11a
359
(K11a
359
)
A knot diagram
1
Linearized knot diagam
7 9 8 1 11 10 2 3 4 6 5
Solving Sequence
2,9
3 8 4 10 7 1 5 6 11
c
2
c
8
c
3
c
9
c
7
c
1
c
4
c
6
c
11
c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
26
− u
25
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 26 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
26
− u
25
+ · · · − u − 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
8
=
u
u
3
+ u
a
4
=
u
2
+ 1
u
4
+ 2u
2
a
10
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
7
=
u
3
+ 2u
u
3
+ u
a
1
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
6
− 2u
4
− u
2
a
5
=
−u
16
− 7u
14
− 19u
12
− 22u
10
− 3u
8
+ 14u
6
+ 6u
4
− 2u
2
+ 1
−u
16
− 6u
14
− 14u
12
− 14u
10
− 2u
8
+ 6u
6
+ 4u
4
+ 2u
2
a
6
=
−u
15
− 6u
13
− 14u
11
− 14u
9
− 2u
7
+ 6u
5
+ 4u
3
+ 2u
−u
17
− 7u
15
− 19u
13
− 22u
11
− 3u
9
+ 14u
7
+ 6u
5
− 2u
3
+ u
a
11
=
−u
25
− 10u
23
+ ··· − 8u
3
− u
−u
25
+ u
24
+ ··· − u − 1
a
11
=
−u
25
− 10u
23
+ ··· − 8u
3
− u
−u
25
+ u
24
+ ··· − u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
24
+ 4u
23
− 40u
22
+ 36u
21
− 172u
20
+ 136u
19
− 396u
18
+
264u
17
− 472u
16
+ 236u
15
− 136u
14
− 20u
13
+ 344u
12
− 220u
11
+ 384u
10
− 140u
9
+
48u
8
− 108u
6
+ 16u
5
− 40u
4
+ 16u
3
− 8u
2
+ 16u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
26
+ u
25
+ ··· − 9u − 5
c
2
, c
3
, c
8
u
26
− u
25
+ ··· − u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
26
+ u
25
+ ··· − 3u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
26
− 23y
25
+ ··· − 151y + 25
c
2
, c
3
, c
8
y
26
+ 21y
25
+ ··· − 11y + 1
c
4
, c
5
, c
6
c
10
, c
11
y
26
+ 33y
25
+ ··· − 11y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841791 + 0.094185I
5.20604 − 5.29901I −9.93823 + 3.19957I
u = 0.841791 − 0.094185I
5.20604 + 5.29901I −9.93823 − 3.19957I
u = −0.828402 + 0.050333I
−3.49265 + 3.42603I −11.85459 − 4.34345I
u = −0.828402 − 0.050333I
−3.49265 − 3.42603I −11.85459 + 4.34345I
u = 0.829469
−6.03489 −16.5470
u = −0.063117 + 1.217600I
3.01166 + 1.26256I −8.17654 − 5.12241I
u = −0.063117 − 1.217600I
3.01166 − 1.26256I −8.17654 + 5.12241I
u = 0.392131 + 1.168430I
8.49921 + 0.85694I −6.81756 + 0.45709I
u = 0.392131 − 1.168430I
8.49921 − 0.85694I −6.81756 − 0.45709I
u = −0.370693 + 1.223000I
0.117817 + 0.889406I −8.45807 + 0.89318I
u = −0.370693 − 1.223000I
0.117817 − 0.889406I −8.45807 − 0.89318I
u = 0.373903 + 1.269520I
−2.09387 − 4.32460I −12.48733 + 3.68089I
u = 0.373903 − 1.269520I
−2.09387 + 4.32460I −12.48733 − 3.68089I
u = 0.116826 + 1.320420I
6.90824 − 2.96972I −1.89605 + 4.34441I
u = 0.116826 − 1.320420I
6.90824 + 2.96972I −1.89605 − 4.34441I
u = −0.475175 + 0.446398I
10.68300 + 1.72593I −6.44509 − 3.70709I
u = −0.475175 − 0.446398I
10.68300 − 1.72593I −6.44509 + 3.70709I
u = −0.371528 + 1.305530I
0.74252 + 7.74244I −7.42357 − 6.92511I
u = −0.371528 − 1.305530I
0.74252 − 7.74244I −7.42357 + 6.92511I
u = −0.127500 + 1.375760I
16.3951 + 3.6931I −1.57713 − 3.06120I
u = −0.127500 − 1.375760I
16.3951 − 3.6931I −1.57713 + 3.06120I
u = 0.374153 + 1.333360I
9.68283 − 9.67188I −5.67938 + 5.45420I
u = 0.374153 − 1.333360I
9.68283 + 9.67188I −5.67938 − 5.45420I
u = 0.373827 + 0.329514I
1.88313 − 1.28751I −6.75058 + 5.74185I
u = 0.373827 − 0.329514I
1.88313 + 1.28751I −6.75058 − 5.74185I
u = −0.301902
−0.485500 −20.4450
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
26
+ u
25
+ ··· − 9u − 5
c
2
, c
3
, c
8
u
26
− u
25
+ ··· − u − 1
c
4
, c
5
, c
6
c
10
, c
11
u
26
+ u
25
+ ··· − 3u − 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
26
− 23y
25
+ ··· − 151y + 25
c
2
, c
3
, c
8
y
26
+ 21y
25
+ ··· − 11y + 1
c
4
, c
5
, c
6
c
10
, c
11
y
26
+ 33y
25
+ ··· − 11y + 1
7
