10
3
(K10a
117
)
A knot diagram
1
Linearized knot diagam
5 9 8 2 1 10 4 3 7 6
Solving Sequence
1,6
5 2 4 10 7 8 3 9
c
5
c
1
c
4
c
10
c
6
c
7
c
3
c
9
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
12
− u
11
+ 9u
10
− 8u
9
+ 29u
8
− 22u
7
+ 40u
6
− 24u
5
+ 22u
4
− 9u
3
+ 3u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 12 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
12
−u
11
+9u
10
−8u
9
+29u
8
−22u
7
+40u
6
−24u
5
+22u
4
−9u
3
+3u
2
+1i
(i) Arc colorings
a
1
=
0
u
a
6
=
1
0
a
5
=
1
−u
2
a
2
=
−u
u
3
+ u
a
4
=
u
2
+ 1
−u
4
− 2u
2
a
10
=
u
u
a
7
=
u
2
+ 1
u
2
a
8
=
u
8
+ 5u
6
+ 7u
4
+ 4u
2
+ 1
−u
10
− 6u
8
− 11u
6
− 6u
4
+ u
2
a
3
=
u
9
+ 6u
7
+ 11u
5
+ 6u
3
− u
u
9
+ 5u
7
+ 7u
5
+ 4u
3
+ u
a
9
=
u
3
+ 2u
u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
10
− 4u
9
+ 32u
8
− 28u
7
+ 88u
6
− 64u
5
+ 96u
4
− 52u
3
+ 36u
2
− 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
10
u
12
− u
11
+ ··· + 3u
2
+ 1
c
2
, c
3
, c
7
c
8
u
12
− u
11
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
10
y
12
+ 17y
11
+ ··· + 6y + 1
c
2
, c
3
, c
7
c
8
y
12
+ 13y
11
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.088430 + 1.124390I
4.57295 + 1.88989I 3.52820 − 3.98383I
u = −0.088430 − 1.124390I
4.57295 − 1.88989I 3.52820 + 3.98383I
u = 0.262297 + 1.106610I
−1.85830 − 4.37390I −0.54525 + 3.77995I
u = 0.262297 − 1.106610I
−1.85830 + 4.37390I −0.54525 − 3.77995I
u = 0.520232 + 0.348843I
−6.43201 − 1.71442I −5.08194 + 3.66811I
u = 0.520232 − 0.348843I
−6.43201 + 1.71442I −5.08194 − 3.66811I
u = −0.237731 + 0.323766I
−0.073452 + 0.847212I −1.79874 − 8.22796I
u = −0.237731 − 0.323766I
−0.073452 − 0.847212I −1.79874 + 8.22796I
u = 0.06408 + 1.75550I
8.44501 − 5.73210I 0.29636 + 2.78231I
u = 0.06408 − 1.75550I
8.44501 + 5.73210I 0.29636 − 2.78231I
u = −0.02045 + 1.76385I
15.0850 + 2.3421I 3.60137 − 2.79467I
u = −0.02045 − 1.76385I
15.0850 − 2.3421I 3.60137 + 2.79467I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
10
u
12
− u
11
+ ··· + 3u
2
+ 1
c
2
, c
3
, c
7
c
8
u
12
− u
11
+ ··· − 2u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
, c
5
c
6
, c
9
, c
10
y
12
+ 17y
11
+ ··· + 6y + 1
c
2
, c
3
, c
7
c
8
y
12
+ 13y
11
+ ··· + 6y + 1
7
