10
148
(K10n
12
)
A knot diagram
1
Linearized knot diagam
9 5 10 7 2 8 5 1 3 8
Solving Sequence
2,9 1,6
5 3 8 7 10 4
c
1
c
5
c
2
c
8
c
7
c
10
c
3
c
4
, c
6
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4617u
16
− 7857u
15
+ ··· + 51929b + 5902, −25871u
16
− 67713u
15
+ ··· + 51929a + 130136,
u
17
+ 2u
16
+ ··· + u + 1i
I
u
2
= hb, a − u − 2, u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 19 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
= h−4617u
16
− 7857u
15
+ · · · + 51929b + 5902, −2.59 × 10
4
u
16
− 6.77 ×
10
4
u
15
+ · · · + 5.19 × 10
4
a + 1.30 × 10
5
, u
17
+ 2u
16
+ · · · + u + 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
u
2
a
6
=
0.498199u
16
+ 1.30395u
15
+ ··· − 1.04462u − 2.50604
0.0889099u
16
+ 0.151303u
15
+ ··· + 1.44389u − 0.113655
a
5
=
0.409290u
16
+ 1.15265u
15
+ ··· − 2.48851u − 2.39238
0.0889099u
16
+ 0.151303u
15
+ ··· + 1.44389u − 0.113655
a
3
=
−0.392305u
16
− 0.597431u
15
+ ··· + 3.04310u + 0.331684
−0.848871u
16
− 1.42703u
15
+ ··· − 0.126557u − 0.846213
a
8
=
−u
−u
3
+ u
a
7
=
0.189913u
16
+ 0.972308u
15
+ ··· − 1.24568u − 2.24559
−0.266730u
16
− 0.453908u
15
+ ··· + 1.66832u − 0.659034
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−0.388319u
16
− 0.222227u
15
+ ··· + 2.71407u + 0.521520
−1.37763u
16
− 1.94088u
15
+ ··· − 0.892738u − 1.79559
(ii) Obstruction class = −1
(iii) Cusp Shapes =
237738
51929
u
16
+
516629
51929
u
15
+ ··· +
7520
51929
u −
55125
51929
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
10
u
17
+ 2u
16
+ ··· + u + 1
c
2
, c
5
u
17
+ 3u
16
+ ··· + 20u − 4
c
3
, c
9
u
17
− 2u
16
+ ··· + u − 1
c
4
, c
7
u
17
− 3u
16
+ ··· − 6u + 1
c
6
u
17
+ 19u
16
+ ··· + 90u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
y
17
− 12y
16
+ ··· + 3y −1
c
2
, c
5
y
17
+ 15y
16
+ ··· + 168y −16
c
3
, c
9
y
17
+ 18y
15
+ ··· + 3y −1
c
4
, c
7
y
17
− 19y
16
+ ··· + 90y −1
c
6
y
17
− 39y
16
+ ··· + 6538y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060610 + 0.200554I
a = −1.100330 + 0.165877I
b = −0.126302 − 0.644532I
1.19150 + 0.82781I 6.36851 + 0.89620I
u = 1.060610 − 0.200554I
a = −1.100330 − 0.165877I
b = −0.126302 + 0.644532I
1.19150 − 0.82781I 6.36851 − 0.89620I
u = 0.886101
a = 4.18127
b = 0.394058
−0.349343 37.8910
u = −0.028909 + 1.130360I
a = −0.094574 − 0.284355I
b = −0.39410 − 1.60622I
−9.74801 + 4.21913I 0.41910 − 2.45985I
u = −0.028909 − 1.130360I
a = −0.094574 + 0.284355I
b = −0.39410 + 1.60622I
−9.74801 − 4.21913I 0.41910 + 2.45985I
u = −1.086970 + 0.371718I
a = 1.32093 − 0.74097I
b = 0.66882 − 1.55232I
0.79066 − 4.66548I 5.23718 + 7.00226I
