11a
96
(K11a
96
)
A knot diagram
1
Linearized knot diagam
6 1 10 8 2 3 5 11 4 9 7
Solving Sequence
1,6
2 3 7 5 8 4 11 9 10
c
1
c
2
c
6
c
5
c
7
c
4
c
11
c
8
c
10
c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
60
− u
59
+ ··· + u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 60 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
60
− u
59
+ · · · + u
2
+ 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
−u
2
a
3
=
u
2
+ 1
−u
2
a
7
=
−u
5
− 2u
3
− u
u
5
+ u
3
+ u
a
5
=
−u
u
3
+ u
a
8
=
−u
9
− 2u
7
− 3u
5
− 2u
3
− u
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
4
=
−u
17
− 4u
15
− 9u
13
− 12u
11
− 11u
9
− 6u
7
− 2u
5
− u
u
19
+ 5u
17
+ 12u
15
+ 17u
13
+ 15u
11
+ 9u
9
+ 4u
7
+ 2u
5
+ u
3
+ u
a
11
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
−u
10
− 2u
8
− 3u
6
− 2u
4
− u
2
a
9
=
−u
31
− 8u
29
+ ··· − 4u
3
− 2u
u
31
+ 7u
29
+ ··· + 2u
3
+ u
a
10
=
u
52
+ 13u
50
+ ··· + 3u
2
+ 1
−u
52
− 12u
50
+ ··· − 5u
4
− 2u
2
a
10
=
u
52
+ 13u
50
+ ··· + 3u
2
+ 1
−u
52
− 12u
50
+ ··· − 5u
4
− 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
59
+ 4u
58
+ ··· − 4u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
60
− u
59
+ ··· + u
2
+ 1
c
2
u
60
+ 29u
59
+ ··· + 2u + 1
c
3
, c
9
u
60
− u
59
+ ··· + u
2
+ 1
c
4
, c
7
u
60
+ 5u
59
+ ··· + 122u + 13
c
6
u
60
+ u
59
+ ··· − 118u + 37
c
8
, c
10
u
60
+ 21u
59
+ ··· + 2u + 1
c
11
u
60
− 5u
59
+ ··· − 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
60
+ 29y
59
+ ··· + 2y + 1
c
2
y
60
+ 5y
59
+ ··· + 14y + 1
c
3
, c
9
y
60
+ 21y
59
+ ··· + 2y + 1
c
4
, c
7
y
60
+ 41y
59
+ ··· + 4330y + 169
c
6
y
60
− 19y
59
+ ··· + 12050y + 1369
c
8
, c
10
y
60
+ 37y
59
+ ··· + 22y + 1
c
11
y
60
+ y
59
+ ··· + 38y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544109 + 0.871535I
0.80579 + 3.33102I 2.01338 − 1.91534I
u = −0.544109 − 0.871535I
0.80579 − 3.33102I 2.01338 + 1.91534I
u = 0.525209 + 0.910684I
1.69680 + 2.03222I 3.90722 − 3.29370I
u = 0.525209 − 0.910684I
1.69680 − 2.03222I 3.90722 + 3.29370I
u = −0.622652 + 0.677380I
1.38479 − 7.95567I 3.11940 + 8.08739I
u = −0.622652 − 0.677380I
1.38479 + 7.95567I 3.11940 − 8.08739I
u = −0.552672 + 0.728082I
−3.08637 − 2.17441I −2.78142 + 3.98454I
u = −0.552672 − 0.728082I
−3.08637 + 2.17441I −2.78142 − 3.98454I
u = −0.074861 + 0.899343I
0.55103 + 2.51832I −0.80649 − 3.33072I
u = −0.074861 − 0.899343I
0.55103 − 2.51832I −0.80649 + 3.33072I
u = 0.610444 + 0.652587I
2.44765 + 2.49685I 5.32046 − 3.18664I
u = 0.610444 − 0.652587I
2.44765 − 2.49685I 5.32046 + 3.18664I
u = −0.381105 + 1.041640I
−3.34743 − 1.08708I −6.46120 + 0.I
u = −0.381105 − 1.041640I
−3.34743 + 1.08708I −6.46120 + 0.I
u = 0.484539 + 1.021160I
−0.56534 + 3.02304I 0
u = 0.484539 − 1.021160I
−0.56534 − 3.02304I 0
u = −0.260652 + 1.137700I
−3.60470 + 1.42729I 0
u = −0.260652 − 1.137700I
−3.60470 − 1.42729I 0
u = −0.313837 + 1.128650I
−4.20665 − 1.05171I 0
