12a
0774
(K12a
0774
)
A knot diagram
1
Linearized knot diagam
3 8 10 12 11 9 2 7 1 6 5 4
Solving Sequence
3,8
2 1 7 9 10 4 6 11 5 12
c
2
c
1
c
7
c
8
c
9
c
3
c
6
c
10
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
44
− u
43
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 44 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
44
− u
43
+ · · · − u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
1
−u
2
a
1
=
−u
2
+ 1
−u
2
a
7
=
u
−u
3
+ u
a
9
=
−u
3
u
5
− u
3
+ u
a
10
=
u
9
− 2u
7
+ 3u
5
− 4u
3
+ u
u
9
− u
7
+ 3u
5
− 2u
3
+ u
a
4
=
−u
18
+ 3u
16
− 8u
14
+ 15u
12
− 19u
10
+ 21u
8
− 14u
6
+ 6u
4
− u
2
+ 1
−u
18
+ 2u
16
− 7u
14
+ 10u
12
− 15u
10
+ 14u
8
− 10u
6
+ 4u
4
− u
2
a
6
=
u
5
+ u
−u
7
+ u
5
− 2u
3
+ u
a
11
=
u
21
− 2u
19
+ ··· − 4u
3
+ u
−u
23
+ 3u
21
+ ··· − 2u
3
+ u
a
5
=
u
37
− 4u
35
+ ··· + 5u
5
+ u
−u
39
+ 5u
37
+ ··· − 2u
3
+ u
a
12
=
−u
34
+ 5u
32
+ ··· − u
2
+ 1
−u
34
+ 4u
32
+ ··· − 4u
6
− u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
43
− 24u
41
+ ··· − 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
44
+ 11u
43
+ ··· + 2u + 1
c
2
, c
7
u
44
+ u
43
+ ··· − u
2
+ 1
c
3
u
44
+ u
43
+ ··· − 20u + 1
c
4
, c
5
, c
10
c
11
, c
12
u
44
+ u
43
+ ··· + 2u + 1
c
9
u
44
− 7u
43
+ ··· − 82u + 7
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
44
+ 45y
43
+ ··· + 22y + 1
c
2
, c
7
y
44
− 11y
43
+ ··· − 2y + 1
c
3
y
44
+ y
43
+ ··· − 146y + 1
c
4
, c
5
, c
10
c
11
, c
12
y
44
+ 57y
43
+ ··· − 2y + 1
c
9
y
44
+ 5y
43
+ ··· − 662y + 49
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.973577 + 0.164922I
−15.0825 + 1.6902I −8.15131 + 0.48221I
u = 0.973577 − 0.164922I
−15.0825 − 1.6902I −8.15131 − 0.48221I
u = 0.953126 + 0.350659I
−4.40949 − 6.07307I −4.94666 + 8.49917I
u = 0.953126 − 0.350659I
−4.40949 + 6.07307I −4.94666 − 8.49917I
u = −0.895823 + 0.344349I
−0.76004 + 3.52272I 0.90093 − 8.67149I
u = −0.895823 − 0.344349I
−0.76004 − 3.52272I 0.90093 + 8.67149I
u = −0.984525 + 0.354824I
−13.9897 + 7.4569I −5.72896 − 6.66961I
u = −0.984525 − 0.354824I
−13.9897 − 7.4569I −5.72896 + 6.66961I
u = −0.925891 + 0.175432I
−5.40173 − 0.74499I −8.08077 + 0.34406I
u = −0.925891 − 0.175432I
−5.40173 + 0.74499I −8.08077 − 0.34406I
u = 0.827466 + 0.255178I
−1.38547 − 0.92460I −2.73817 + 0.09424I
u = 0.827466 − 0.255178I
−1.38547 + 0.92460I −2.73817 − 0.09424I
u = −0.615862 + 0.604835I
−9.75255 + 2.21449I 0.08262 − 3.14030I
u = −0.615862 − 0.604835I
−9.75255 − 2.21449I 0.08262 + 3.14030I
