11a
205
(K11a
205
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 8 2 6 3 4 5 9
Solving Sequence
5,11
10 4 3 9 1 2 8 6 7
c
10
c
4
c
3
c
9
c
11
c
2
c
8
c
5
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
45
− u
44
+ ··· − u − 1i
* 1 irreducible components of dim
C
= 0, with total 45 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
45
− u
44
+ · · · − u − 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
3
=
u
3
− 2u
−u
3
+ u
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
1
=
u
6
− 3u
4
+ 2u
2
+ 1
u
8
− 4u
6
+ 4u
4
a
2
=
−u
17
+ 8u
15
− 25u
13
+ 36u
11
− 19u
9
− 4u
7
+ 2u
5
+ 4u
3
− u
−u
19
+ 9u
17
− 32u
15
+ 55u
13
− 43u
11
+ 9u
9
+ 4u
5
− u
3
+ u
a
8
=
−u
10
+ 5u
8
− 8u
6
+ 3u
4
+ u
2
+ 1
u
10
− 4u
8
+ 5u
6
− 2u
4
+ u
2
a
6
=
−u
21
+ 10u
19
+ ··· − 2u
3
− u
u
21
− 9u
19
+ 33u
17
− 62u
15
+ 62u
13
− 33u
11
+ 13u
9
− 6u
7
+ u
5
− u
3
+ u
a
7
=
−u
32
+ 15u
30
+ ··· + 2u
2
+ 1
u
32
− 14u
30
+ ··· + 2u
6
− 2u
4
a
7
=
−u
32
+ 15u
30
+ ··· + 2u
2
+ 1
u
32
− 14u
30
+ ··· + 2u
6
− 2u
4
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
42
+ 76u
40
+ ··· − 4u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
45
+ u
44
+ ··· + u − 1
c
2
, c
5
, c
7
u
45
+ 11u
44
+ ··· − u − 1
c
3
u
45
+ 3u
44
+ ··· + 7u + 3
c
4
, c
9
, c
10
u
45
− u
44
+ ··· − u − 1
c
8
u
45
+ u
44
+ ··· + 44u − 40
c
11
u
45
− 9u
44
+ ··· + 729u − 89
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
45
+ 11y
44
+ ··· − y −1
c
2
, c
5
, c
7
y
45
+ 47y
44
+ ··· − 9y −1
c
3
y
45
− 5y
44
+ ··· + 31y −9
c
4
, c
9
, c
10
y
45
− 41y
44
+ ··· − y −1
c
8
y
45
+ 7y
44
+ ··· − 11024y −1600
c
11
y
45
+ 19y
44
+ ··· − 92805y −7921
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.081740 + 0.103222I
−0.55475 − 2.53820I −1.85794 + 4.98062I
u = −1.081740 − 0.103222I
−0.55475 + 2.53820I −1.85794 − 4.98062I
u = 1.17086
2.04246 5.49400
u = −1.177900 + 0.221582I
5.59455 − 6.24371I 4.08567 + 6.12076I
u = −1.177900 − 0.221582I
5.59455 + 6.24371I 4.08567 − 6.12076I
u = −0.327711 + 0.702255I
5.55749 − 9.33109I 3.17264 + 7.99089I
u = −0.327711 − 0.702255I
5.55749 + 9.33109I 3.17264 − 7.99089I
u = 0.336008 + 0.691887I
5.95973 + 3.04960I 4.06449 − 3.14119I
u = 0.336008 − 0.691887I
5.95973 − 3.04960I 4.06449 + 3.14119I
u = 1.213100 + 0.213850I
5.84619 + 0.30511I 4.74215 + 0.I
u = 1.213100 − 0.213850I
5.84619 − 0.30511I 4.74215 + 0.I
u = −0.591876 + 0.448289I
6.60488 + 5.35917I 5.58298 − 2.28264I
u = −0.591876 − 0.448289I
6.60488 − 5.35917I 5.58298 + 2.28264I
u = 0.568197 + 0.462450I
6.90053 + 0.89679I 6.21998 − 2.86996I
u = 0.568197 − 0.462450I
6.90053 − 0.89679I 6.21998 + 2.86996I
u = −0.269512 + 0.670457I
−1.92036 − 5.51147I −2.23282 + 8.80193I
u = −0.269512 − 0.670457I
−1.92036 + 5.51147I −2.23282 − 8.80193I
u = −0.019331 + 0.669875I
2.10207 + 2.93926I −0.68998 − 2.61803I
u = −0.019331 − 0.669875I
2.10207 − 2.93926I −0.68998 + 2.61803I
u = 0.283883 + 0.605501I
0.18779 + 2.08707I 3.93114 − 4.06148I
u = 0.283883 − 0.605501I
0.18779 − 2.08707I 3.93114 + 4.06148I
u = −0.174737 + 0.630370I
−3.06951 − 0.40423I −6.40296 + 0.79013I
u = −0.174737 − 0.630370I
−3.06951 + 0.40423I −6.40296 − 0.79013I
u = 1.370030 + 0.236669I
1.84057 + 3.53925I 0
u = 1.370030 − 0.236669I
1.84057 − 3.53925I 0
u = 1.389940 + 0.138970I
5.13702 − 0.60420I 0
u = 1.389940 − 0.138970I
5.13702 + 0.60420I 0
u = −0.535574 + 0.250743I
−0.56423 + 2.11330I 1.09230 − 3.69401I
u = −0.535574 − 0.250743I
−0.56423 − 2.11330I 1.09230 + 3.69401I
u = −1.40867 + 0.18655I
6.35213 − 3.35003I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.40867 − 0.18655I
6.35213 + 3.35003I 0
u = −1.41039 + 0.23841I
5.60817 − 5.19685I 0
u = −1.41039 − 0.23841I
5.60817 + 5.19685I 0
u = 1.40670 + 0.26177I
3.43096 + 8.91009I 0
u = 1.40670 − 0.26177I
3.43096 − 8.91009I 0
u = 0.346105 + 0.427336I
0.805234 + 0.974268I 6.02798 − 5.00492I
u = 0.346105 − 0.427336I
0.805234 − 0.974268I 6.02798 + 5.00492I
u = 1.43383 + 0.27147I
11.2002 + 12.8798I 0
u = 1.43383 − 0.27147I
11.2002 − 12.8798I 0
u = −1.43584 + 0.26614I
11.63810 − 6.54354I 0
u = −1.43584 − 0.26614I
11.63810 + 6.54354I 0
u = 1.45671 + 0.13963I
13.09220 − 3.34284I 0
u = 1.45671 − 0.13963I
13.09220 + 3.34284I 0
u = −1.45665 + 0.14856I
13.32800 − 3.02786I 0
u = −1.45665 − 0.14856I
13.32800 + 3.02786I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
45
+ u
44
+ ··· + u − 1
c
2
, c
5
, c
7
u
45
+ 11u
44
+ ··· − u − 1
c
3
u
45
+ 3u
44
+ ··· + 7u + 3
c
4
, c
9
, c
10
u
45
− u
44
+ ··· − u − 1
c
8
u
45
+ u
44
+ ··· + 44u − 40
c
11
u
45
− 9u
44
+ ··· + 729u − 89
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
45
+ 11y
44
+ ··· − y −1
c
2
, c
5
, c
7
y
45
+ 47y
44
+ ··· − 9y −1
c
3
y
45
− 5y
44
+ ··· + 31y −9
c
4
, c
9
, c
10
y
45
− 41y
44
+ ··· − y −1
c
8
y
45
+ 7y
44
+ ··· − 11024y −1600
c
11
y
45
+ 19y
44
+ ··· − 92805y −7921
8
