10
18
(K10a
63
)
A knot diagram
1
Linearized knot diagam
7 5 9 8 10 1 6 4 3 2
Solving Sequence
4,9
3 10 8 5 6 2 1 7
c
3
c
9
c
8
c
4
c
5
c
2
c
10
c
7
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
27
− u
26
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 27 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
27
− u
26
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
3
=
1
u
2
a
10
=
u
u
3
+ u
a
8
=
−u
u
a
5
=
u
2
+ 1
−u
2
a
6
=
u
6
+ 3u
4
+ 2u
2
+ 1
u
8
+ 4u
6
+ 4u
4
a
2
=
u
6
+ 3u
4
+ 2u
2
+ 1
−u
6
− 2u
4
+ u
2
a
1
=
−u
15
− 8u
13
− 24u
11
− 34u
9
− 26u
7
− 14u
5
− 4u
3
u
15
+ 7u
13
+ 16u
11
+ 11u
9
− 2u
7
+ u
a
7
=
u
15
+ 8u
13
+ 24u
11
+ 34u
9
+ 26u
7
+ 14u
5
+ 4u
3
u
17
+ 9u
15
+ 31u
13
+ 50u
11
+ 37u
9
+ 12u
7
+ 4u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
25
− 4u
24
+ 60u
23
− 56u
22
+ 384u
21
− 332u
20
+ 1364u
19
−
1084u
18
+ 2936u
17
− 2136u
16
+ 3956u
15
− 2664u
14
+ 3412u
13
− 2236u
12
+ 2008u
11
−
1396u
10
+ 896u
9
− 656u
8
+ 304u
7
− 204u
6
+ 124u
5
− 64u
4
+ 60u
3
− 20u
2
+ 12u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
27
− u
26
+ ··· + u
2
+ 1
c
2
u
27
− 7u
26
+ ··· + 8u − 1
c
3
, c
4
, c
8
c
9
u
27
+ u
26
+ ··· + 2u + 1
c
5
u
27
+ u
26
+ ··· + 8u + 4
c
7
, c
10
u
27
+ 9u
26
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
27
− 9y
26
+ ··· − 2y −1
c
2
y
27
− y
26
+ ··· − 34y −1
c
3
, c
4
, c
8
c
9
y
27
+ 31y
26
+ ··· − 2y −1
c
5
y
27
− 5y
26
+ ··· + 56y −16
c
7
, c
10
y
27
+ 19y
26
+ ··· − 2y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.509948 + 0.671959I
1.37783 + 8.19998I −2.79147 − 8.55054I
u = 0.509948 − 0.671959I
1.37783 − 8.19998I −2.79147 + 8.55054I
u = 0.113525 + 0.797622I
−0.95481 − 2.34352I −6.62935 + 2.39389I
u = 0.113525 − 0.797622I
−0.95481 + 2.34352I −6.62935 − 2.39389I
u = −0.501343 + 0.630190I
2.26803 − 2.57835I −0.81917 + 3.65038I
u = −0.501343 − 0.630190I
2.26803 + 2.57835I −0.81917 − 3.65038I
u = 0.376782 + 0.707314I
−3.62827 + 2.81912I −9.45302 − 5.56399I
u = 0.376782 − 0.707314I
−3.62827 − 2.81912I −9.45302 + 5.56399I
u = 0.576068 + 0.227813I
2.67334 − 4.47788I 0.69991 + 3.02325I
u = 0.576068 − 0.227813I
2.67334 + 4.47788I 0.69991 − 3.02325I
u = −0.548106 + 0.284426I
3.27525 − 1.04588I 2.08117 + 3.01333I
u = −0.548106 − 0.284426I
3.27525 + 1.04588I 2.08117 − 3.01333I
u = −0.312350 + 0.509712I
−0.041447 − 1.170260I −0.65568 + 5.80154I
u = −0.312350 − 0.509712I
−0.041447 + 1.170260I −0.65568 − 5.80154I
u = −0.02510 + 1.42921I
−1.89158 − 2.85128I −2.36117 + 2.96428I
u = −0.02510 − 1.42921I
−1.89158 + 2.85128I −2.36117 − 2.96428I
u = 0.459274
−1.66811 −4.57270
u = −0.07989 + 1.56731I
−7.20164 − 2.51533I −4.12254 + 2.69602I
u = −0.07989 − 1.56731I
−7.20164 + 2.51533I −4.12254 − 2.69602I
u = −0.14253 + 1.58020I
−5.18836 − 4.92710I −3.80267 + 2.17668I
u = −0.14253 − 1.58020I
−5.18836 + 4.92710I −3.80267 − 2.17668I
u = 0.14900 + 1.59440I
−6.28352 + 10.63980I −5.63394 − 6.90100I
u = 0.14900 − 1.59440I
−6.28352 − 10.63980I −5.63394 + 6.90100I
u = 0.04709 + 1.60412I
−9.06338 − 1.66777I −8.35861 + 2.79123I
u = 0.04709 − 1.60412I
−9.06338 + 1.66777I −8.35861 − 2.79123I
u = 0.10726 + 1.60486I
−11.51840 + 4.62424I −10.86711 − 3.60523I
u = 0.10726 − 1.60486I
−11.51840 − 4.62424I −10.86711 + 3.60523I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
27
− u
26
+ ··· + u
2
+ 1
c
2
u
27
− 7u
26
+ ··· + 8u − 1
c
3
, c
4
, c
8
c
9
u
27
+ u
26
+ ··· + 2u + 1
c
5
u
27
+ u
26
+ ··· + 8u + 4
c
7
, c
10
u
27
+ 9u
26
+ ··· − 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
27
− 9y
26
+ ··· − 2y −1
c
2
y
27
− y
26
+ ··· − 34y −1
c
3
, c
4
, c
8
c
9
y
27
+ 31y
26
+ ··· − 2y −1
c
5
y
27
− 5y
26
+ ··· + 56y −16
c
7
, c
10
y
27
+ 19y
26
+ ··· − 2y −1
7