u = −1.086970 − 0.371718I
a = 1.32093 + 0.74097I
b = 0.66882 + 1.55232I
0.79066 + 4.66548I 5.23718 − 7.00226I
u = −0.753939 + 0.337936I
a = −1.89995 − 1.01730I
b = −1.40441 − 0.70064I
−2.60021 − 1.61334I −0.56805 + 3.90220I
u = −0.753939 − 0.337936I
a = −1.89995 + 1.01730I
b = −1.40441 + 0.70064I
−2.60021 + 1.61334I −0.56805 − 3.90220I
u = −1.35486 + 0.58404I
a = −1.65394 + 0.65249I
b = −0.86824 + 1.50423I
−5.64268 − 10.26020I 3.51255 + 5.70568I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.35486 − 0.58404I
a = −1.65394 − 0.65249I
b = −0.86824 − 1.50423I
−5.64268 + 10.26020I 3.51255 − 5.70568I
u = 0.490972
a = −0.403318
b = 0.331229
0.859712 11.9140
u = 1.40843 + 0.58705I
a = 0.860646 + 1.071670I
b = 0.12824 + 1.41329I
−5.29829 + 1.87159I 2.27258 − 1.08933I
u = 1.40843 − 0.58705I
a = 0.860646 − 1.071670I
b = 0.12824 − 1.41329I
−5.29829 − 1.87159I 2.27258 + 1.08933I
u = −0.152522 + 0.439635I
a = −1.64573 − 0.72471I
b = −0.155264 + 1.014090I
−1.71156 + 1.29590I −0.73837 − 2.68816I
u = −0.152522 − 0.439635I
a = −1.64573 + 0.72471I
b = −0.155264 − 1.014090I
−1.71156 − 1.29590I −0.73837 + 2.68816I
u = −1.56075
a = 0.647938
b = 0.577229
7.69334 17.1880
6
II. I
u
2
= hb, a − u − 2, u
2
+ u − 1i
(i) Arc colorings
a
2
=
1
0
a
9
=
0
u
a
1
=
1
−u + 1
a
6
=
u + 2
0
a
5
=
u + 2
0
a
3
=
1
0
a
8
=
−u
−u + 1
a
7
=
2
−u + 1
a
10
=
u
u
a
4
=
u
u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −1
7
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
10
u
2
+ u − 1
c
2
, c
5
u
2
c
4
, c
6
(u − 1)
2
c
7
(u + 1)
2
c
8
, c
9
u
2
− u − 1
8
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
8
c
9
, c
10
y
2
− 3y + 1
c
2
, c
5
y
2
c
4
, c
6
, c
7
(y −1)
2
9
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.618034
a = 2.61803
b = 0
−0.657974 −1.00000
u = −1.61803
a = 0.381966
b = 0
7.23771 −1.00000
10
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
10
(u
2
+ u − 1)(u
17
+ 2u
16
+ ··· + u + 1)
c
2
, c
5
u
2
(u
17
+ 3u
16
+ ··· + 20u − 4)
c
3
(u
2
+ u − 1)(u
17
− 2u
16
+ ··· + u − 1)
c
4
((u − 1)
2
)(u
17
− 3u
16
+ ··· − 6u + 1)
c
6
((u − 1)
2
)(u
17
+ 19u
16
+ ··· + 90u + 1)
c
7
((u + 1)
2
)(u
17
− 3u
16
+ ··· − 6u + 1)
c
8
(u
2
− u − 1)(u
17
+ 2u
16
+ ··· + u + 1)
c
9
(u
2
− u − 1)(u
17
− 2u
16
+ ··· + u − 1)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
, c
10
(y
2
− 3y + 1)(y
17
− 12y
16
+ ··· + 3y −1)
c
2
, c
5
y
2
(y
17
+ 15y
16
+ ··· + 168y −16)
c
3
, c
9
(y
2
− 3y + 1)(y
17
+ 18y
15
+ ··· + 3y −1)
c
4
, c
7
((y −1)
2
)(y
17
− 19y
16
+ ··· + 90y −1)
c
6
((y −1)
2
)(y
17
− 39y
16
+ ··· + 6538y −1)
12
