11a
208
(K11a
208
)
A knot diagram
1
Linearized knot diagam
7 1 11 10 9 2 6 3 4 5 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
52
+ u
51
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 52 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
52
+ u
51
+ · · · + 2u − 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
51
+ 8u
49
+ ··· + u
3
+ 2u
−u
51
− 9u
49
+ ··· + u
3
+ u
a
10
=
u
51
+ 8u
49
+ ··· + u
3
+ 2u
−u
51
− 9u
49
+ ··· + u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
50
+ 4u
49
+ ··· + 4u
2
+ 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
52
+ u
51
+ ··· + 2u − 1
c
2
, c
7
u
52
+ 17u
51
+ ··· − 6u + 1
c
3
, c
5
u
52
+ 3u
51
+ ··· + 37u + 16
c
4
, c
9
, c
10
u
52
− u
51
+ ··· + 3u
2
− 1
c
8
u
52
+ u
51
+ ··· − 28u − 40
c
11
u
52
− 5u
51
+ ··· + 96u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
52
+ 17y
51
+ ··· − 6y + 1
c
2
, c
7
y
52
+ 37y
51
+ ··· − 54y + 1
c
3
, c
5
y
52
+ 33y
51
+ ··· − 2425y + 256
c
4
, c
9
, c
10
y
52
− 43y
51
+ ··· − 6y + 1
c
8
y
52
− 7y
51
+ ··· − 38704y + 1600
c
11
y
52
+ 5y
51
+ ··· + 5856y + 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768826 + 0.671773I
2.57641 + 0.11774I 9.48504 + 0.88977I
u = −0.768826 − 0.671773I
2.57641 − 0.11774I 9.48504 − 0.88977I
u = 0.797976 + 0.676802I
−0.37697 − 4.15655I 6.46155 + 2.97848I
u = 0.797976 − 0.676802I
−0.37697 + 4.15655I 6.46155 − 2.97848I
u = −0.189335 + 0.934390I
3.08561 − 2.46256I 8.42989 + 4.48427I
u = −0.189335 − 0.934390I
3.08561 + 2.46256I 8.42989 − 4.48427I
u = −0.749484 + 0.734944I
3.28879 + 0.58865I 11.43703 − 2.08567I
u = −0.749484 − 0.734944I
3.28879 − 0.58865I 11.43703 + 2.08567I
u = 0.085244 + 1.047640I
−3.32915 − 0.06069I 1.99003 − 0.27621I
u = 0.085244 − 1.047640I
−3.32915 + 0.06069I 1.99003 + 0.27621I
u = −0.113059 + 1.052610I
−6.59928 − 4.05816I −1.05392 + 4.39886I
u = −0.113059 − 1.052610I
−6.59928 + 4.05816I −1.05392 − 4.39886I
u = 0.063300 + 0.938721I
−2.09979 + 1.29128I 2.50126 − 5.46837I
u = 0.063300 − 0.938721I
−2.09979 − 1.29128I 2.50126 + 5.46837I
u = −0.812741 + 0.682085I
4.28204 + 8.22013I 11.15083 − 4.69120I
u = −0.812741 − 0.682085I
4.28204 − 8.22013I 11.15083 + 4.69120I
u = 0.132755 + 1.056620I
−2.13743 + 8.17751I 3.80777 − 6.73213I
u = 0.132755 − 1.056620I
−2.13743 − 8.17751I 3.80777 + 6.73213I
u = 0.506635 + 0.944324I
−0.02731 − 2.14885I 5.90152 + 0.32388I
u = 0.506635 − 0.944324I
−0.02731 + 2.14885I 5.90152 − 0.32388I
u = 0.731364 + 0.804742I
1.86476 + 2.42134I 7.78972 − 4.58127I
u = 0.731364 − 0.804742I
1.86476 − 2.42134I 7.78972 + 4.58127I
u = 0.797362 + 0.743175I
9.36019 − 1.41507I 15.5003 + 0.7140I
u = 0.797362 − 0.743175I
9.36019 + 1.41507I 15.5003 − 0.7140I
u = −0.542555 + 0.954190I
−4.16270 − 1.90381I 1.38256 + 2.60810I
u = −0.542555 − 0.954190I
−4.16270 + 1.90381I 1.38256 − 2.60810I
u = −0.772975 + 0.816132I
6.58267 − 5.63550I 13.2814 + 5.3850I
u = −0.772975 − 0.816132I
6.58267 + 5.63550I 13.2814 − 5.3850I
u = 0.573285 + 0.968251I
−0.49912 + 5.98276I 5.45137 − 6.27101I
u = 0.573285 − 0.968251I
−0.49912 − 5.98276I 5.45137 + 6.27101I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.697455 + 0.924225I
1.49374 + 3.03580I 6.84419 + 0.I
u = 0.697455 − 0.924225I
1.49374 − 3.03580I 6.84419 + 0.I
u = −0.741062 + 0.918318I
6.26590 − 0.08152I 12.71506 + 0.I
u = −0.741062 − 0.918318I
6.26590 + 0.08152I 12.71506 + 0.I
u = −0.704555 + 0.970451I
2.57341 − 6.12702I 9.43955 + 7.72623I
u = −0.704555 − 0.970451I
2.57341 + 6.12702I 9.43955 − 7.72623I
u = 0.733151 + 0.979368I
8.63821 + 7.17962I 13.94643 + 0.I
u = 0.733151 − 0.979368I
8.63821 − 7.17962I 13.94643 + 0.I
u = −0.699306 + 1.006300I
1.57520 − 5.69142I 0
u = −0.699306 − 1.006300I
1.57520 + 5.69142I 0
u = 0.711550 + 1.013250I
−1.39365 + 9.84829I 0
u = 0.711550 − 1.013250I
−1.39365 − 9.84829I 0
u = −0.719515 + 1.016110I
3.2680 − 13.9792I 0
u = −0.719515 − 1.016110I
3.2680 + 13.9792I 0
u = 0.548113 + 0.343853I
0.91864 − 1.70258I 9.13001 + 0.33121I
u = 0.548113 − 0.343853I
0.91864 + 1.70258I 9.13001 − 0.33121I
u = 0.612012 + 0.204828I
1.88978 + 5.96132I 11.11302 − 5.64995I
u = 0.612012 − 0.204828I
1.88978 − 5.96132I 11.11302 + 5.64995I
u = −0.575732 + 0.249215I
−2.51014 − 2.07572I 5.84325 + 3.66425I
u = −0.575732 − 0.249215I
−2.51014 + 2.07572I 5.84325 − 3.66425I
u = −0.564176
5.97021 16.1930
u = 0.362065
0.641117 15.5690
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
52
+ u
51
+ ··· + 2u − 1
c
2
, c
7
u
52
+ 17u
51
+ ··· − 6u + 1
c
3
, c
5
u
52
+ 3u
51
+ ··· + 37u + 16
c
4
, c
9
, c
10
u
52
− u
51
+ ··· + 3u
2
− 1
c
8
u
52
+ u
51
+ ··· − 28u − 40
c
11
u
52
− 5u
51
+ ··· + 96u − 16
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
52
+ 17y
51
+ ··· − 6y + 1
c
2
, c
7
y
52
+ 37y
51
+ ··· − 54y + 1
c
3
, c
5
y
52
+ 33y
51
+ ··· − 2425y + 256
c
4
, c
9
, c
10
y
52
− 43y
51
+ ··· − 6y + 1
c
8
y
52
− 7y
51
+ ··· − 38704y + 1600
c
11
y
52
+ 5y
51
+ ··· + 5856y + 256
8
