10
6
(K10a
70
)
A knot diagram
1
Linearized knot diagam
6 8 9 10 7 1 5 3 4 2
Solving Sequence
1,7
6 2 5 8 3 10 4 9
c
6
c
1
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
18
− u
17
+ ··· + u − 1i
* 1 irreducible components of dim
C
= 0, with total 18 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
18
− u
17
+ 3u
16
− 2u
15
+ 8u
14
− 5u
13
+ 13u
12
− 6u
11
+ 17u
10
−
5u
9
+ 15u
8
− 2u
7
+ 10u
6
+ 2u
5
+ 2u
4
+ 4u
3
− u
2
+ u − 1i
(i) Arc colorings
a
1
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
2
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
2
a
8
=
u
4
+ u
2
+ 1
u
4
a
3
=
−u
11
− 2u
9
− 4u
7
− 4u
5
− 3u
3
−u
11
− u
9
− 2u
7
− u
5
+ u
3
+ u
a
10
=
u
3
u
5
+ u
3
+ u
a
4
=
−u
10
− u
8
− 2u
6
− u
4
+ u
2
+ 1
−u
12
− 2u
10
− 4u
8
− 4u
6
− 3u
4
a
9
=
−u
17
− 2u
15
− 5u
13
− 6u
11
− 5u
9
− 2u
7
+ 2u
5
+ 4u
3
+ u
−u
17
+ u
16
+ ··· + u − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
16
− 4u
15
+ 8u
14
− 8u
13
+ 24u
12
− 20u
11
+ 28u
10
− 24u
9
+
36u
8
− 20u
7
+ 20u
6
− 12u
5
+ 8u
4
+ 4u
3
− 8u
2
+ 8u − 10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
18
+ u
17
+ ··· − u − 1
c
2
, c
3
, c
4
c
8
, c
9
u
18
+ u
17
+ ··· − 3u − 1
c
5
, c
7
, c
10
u
18
+ 5u
17
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
18
+ 5y
17
+ ··· + y + 1
c
2
, c
3
, c
4
c
8
, c
9
y
18
− 23y
17
+ ··· + y + 1
c
5
, c
7
, c
10
y
18
+ 17y
17
+ ··· − 23y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.261770 + 0.920605I
−3.83985 + 2.54428I −13.6710 − 5.1939I
u = 0.261770 − 0.920605I
−3.83985 − 2.54428I −13.6710 + 5.1939I
u = −0.272828 + 1.039360I
−13.13100 − 3.24976I −13.8187 + 3.4932I
u = −0.272828 − 1.039360I
−13.13100 + 3.24976I −13.8187 − 3.4932I
u = 0.855326 + 0.759946I
−5.70958 − 2.31893I −7.86761 + 0.27178I
u = 0.855326 − 0.759946I
−5.70958 + 2.31893I −7.86761 − 0.27178I
u = −0.813352 + 0.821748I
2.79760 + 0.47412I −6.24213 − 1.46151I
u = −0.813352 − 0.821748I
2.79760 − 0.47412I −6.24213 + 1.46151I
u = 0.798203 + 0.890045I
5.14256 + 2.99347I −2.16456 − 2.96884I
u = 0.798203 − 0.890045I
5.14256 − 2.99347I −2.16456 + 2.96884I
u = −0.779702 + 0.947695I
2.41083 − 6.44838I −7.16819 + 6.55335I
u = −0.779702 − 0.947695I
2.41083 + 6.44838I −7.16819 − 6.55335I
u = 0.774589 + 0.997585I
−6.44242 + 8.39094I −9.04735 − 5.13904I
u = 0.774589 − 0.997585I
−6.44242 − 8.39094I −9.04735 + 5.13904I
u = −0.703368
−9.78395 −7.88600
u = −0.211837 + 0.649664I
−0.370697 − 0.965885I −6.45922 + 6.93392I
u = −0.211837 − 0.649664I
−0.370697 + 0.965885I −6.45922 − 6.93392I
u = 0.479029
−1.27899 −7.23650
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
18
+ u
17
+ ··· − u − 1
c
2
, c
3
, c
4
c
8
, c
9
u
18
+ u
17
+ ··· − 3u − 1
c
5
, c
7
, c
10
u
18
+ 5u
17
+ ··· + u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
18
+ 5y
17
+ ··· + y + 1
c
2
, c
3
, c
4
c
8
, c
9
y
18
− 23y
17
+ ··· + y + 1
c
5
, c
7
, c
10
y
18
+ 17y
17
+ ··· − 23y + 1
7
