11a
211
(K11a
211
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 6 3 5 4 8
Solving Sequence
2,7
1 3 6 8 9 5 11 4 10
c
1
c
2
c
6
c
7
c
8
c
5
c
11
c
3
c
10
c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
33
+ u
32
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 33 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
33
+ u
32
+ · · · + u − 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
6
=
−u
u
a
8
=
−u
3
u
3
+ u
a
9
=
u
9
+ 2u
7
+ 3u
5
+ 2u
3
+ u
u
11
+ u
9
+ 2u
7
+ u
5
+ u
3
+ u
a
5
=
−u
21
− 4u
19
+ ··· − 2u
3
− u
−u
23
− 3u
21
+ ··· − 2u
3
+ u
a
11
=
−u
8
− u
6
− u
4
+ 1
u
8
+ 2u
6
+ 2u
4
+ 2u
2
a
4
=
u
20
+ 3u
18
+ 7u
16
+ 10u
14
+ 10u
12
+ 7u
10
+ u
8
− 2u
6
− 3u
4
− u
2
+ 1
−u
20
− 4u
18
− 10u
16
− 18u
14
− 23u
12
− 24u
10
− 18u
8
− 10u
6
− 3u
4
a
10
=
−u
32
− 5u
30
+ ··· − 2u
2
+ 1
u
32
+ 6u
30
+ ··· + 2u
4
+ 2u
2
a
10
=
−u
32
− 5u
30
+ ··· − 2u
2
+ 1
u
32
+ 6u
30
+ ··· + 2u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
31
+ 4u
30
+ 20u
29
+ 20u
28
+ 72u
27
+ 68u
26
+ 176u
25
+ 164u
24
+ 344u
23
+ 308u
22
+
536u
21
+476u
20
+688u
19
+600u
18
+736u
17
+644u
16
+644u
15
+572u
14
+468u
13
+424u
12
+
268u
11
+ 260u
10
+ 120u
9
+ 120u
8
+ 52u
7
+ 48u
6
+ 20u
5
+ 12u
4
+ 20u
3
+ 4u
2
+ 8u + 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
33
+ u
32
+ ··· + u − 1
c
2
, c
7
u
33
+ 11u
32
+ ··· + 5u − 1
c
3
, c
4
, c
5
c
9
, c
10
u
33
+ u
32
+ ··· − u − 1
c
8
u
33
+ u
32
+ ··· + 21u − 5
c
11
u
33
− 5u
32
+ ··· + 33u − 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
33
+ 11y
32
+ ··· + 5y −1
c
2
, c
7
y
33
+ 23y
32
+ ··· + 41y −1
c
3
, c
4
, c
5
c
9
, c
10
y
33
+ 43y
32
+ ··· + 5y −1
c
8
y
33
+ 3y
32
+ ··· − 299y −25
c
11
y
33
+ 7y
32
+ ··· − 563y −49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.783792 + 0.681225I
−0.01786 − 3.59856I 5.28807 + 3.52073I
u = 0.783792 − 0.681225I
−0.01786 + 3.59856I 5.28807 − 3.52073I
u = −0.101718 + 1.035980I
−6.05867 − 3.57865I −2.55817 + 4.87055I
u = −0.101718 − 1.035980I
−6.05867 + 3.57865I −2.55817 − 4.87055I
u = −0.812759 + 0.656775I
−9.39854 + 5.15635I 4.07009 − 1.99825I
u = −0.812759 − 0.656775I
−9.39854 − 5.15635I 4.07009 + 1.99825I
u = 0.064287 + 0.949488I
−2.15241 + 1.32489I 2.26975 − 5.19264I
u = 0.064287 − 0.949488I
−2.15241 − 1.32489I 2.26975 + 5.19264I
u = −0.755741 + 0.727580I
3.31791 + 0.71142I 11.21363 − 1.67863I
u = −0.755741 − 0.727580I
3.31791 − 0.71142I 11.21363 + 1.67863I
u = 0.721580 + 0.791474I
1.87533 + 2.23676I 7.14983 − 4.95590I
u = 0.721580 − 0.791474I
1.87533 − 2.23676I 7.14983 + 4.95590I
u = 0.113164 + 1.080920I
−15.7697 + 4.7978I −2.88521 − 3.43471I
u = 0.113164 − 1.080920I
−15.7697 − 4.7978I −2.88521 + 3.43471I
u = −0.564868 + 0.931483I
−3.48793 − 2.09474I 0.20074 + 2.52182I
u = −0.564868 − 0.931483I
−3.48793 + 2.09474I 0.20074 − 2.52182I
u = 0.529302 + 0.992831I
−13.31430 + 1.59055I −0.39166 − 2.82040I
u = 0.529302 − 0.992831I
−13.31430 − 1.59055I −0.39166 + 2.82040I
u = −0.767004 + 0.867736I
−5.87675 − 2.88651I 5.60693 + 2.86051I
u = −0.767004 − 0.867736I
−5.87675 + 2.88651I 5.60693 − 2.86051I
u = 0.689725 + 0.931969I
1.43951 + 3.16744I 6.20217 − 0.82428I
u = 0.689725 − 0.931969I
1.43951 − 3.16744I 6.20217 + 0.82428I
u = −0.704961 + 0.976337I
2.56175 − 6.26830I 9.09411 + 7.22384I
u = −0.704961 − 0.976337I
2.56175 + 6.26830I 9.09411 − 7.22384I
u = 0.706642 + 1.006440I
−0.99856 + 9.23572I 3.44794 − 8.32004I
u = 0.706642 − 1.006440I
−0.99856 − 9.23572I 3.44794 + 8.32004I
u = −0.710292 + 1.026450I
−10.5163 − 10.8805I 2.22808 + 6.70699I
u = −0.710292 − 1.026450I
−10.5163 + 10.8805I 2.22808 − 6.70699I
u = 0.648089 + 0.272678I
−11.39430 + 2.64374I 3.80222 − 2.50255I
u = 0.648089 − 0.272678I
−11.39430 − 2.64374I 3.80222 + 2.50255I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.526368 + 0.248614I
−2.09314 − 1.78280I 4.63198 + 4.39540I
u = −0.526368 − 0.248614I
−2.09314 + 1.78280I 4.63198 − 4.39540I
u = 0.374260
0.658769 15.2590
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
33
+ u
32
+ ··· + u − 1
c
2
, c
7
u
33
+ 11u
32
+ ··· + 5u − 1
c
3
, c
4
, c
5
c
9
, c
10
u
33
+ u
32
+ ··· − u − 1
c
8
u
33
+ u
32
+ ··· + 21u − 5
c
11
u
33
− 5u
32
+ ··· + 33u − 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
33
+ 11y
32
+ ··· + 5y −1
c
2
, c
7
y
33
+ 23y
32
+ ··· + 41y −1
c
3
, c
4
, c
5
c
9
, c
10
y
33
+ 43y
32
+ ··· + 5y −1
c
8
y
33
+ 3y
32
+ ··· − 299y −25
c
11
y
33
+ 7y
32
+ ··· − 563y −49
8
