12a
1287
(K12a
1287
)
A knot diagram
1
Linearized knot diagam
5 10 9 8 1 12 11 4 3 2 7 6
Solving Sequence
6,12
7 1 5 2 11 8 4 9 3 10
c
6
c
12
c
5
c
1
c
11
c
7
c
4
c
8
c
3
c
10
c
2
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= hu
18
+ u
17
+ ··· + 3u + 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
+ 13u
16
+ 12u
15
+ 68u
14
+ 57u
13
+ 183u
12
+ 136u
11
+
269u
10
+ 171u
9
+ 211u
8
+ 108u
7
+ 80u
6
+ 28u
5
+ 18u
4
+ 4u
3
+ 9u
2
+ 3u + 1i
(i) Arc colorings
a
6
=
1
0
a
12
=
0
u
a
7
=
1
u
2
a
1
=
−u
u
a
5
=
u
2
+ 1
−u
2
a
2
=
−u
3
− 2u
u
3
+ u
a
11
=
u
u
3
+ u
a
8
=
u
2
+ 1
u
4
+ 2u
2
a
4
=
u
8
+ 5u
6
+ 7u
4
+ 4u
2
+ 1
u
10
+ 6u
8
+ 11u
6
+ 6u
4
− u
2
a
9
=
u
14
+ 9u
12
+ 30u
10
+ 47u
8
+ 38u
6
+ 16u
4
+ 4u
2
+ 1
u
16
+ 10u
14
+ 38u
12
+ 68u
10
+ 56u
8
+ 14u
6
− 2u
4
+ 2u
2
a
3
=
−u
15
− 10u
13
− 38u
11
− 68u
9
− 56u
7
− 14u
5
+ 2u
3
− 2u
u
15
+ 9u
13
+ 30u
11
+ 47u
9
+ 38u
7
+ 16u
5
+ 4u
3
+ u
a
10
=
−u
9
− 6u
7
− 11u
5
− 6u
3
+ u
u
9
+ 5u
7
+ 7u
5
+ 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
17
− 4u
16
− 52u
15
− 48u
14
− 272u
13
− 224u
12
− 728u
11
−
508u
10
− 1044u
9
− 568u
8
− 756u
7
− 272u
6
− 224u
5
− 24u
4
− 36u
3
− 4u
2
− 36u − 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
18
+ u
17
+ ··· + 3u + 1
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
18
− u
17
+ ··· − 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
18
+ 25y
17
+ ··· + 9y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.065042 + 1.102700I
4.46708 + 1.50403I 5.18929 − 4.54490I
u = −0.065042 − 1.102700I
4.46708 − 1.50403I 5.18929 + 4.54490I
u = 0.205535 + 1.091440I
− 3.71533I 0. + 4.49065I
u = 0.205535 − 1.091440I
3.71533I 0. − 4.49065I
u = −0.297449 + 1.108730I
−10.26620 + 4.74487I −0.82347 − 3.51953I
u = −0.297449 − 1.108730I
−10.26620 − 4.74487I −0.82347 + 3.51953I
u = −0.558415 + 0.355021I
−14.8588 + 1.8284I −5.01513 − 3.29027I
u = −0.558415 − 0.355021I
−14.8588 − 1.8284I −5.01513 + 3.29027I
u = 0.451254 + 0.331288I
−4.46708 − 1.50403I −5.18929 + 4.54490I
u = 0.451254 − 0.331288I
−4.46708 + 1.50403I −5.18929 − 4.54490I
u = −0.193258 + 0.297102I
0.701427I 0. − 9.96307I
u = −0.193258 − 0.297102I
− 0.701427I 0. + 9.96307I
u = 0.04734 + 1.75261I
10.26620 − 4.74487I 0.82347 + 3.51953I
u = 0.04734 − 1.75261I
10.26620 + 4.74487I 0.82347 − 3.51953I
u = −0.07535 + 1.75351I
6.30909I 0. − 2.51986I
u = −0.07535 − 1.75351I
− 6.30909I 0. + 2.51986I
u = −0.01462 + 1.75753I
14.8588 + 1.8284I 5.01513 − 3.29027I
u = −0.01462 − 1.75753I
14.8588 − 1.8284I 5.01513 + 3.29027I
5
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
7
, c
11
, c
12
u
18
+ u
17
+ ··· + 3u + 1
c
2
, c
3
, c
4
c
8
, c
9
, c
10
u
18
− u
17
+ ··· − 3u + 1
6
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
18
+ 25y
17
+ ··· + 9y + 1
7