u = −0.902990 + 0.718759I
−10.10340 + 2.72623I −2.70072 − 3.12149I
u = −0.902990 − 0.718759I
−10.10340 − 2.72623I −2.70072 + 3.12149I
u = 0.892831 + 0.769198I
−0.21070 − 2.90742I −2.24337 + 2.68440I
u = 0.892831 − 0.769198I
−0.21070 + 2.90742I −2.24337 − 2.68440I
u = 0.817945 + 0.876060I
−6.01810 + 5.50586I 0. − 1.93289I
u = 0.817945 − 0.876060I
−6.01810 − 5.50586I 0. + 1.93289I
u = −0.829954 + 0.866717I
3.36907 − 3.82326I 1.37231 + 3.41233I
u = −0.829954 − 0.866717I
3.36907 + 3.82326I 1.37231 − 3.41233I
u = 0.848035 + 0.857865I
6.75596 + 0.77249I 6.88350 − 1.61671I
u = 0.848035 − 0.857865I
6.75596 − 0.77249I 6.88350 + 1.61671I
u = −0.869487 + 0.843192I
5.36576 + 2.39601I 3.40471 − 4.61138I
u = −0.869487 − 0.843192I
5.36576 − 2.39601I 3.40471 + 4.61138I
u = −0.932920 + 0.818861I
5.16549 + 3.79714I 3.00062 + 0.I
u = −0.932920 − 0.818861I
5.16549 − 3.79714I 3.00062 + 0.I
u = 0.909164 + 0.854591I
−2.08909 − 3.16925I 2.00000 + 2.55615I
u = 0.909164 − 0.854591I
−2.08909 + 3.16925I 2.00000 − 2.55615I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.954586 + 0.818188I
6.42188 − 7.00665I 5.98798 + 6.76938I
u = 0.954586 − 0.818188I
6.42188 + 7.00665I 5.98798 − 6.76938I
u = −0.969590 + 0.814117I
2.93183 + 10.06920I 0. − 8.25971I
u = −0.969590 − 0.814117I
2.93183 − 10.06920I 0. + 8.25971I
u = 0.980677 + 0.812716I
−6.52850 − 11.77360I 0. + 6.74145I
u = 0.980677 − 0.812716I
−6.52850 + 11.77360I 0. − 6.74145I
u = 0.554006 + 0.459665I
−0.93127 − 1.66423I 1.39492 + 5.36634I
u = 0.554006 − 0.459665I
−0.93127 + 1.66423I 1.39492 − 5.36634I
u = −0.177999 + 0.637957I
−11.46970 − 3.90382I −0.05667 + 2.21807I
u = −0.177999 − 0.637957I
−11.46970 + 3.90382I −0.05667 − 2.21807I
u = 0.196554 + 0.570963I
−2.11354 + 2.70365I 0.96683 − 3.89024I
u = 0.196554 − 0.570963I
−2.11354 − 2.70365I 0.96683 + 3.89024I
u = −0.302925 + 0.453673I
1.018180 − 0.410960I 9.05285 + 1.73879I
u = −0.302925 − 0.453673I
1.018180 + 0.410960I 9.05285 − 1.73879I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
, c
8
u
44
+ 11u
43
+ ··· + 2u + 1
c
2
, c
7
u
44
+ u
43
+ ··· − u
2
+ 1
c
3
u
44
+ u
43
+ ··· − 20u + 1
c
4
, c
5
, c
10
c
11
, c
12
u
44
+ u
43
+ ··· + 2u + 1
c
9
u
44
− 7u
43
+ ··· − 82u + 7
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
, c
8
y
44
+ 45y
43
+ ··· + 22y + 1
c
2
, c
7
y
44
− 11y
43
+ ··· − 2y + 1
c
3
y
44
+ y
43
+ ··· − 146y + 1
c
4
, c
5
, c
10
c
11
, c
12
y
44
+ 57y
43
+ ··· − 2y + 1
c
9
y
44
+ 5y
43
+ ··· − 662y + 49
8
