10
16
(K10a
115
)
A knot diagram
1
Linearized knot diagam
6 8 9 10 2 1 5 4 3 7
Solving Sequence
2,6
1 7 5 8 3 10 4 9
c
1
c
6
c
5
c
7
c
2
c
10
c
4
c
9
c
3
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
23
− u
22
+ ··· − 2u + 1i
* 1 irreducible components of dim
C
= 0, with total 23 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
23
− u
22
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
7
=
u
u
3
+ u
a
5
=
−u
u
a
8
=
−u
5
− 2u
3
+ u
u
5
+ 3u
3
+ u
a
3
=
−u
10
− 5u
8
− 6u
6
+ u
4
+ u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 6u
4
+ u
2
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
u
7
+ 4u
5
+ 4u
3
u
9
+ 5u
7
+ 7u
5
+ 2u
3
+ u
a
9
=
−u
21
− 12u
19
+ ··· − 2u
3
+ u
−u
22
+ u
21
+ ··· − u + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
22
+4u
21
−56u
20
+52u
19
−324u
18
+276u
17
−996u
16
+764u
15
−1744u
14
+1172u
13
−
1748u
12
+1000u
11
−988u
10
+504u
9
−304u
8
+188u
7
−8u
6
+32u
5
+12u
4
+12u
3
+4u
2
−16u+2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
23
− u
22
+ ··· − 2u + 1
c
2
, c
4
u
23
− u
22
+ ··· + 4u + 5
c
3
, c
8
, c
9
u
23
+ u
22
+ ··· + 2u + 1
c
7
u
23
− 7u
22
+ ··· + 40u − 17
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
23
+ 27y
22
+ ··· − 4y −1
c
2
, c
4
y
23
− 17y
22
+ ··· − 144y −25
c
3
, c
8
, c
9
y
23
+ 19y
22
+ ··· − 4y −1
c
7
y
23
− 9y
22
+ ··· + 1260y −289
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.473302 + 0.738923I
0.16340 + 7.25342I −3.09734 − 7.25802I
u = 0.473302 − 0.738923I
0.16340 − 7.25342I −3.09734 + 7.25802I
u = −0.413689 + 0.761868I
−4.21185 − 3.22031I −8.22079 + 4.90443I
u = −0.413689 − 0.761868I
−4.21185 + 3.22031I −8.22079 − 4.90443I
u = 0.324148 + 0.802707I
−0.817157 − 0.745308I −5.08009 − 0.73522I
u = 0.324148 − 0.802707I
−0.817157 + 0.745308I −5.08009 + 0.73522I
u = −0.477903 + 0.451361I
4.96840 − 1.68040I 2.82272 + 4.29991I
u = −0.477903 − 0.451361I
4.96840 + 1.68040I 2.82272 − 4.29991I
u = 0.581337 + 0.108709I
2.00599 − 3.66457I 0.82434 + 2.67133I
u = 0.581337 − 0.108709I
2.00599 + 3.66457I 0.82434 − 2.67133I
u = −0.546774
−2.00773 −4.01170
u = 0.228067 + 0.467269I
−0.140168 + 0.925919I −2.94249 − 7.44214I
u = 0.228067 − 0.467269I
−0.140168 − 0.925919I −2.94249 + 7.44214I
u = −0.08584 + 1.50808I
−1.46467 − 3.53591I −1.36507 + 3.24061I
u = −0.08584 − 1.50808I
−1.46467 + 3.53591I −1.36507 − 3.24061I
u = 0.03322 + 1.55779I
−7.11725 + 1.68405I −6.35516 − 3.83025I
u = 0.03322 − 1.55779I
−7.11725 − 1.68405I −6.35516 + 3.83025I
u = 0.13674 + 1.61894I
−7.87123 + 9.54664I −5.28748 − 5.57899I
u = 0.13674 − 1.61894I
−7.87123 − 9.54664I −5.28748 + 5.57899I
u = −0.11785 + 1.62483I
−12.38020 − 5.22748I −9.66631 + 3.33432I
u = −0.11785 − 1.62483I
−12.38020 + 5.22748I −9.66631 − 3.33432I
u = 0.09185 + 1.62814I
−9.14246 + 0.83337I −6.62647 + 0.43888I
u = 0.09185 − 1.62814I
−9.14246 − 0.83337I −6.62647 − 0.43888I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
10
u
23
− u
22
+ ··· − 2u + 1
c
2
, c
4
u
23
− u
22
+ ··· + 4u + 5
c
3
, c
8
, c
9
u
23
+ u
22
+ ··· + 2u + 1
c
7
u
23
− 7u
22
+ ··· + 40u − 17
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
10
y
23
+ 27y
22
+ ··· − 4y −1
c
2
, c
4
y
23
− 17y
22
+ ··· − 144y −25
c
3
, c
8
, c
9
y
23
+ 19y
22
+ ··· − 4y −1
c
7
y
23
− 9y
22
+ ··· + 1260y −289
7
