12a
0644
(K12a
0644
)
A knot diagram
1
Linearized knot diagam
3 7 10 11 8 2 6 1 12 5 4 9
Solving Sequence
4,12
11 5 10 3 9 1 2 8 6 7
c
11
c
4
c
10
c
3
c
9
c
12
c
1
c
8
c
5
c
7
c
2
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
56
− u
55
+ ··· − 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 56 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
56
− u
55
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
4
=
0
u
a
12
=
1
0
a
11
=
1
u
2
a
5
=
u
u
3
+ u
a
10
=
u
2
+ 1
u
4
+ 2u
2
a
3
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
9
=
−u
4
− u
2
+ 1
u
4
+ 2u
2
a
1
=
u
8
+ 3u
6
+ u
4
− 2u
2
+ 1
−u
8
− 4u
6
− 4u
4
a
2
=
u
20
+ 9u
18
+ ··· − 3u
2
+ 1
u
22
+ 10u
20
+ ··· − 10u
4
+ u
2
a
8
=
−u
12
− 5u
10
− 7u
8
+ 2u
4
− 3u
2
+ 1
u
12
+ 6u
10
+ 12u
8
+ 8u
6
+ u
4
+ 2u
2
a
6
=
−u
27
− 12u
25
+ ··· − 12u
5
+ 7u
3
u
27
+ 13u
25
+ ··· − u
3
+ u
a
7
=
−u
42
− 19u
40
+ ··· − 3u
2
+ 1
u
42
+ 20u
40
+ ··· + 6u
4
+ u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
55
+ 4u
54
+ ··· + 16u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
56
+ 15u
55
+ ··· + 4u + 1
c
2
, c
6
u
56
− u
55
+ ··· − 2u
2
+ 1
c
3
u
56
+ u
55
+ ··· + 202u + 65
c
4
, c
10
, c
11
u
56
− u
55
+ ··· − 2u
2
+ 1
c
8
, c
9
, c
12
u
56
+ 7u
55
+ ··· + 16u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
56
+ 53y
55
+ ··· + 28y + 1
c
2
, c
6
y
56
− 15y
55
+ ··· − 4y + 1
c
3
y
56
+ 25y
55
+ ··· + 239476y + 4225
c
4
, c
10
, c
11
y
56
+ 53y
55
+ ··· − 4y + 1
c
8
, c
9
, c
12
y
56
+ 57y
55
+ ··· + 220y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.020209 + 1.098890I
3.96215 + 3.06271I 0
u = 0.020209 − 1.098890I
3.96215 − 3.06271I 0
u = 0.686155 + 0.430676I
−0.39671 + 10.08050I 1.51974 − 8.22030I
u = 0.686155 − 0.430676I
−0.39671 − 10.08050I 1.51974 + 8.22030I
u = 0.665754 + 0.458645I
−7.13653 + 5.26062I −3.80676 − 6.87867I
u = 0.665754 − 0.458645I
−7.13653 − 5.26062I −3.80676 + 6.87867I
u = 0.641196 + 0.486930I
−7.24731 − 0.92940I −4.28257 + 0.58840I
u = 0.641196 − 0.486930I
−7.24731 + 0.92940I −4.28257 − 0.58840I
u = 0.611386 + 0.518123I
−0.73492 − 5.76075I 0.62706 + 2.25622I
u = 0.611386 − 0.518123I
−0.73492 + 5.76075I 0.62706 − 2.25622I
u = −0.678468 + 0.424262I
0.23798 − 3.99471I 2.63926 + 3.39930I
u = −0.678468 − 0.424262I
0.23798 + 3.99471I 2.63926 − 3.39930I
u = −0.599558 + 0.509189I
−0.103709 − 0.253528I 1.72073 + 2.79096I
u = −0.599558 − 0.509189I
−0.103709 + 0.253528I 1.72073 − 2.79096I
u = −0.637539 + 0.456579I
−4.01617 − 2.09773I 2.12497 + 3.25564I
u = −0.637539 − 0.456579I
−4.01617 + 2.09773I 2.12497 − 3.25564I
u = 0.060580 + 1.263240I
