12a
1278
(K12a
1278
)
A knot diagram
1
Linearized knot diagam
5 8 9 10 1 12 11 3 4 2 7 6
Solving Sequence
3,9
4 10 5 8 2 11 1 6 7 12
c
3
c
9
c
4
c
8
c
2
c
10
c
1
c
5
c
7
c
12
c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
20
− u
19
+ ··· + 2u − 1i
* 1 irreducible components of dim
C
= 0, with total 20 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
20
− u
19
+ · · · + 2u − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
10
=
u
−u
3
+ u
a
5
=
−u
2
+ 1
u
4
− 2u
2
a
8
=
−u
u
a
2
=
−u
2
+ 1
u
2
a
11
=
−u
7
+ 4u
5
− 4u
3
+ 2u
u
7
− 3u
5
+ u
a
1
=
−u
8
+ 5u
6
− 7u
4
+ 2u
2
+ 1
u
10
− 6u
8
+ 11u
6
− 6u
4
+ u
2
a
6
=
−u
14
+ 9u
12
− 30u
10
+ 45u
8
− 28u
6
+ 2u
4
+ 2u
2
+ 1
u
16
− 10u
14
+ 38u
12
− 68u
10
+ 58u
8
− 22u
6
+ 4u
4
− 2u
2
a
7
=
−u
13
+ 8u
11
− 23u
9
+ 30u
7
− 20u
5
+ 6u
3
− u
u
13
− 7u
11
+ 15u
9
− 8u
7
− 4u
5
+ 3u
3
+ u
a
12
=
−u
19
+ 12u
17
+ ··· − 7u
3
+ 2u
u
19
− 11u
17
+ 46u
15
− 89u
13
+ 73u
11
− 5u
9
− 22u
7
+ 2u
5
+ 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
+ 48u
15
− 228u
13
+ 544u
11
− 4u
10
− 684u
9
+ 28u
8
+
432u
7
− 64u
6
− 116u
5
+ 52u
4
+ 32u
3
− 12u
2
− 24u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
20
+ u
19
+ ··· − 2u − 1
c
2
, c
3
, c
4
c
8
, c
9
u
20
− u
19
+ ··· + 2u − 1
c
10
u
20
− 5u
19
+ ··· − 238u + 95
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
20
+ 29y
19
+ ··· + 6y + 1
c
2
, c
3
, c
4
c
8
, c
9
y
20
− 27y
19
+ ··· + 6y + 1
c
10
y
20
− 19y
19
+ ··· − 60634y + 9025
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.957042 + 0.156119I
3.42442 − 2.40418I 8.88830 + 6.40859I
u = −0.957042 − 0.156119I
3.42442 + 2.40418I 8.88830 − 6.40859I
u = 1.053290 + 0.250152I
9.25346 + 4.00690I 11.03271 − 4.36295I
u = 1.053290 − 0.250152I
9.25346 − 4.00690I 11.03271 + 4.36295I
u = 0.872181
1.81973 3.09740
u = −1.102630 + 0.306812I
−19.0311 − 4.8024I 11.07225 + 3.50232I
u = −1.102630 − 0.306812I
−19.0311 + 4.8024I 11.07225 − 3.50232I
u = 0.352552 + 0.563000I
15.8889 + 1.8393I 6.96532 − 3.24641I
u = 0.352552 − 0.563000I
15.8889 − 1.8393I 6.96532 + 3.24641I
u = −0.313620 + 0.473687I
5.00086 − 1.54932I 6.51491 + 4.26161I
u = −0.313620 − 0.473687I
5.00086 + 1.54932I 6.51491 − 4.26161I
u = 0.153630 + 0.311091I
0.036981 + 0.768397I 1.20151 − 8.96620I
u = 0.153630 − 0.311091I
0.036981 − 0.768397I 1.20151 + 8.96620I
u = −1.70374
11.1012 4.65580
u = 1.71447 + 0.03374I
12.98260 + 3.12195I 9.08784 − 4.56508I
u = 1.71447 − 0.03374I
12.98260 − 3.12195I 9.08784 + 4.56508I
u = −1.73483 + 0.06198I
19.2194 − 5.2785I 11.51082 + 3.23526I
u = −1.73483 − 0.06198I
19.2194 + 5.2785I 11.51082 − 3.23526I
u = 1.74996 + 0.07966I
−8.82272 + 6.42667I 11.84974 − 2.46747I
u = 1.74996 − 0.07966I
−8.82272 − 6.42667I 11.84974 + 2.46747I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
20
+ u
19
+ ··· − 2u − 1
c
2
, c
3
, c
4
c
8
, c
9
u
20
− u
19
+ ··· + 2u − 1
c
10
u
20
− 5u
19
+ ··· − 238u + 95
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
y
20
+ 29y
19
+ ··· + 6y + 1
c
2
, c
3
, c
4
c
8
, c
9
y
20
− 27y
19
+ ··· + 6y + 1
c
10
y
20
− 19y
19
+ ··· − 60634y + 9025
7
