12a
0502
(K12a
0502
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 10 12 2 4 5 1 6 11
Solving Sequence
2,8
7 3 4 9 5 10 6 1 11 12
c
7
c
2
c
3
c
8
c
4
c
9
c
5
c
1
c
10
c
12
c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
45
− u
44
+ ··· − 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 45 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
45
− u
44
+ · · · − 3u + 1i
(i) Arc colorings
a
2
=
0
u
a
8
=
1
0
a
7
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
9
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
10
=
u
12
+ 3u
10
+ 3u
8
− 2u
6
− 4u
4
− u
2
+ 1
−u
12
− 4u
10
− 6u
8
− 2u
6
+ 3u
4
+ 2u
2
a
6
=
−u
15
− 4u
13
− 6u
11
+ 8u
7
+ 6u
5
− 2u
3
− 2u
u
15
+ 5u
13
+ 10u
11
+ 7u
9
− 4u
7
− 8u
5
− 2u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
11
=
u
20
+ 5u
18
+ 11u
16
+ 10u
14
− 7u
10
− 3u
8
− 2u
6
− 3u
4
− u
2
+ 1
u
22
+ 6u
20
+ ··· + 4u
4
+ 3u
2
a
12
=
u
37
+ 10u
35
+ ··· − 9u
5
+ u
u
39
+ 11u
37
+ ··· + 4u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
43
+ 4u
42
+ ··· + 20u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
45
+ 27u
44
+ ··· + 3u − 1
c
2
, c
7
u
45
+ u
44
+ ··· − 3u − 1
c
3
, c
4
, c
5
c
8
, c
9
u
45
− u
44
+ ··· + 11u − 1
c
6
, c
11
u
45
+ u
44
+ ··· − 3u − 1
c
10
, c
12
u
45
+ 17u
44
+ ··· + 3u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
45
− 17y
44
+ ··· + 55y −1
c
2
, c
7
y
45
+ 27y
44
+ ··· + 3y −1
c
3
, c
4
, c
5
c
8
, c
9
y
45
− 61y
44
+ ··· + 99y −1
c
6
, c
11
y
45
− 17y
44
+ ··· + 3y −1
c
10
, c
12
y
45
+ 23y
44
+ ··· − 17y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.427459 + 0.911225I
0.85804 + 6.50089I −8.32802 − 9.97393I
u = 0.427459 − 0.911225I
0.85804 − 6.50089I −8.32802 + 9.97393I
u = 0.070383 + 1.016090I
−1.72179 − 2.04025I −15.9831 + 3.0595I
u = 0.070383 − 1.016090I
−1.72179 + 2.04025I −15.9831 − 3.0595I
u = −0.408478 + 0.865533I
1.39393 − 1.34908I −6.37203 + 4.08552I
u = −0.408478 − 0.865533I
1.39393 + 1.34908I −6.37203 − 4.08552I
u = 0.283223 + 1.012980I
−3.30573 + 2.64852I −17.4700 − 5.8251I
u = 0.283223 − 1.012980I
−3.30573 − 2.64852I −17.4700 + 5.8251I
u = 0.935027
−15.9659 −15.5090
u = 0.930328 + 0.019398I
−11.70540 − 7.28312I −11.98320 + 4.60308I
u = 0.930328 − 0.019398I
−11.70540 + 7.28312I −11.98320 − 4.60308I
u = −0.923476 + 0.012954I
−10.00250 + 1.76256I −9.73819 − 0.10950I
u = −0.923476 − 0.012954I
−10.00250 − 1.76256I −9.73819 + 0.10950I
u = −0.208200 + 0.833837I
−0.603828 − 1.131350I −7.84077 + 5.39431I
u = −0.208200 − 0.833837I
−0.603828 + 1.131350I −7.84077 − 5.39431I
u = 0.358679 + 1.138370I
−4.13553 + 2.70881I −12.96314 − 3.74313I
u = 0.358679 − 1.138370I
−4.13553 − 2.70881I −12.96314 + 3.74313I
u = 0.440538 + 1.122380I
−3.51671 + 4.84200I −11.51709 − 4.49120I
u = 0.440538 − 1.122380I
−3.51671 − 4.84200I −11.51709 + 4.49120I
u = −0.347703 + 1.175290I
−5.60707 + 2.21593I −15.5378 − 1.9663I
u = −0.347703 − 1.175290I
−5.60707 − 2.21593I −15.5378 + 1.9663I
u = −0.458823 + 1.138270I
−4.76002 − 10.14720I −13.4545 + 9.2635I
u = −0.458823 − 1.138270I
−4.76002 + 10.14720I −13.4545 − 9.2635I
u = −0.411367 + 1.171030I
−9.02942 − 4.07847I −18.7916 + 4.0511I
u = −0.411367 − 1.171030I
−9.02942 + 4.07847I −18.7916 − 4.0511I
u = −0.723185
−5.63052 −15.3580
u = −0.705456 + 0.119537I
−1.83649 + 5.83150I −10.37227 − 5.87935I
u = −0.705456 − 0.119537I
−1.83649 − 5.83150I −10.37227 + 5.87935I
u = −0.399313 + 0.551155I
2.22533 − 2.24395I −3.65717 + 3.92179I
u = −0.399313 − 0.551155I
2.22533 + 2.24395I −3.65717 − 3.92179I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.644426 + 0.110335I
−0.671592 − 0.750914I −8.28728 + 0.79803I
u = 0.644426 − 0.110335I
−0.671592 + 0.750914I −8.28728 − 0.79803I
u = −0.482704 + 1.275130I
−13.8679 − 6.7706I 0
u = −0.482704 − 1.275130I
−13.8679 + 6.7706I 0
u = −0.467992 + 1.280780I
−13.9791 − 3.1742I 0
u = −0.467992 − 1.280780I
−13.9791 + 3.1742I 0
u = 0.487764 + 1.277220I
−15.5609 + 12.3367I 0
u = 0.487764 − 1.277220I
−15.5609 − 12.3367I 0
u = 0.465467 + 1.286340I
−15.7305 − 2.3351I 0
u = 0.465467 − 1.286340I
−15.7305 + 2.3351I 0
u = 0.428207 + 0.461832I
2.03862 − 2.79869I −4.43613 + 3.54362I
u = 0.428207 − 0.461832I
2.03862 + 2.79869I −4.43613 − 3.54362I
u = 0.478105 + 1.284620I
19.5602 + 5.0232I 0
u = 0.478105 − 1.284620I
19.5602 − 5.0232I 0
u = 0.386025
−0.813684 −12.1660
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
45
+ 27u
44
+ ··· + 3u − 1
c
2
, c
7
u
45
+ u
44
+ ··· − 3u − 1
c
3
, c
4
, c
5
c
8
, c
9
u
45
− u
44
+ ··· + 11u − 1
c
6
, c
11
u
45
+ u
44
+ ··· − 3u − 1
c
10
, c
12
u
45
+ 17u
44
+ ··· + 3u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
45
− 17y
44
+ ··· + 55y −1
c
2
, c
7
y
45
+ 27y
44
+ ··· + 3y −1
c
3
, c
4
, c
5
c
8
, c
9
y
45
− 61y
44
+ ··· + 99y −1
c
6
, c
11
y
45
− 17y
44
+ ··· + 3y −1
c
10
, c
12
y
45
+ 23y
44
+ ··· − 17y −1
8
