
−12.11660 − 7.17755I −9.14770 + 5.86389I
u = 1.263650 − 0.477439I
−12.11660 + 7.17755I −9.14770 − 5.86389I
u = −1.268830 + 0.488464I
−18.5604 + 10.6275I −12.35486 − 5.78214I
u = −1.268830 − 0.488464I
−18.5604 − 10.6275I −12.35486 + 5.78214I
u = 1.280210 + 0.458189I
−18.7882 + 0.7378I −12.72584 + 0.13438I
u = 1.280210 − 0.458189I
−18.7882 − 0.7378I −12.72584 − 0.13438I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.144298 + 0.527794I
−0.269618 + 1.333490I −2.86164 − 5.19756I
u = 0.144298 − 0.527794I
−0.269618 − 1.333490I −2.86164 + 5.19756I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
32
+ u
31
+ ··· − 2u − 1
c
2
u
32
+ 19u
31
+ ··· − 8u
2
+ 1
c
3
, c
8
, c
9
u
32
− u
31
+ ··· − 2u − 1
c
4
u
32
+ 3u
31
+ ··· + 202u + 77
c
6
, c
7
, c
10
c
11
u
32
+ 3u
31
+ ··· + 16u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
32
− 19y
31
+ ··· − 8y
2
+ 1
c
2
y
32
− 11y
31
+ ··· − 16y + 1
c
3
, c
8
, c
9
y
32
− 31y
31
+ ··· − 16y
2
+ 1
c
4
y
32
− 19y
31
+ ··· − 95320y + 5929
c
6
, c
7
, c
10
c
11
y
32
+ 41y
31
+ ··· − 112y + 1
8