u = −0.313837 − 1.128650I
−4.20665 + 1.05171I 0
u = 0.769876 + 0.302697I
−0.43983 − 9.87486I 1.61763 + 6.92341I
u = 0.769876 − 0.302697I
−0.43983 + 9.87486I 1.61763 − 6.92341I
u = 0.257348 + 1.151700I
−4.93303 − 6.89109I 0
u = 0.257348 − 1.151700I
−4.93303 + 6.89109I 0
u = 0.666201 + 0.472083I
5.00152 + 1.75323I 7.65668 − 2.62236I
u = 0.666201 − 0.472083I
5.00152 − 1.75323I 7.65668 + 2.62236I
u = −0.755668 + 0.307937I
0.80884 + 4.33115I 3.69848 − 2.33072I
u = −0.755668 − 0.307937I
0.80884 − 4.33115I 3.69848 + 2.33072I
u = 0.560154 + 1.046520I
3.31782 + 3.01457I 0
u = 0.560154 − 1.046520I
3.31782 − 3.01457I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.679575 + 0.445417I
4.87624 + 3.78274I 7.16156 − 3.71379I
u = −0.679575 − 0.445417I
4.87624 − 3.78274I 7.16156 + 3.71379I
u = 0.288034 + 1.152760I
−9.39383 − 0.41865I 0
u = 0.288034 − 1.152760I
−9.39383 + 0.41865I 0
u = −0.487828 + 1.088330I
−2.57613 − 5.90818I 0
u = −0.487828 − 1.088330I
−2.57613 + 5.90818I 0
u = 0.321894 + 1.149490I
−5.68245 + 6.13484I 0
u = 0.321894 − 1.149490I
−5.68245 − 6.13484I 0
u = −0.562904 + 1.061080I
3.07462 − 8.59241I 0
u = −0.562904 − 1.061080I
3.07462 + 8.59241I 0
u = 0.751525 + 0.268257I
−5.11292 − 3.55390I −3.52030 + 2.87156I
u = 0.751525 − 0.268257I
−5.11292 + 3.55390I −3.52030 − 2.87156I
u = −0.533131 + 1.124390I
−2.71521 − 6.69056I 0
u = −0.533131 − 1.124390I
−2.71521 + 6.69056I 0
u = 0.719744 + 0.218682I
−1.68268 + 2.83631I −0.28832 − 2.76871I
u = 0.719744 − 0.218682I
−1.68268 − 2.83631I −0.28832 + 2.76871I
u = 0.523358 + 1.138230I
−4.31649 + 1.84933I 0
u = 0.523358 − 1.138230I
−4.31649 − 1.84933I 0
u = 0.493299 + 0.552242I
0.862519 + 1.026220I 5.84285 − 4.48468I
u = 0.493299 − 0.552242I
0.862519 − 1.026220I 5.84285 + 4.48468I
u = −0.689013 + 0.265335I
−0.26353 + 1.99974I 2.67797 − 3.08609I
u = −0.689013 − 0.265335I
−0.26353 − 1.99974I 2.67797 + 3.08609I
u = −0.558377 + 1.131910I
−1.60310 − 9.28831I 0
u = −0.558377 − 1.131910I
−1.60310 + 9.28831I 0
u = 0.545235 + 1.140190I
−7.65214 + 8.43403I 0
u = 0.545235 − 1.140190I
−7.65214 − 8.43403I 0
u = 0.560770 + 1.137600I
−2.8910 + 14.8744I 0
u = 0.560770 − 1.137600I
−2.8910 − 14.8744I 0
u = −0.561245 + 0.222030I
−0.23326 + 1.74631I 0.21628 − 4.30130I
u = −0.561245 − 0.222030I
−0.23326 − 1.74631I 0.21628 + 4.30130I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
60
− u
59
+ ··· + u
2
+ 1
c
2
u
60
+ 29u
59
+ ··· + 2u + 1
c
3
, c
9
u
60
− u
59
+ ··· + u
2
+ 1
c
4
, c
7
u
60
+ 5u
59
+ ··· + 122u + 13
c
6
u
60
+ u
59
+ ··· − 118u + 37
c
8
, c
10
u
60
+ 21u
59
+ ··· + 2u + 1
c
11
u
60
− 5u
59
+ ··· − 12u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
y
60
+ 29y
59
+ ··· + 2y + 1
c
2
y
60
+ 5y
59
+ ··· + 14y + 1
c
3
, c
9
y
60
+ 21y
59
+ ··· + 2y + 1
c
4
, c
7
y
60
+ 41y
59
+ ··· + 4330y + 169
c
6
y
60
− 19y
59
+ ··· + 12050y + 1369
c
8
, c
10
y
60
+ 37y
59
+ ··· + 22y + 1
c
11
y
60
+ y
59
+ ··· + 38y + 1
8