−2.45362 + 1.67355I 0
u = 0.060580 − 1.263240I
−2.45362 − 1.67355I 0
u = 0.219710 + 1.317140I
1.91877 + 2.82951I 0
u = 0.219710 − 1.317140I
1.91877 − 2.82951I 0
u = 0.141123 + 1.328370I
−3.43887 + 2.43530I 0
u = 0.141123 − 1.328370I
−3.43887 − 2.43530I 0
u = −0.225186 + 1.328010I
1.60628 − 8.97008I 0
u = −0.225186 − 1.328010I
1.60628 + 8.97008I 0
u = −0.632474 + 0.159551I
6.26180 − 5.86038I 7.46913 + 7.08001I
u = −0.632474 − 0.159551I
6.26180 + 5.86038I 7.46913 − 7.08001I
u = 0.629195 + 0.140167I
6.46439 − 0.24804I 8.24330 − 1.61547I
u = 0.629195 − 0.140167I
6.46439 + 0.24804I 8.24330 + 1.61547I
u = −0.178389 + 1.364910I
−5.35134 − 5.59825I 0
u = −0.178389 − 1.364910I
−5.35134 + 5.59825I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.038003 + 0.620037I
4.15248 + 2.99392I 1.86170 − 2.59085I
u = −0.038003 − 0.620037I
4.15248 − 2.99392I 1.86170 + 2.59085I
u = −0.103732 + 1.385290I
−6.60466 − 0.87132I 0
u = −0.103732 − 1.385290I
−6.60466 + 0.87132I 0
u = −0.014943 + 1.409750I
−1.92248 + 2.81822I 0
u = −0.014943 − 1.409750I
−1.92248 − 2.81822I 0
u = −0.528451 + 0.222220I
−0.34320 − 3.02564I 1.79724 + 9.78051I
u = −0.528451 − 0.222220I
−0.34320 + 3.02564I 1.79724 − 9.78051I
u = −0.24877 + 1.47151I
−5.88112 − 7.38178I 0
u = −0.24877 − 1.47151I
−5.88112 + 7.38178I 0
u = −0.22908 + 1.47605I
−10.25770 − 5.26519I 0
u = −0.22908 − 1.47605I
−10.25770 + 5.26519I 0
u = 0.25090 + 1.47509I
−6.5513 + 13.5024I 0
u = 0.25090 − 1.47509I
−6.5513 − 13.5024I 0
u = −0.20488 + 1.48243I
−6.53709 − 3.16674I 0
u = −0.20488 − 1.48243I
−6.53709 + 3.16674I 0
u = 0.23824 + 1.48207I
−13.4144 + 8.5605I 0
u = 0.23824 − 1.48207I
−13.4144 − 8.5605I 0
u = 0.20573 + 1.48896I
−7.23525 − 2.80491I 0
u = 0.20573 − 1.48896I
−7.23525 + 2.80491I 0
u = 0.22358 + 1.48669I
−13.63780 + 2.21952I 0
u = 0.22358 − 1.48669I
−13.63780 − 2.21952I 0
u = 0.480726 + 0.076119I
0.967130 + 0.223343I 10.08613 − 1.09515I
u = 0.480726 − 0.076119I
0.967130 − 0.223343I 10.08613 + 1.09515I
u = −0.255017 + 0.348068I
−1.263520 + 0.558795I −4.83816 − 0.54247I
u = −0.255017 − 0.348068I
−1.263520 − 0.558795I −4.83816 + 0.54247I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
7
u
56
+ 15u
55
+ ··· + 4u + 1
c
2
, c
6
u
56
− u
55
+ ··· − 2u
2
+ 1
c
3
u
56
+ u
55
+ ··· + 202u + 65
c
4
, c
10
, c
11
u
56
− u
55
+ ··· − 2u
2
+ 1
c
8
, c
9
, c
12
u
56
+ 7u
55
+ ··· + 16u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
7
y
56
+ 53y
55
+ ··· + 28y + 1
c
2
, c
6
y
56
− 15y
55
+ ··· − 4y + 1
c
3
y
56
+ 25y
55
+ ··· + 239476y + 4225
c
4
, c
10
, c
11
y
56
+ 53y
55
+ ··· − 4y + 1
c
8
, c
9
, c
12
y
56
+ 57y
55
+ ··· + 220y + 1
8
