12a
0763
(K12a
0763
)
A knot diagram
1
Linearized knot diagam
3 8 10 11 12 1 9 2 7 4 6 5
Solving Sequence
6,11
12 5 1 7 4 10 3 2 9 8
c
11
c
5
c
12
c
6
c
4
c
10
c
3
c
1
c
9
c
8
c
2
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= hu
48
+ u
47
+ ··· − 4u − 1i
* 1 irreducible components of dim
C
= 0, with total 48 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
48
+ u
47
+ · · · − 4u − 1i
(i) Arc colorings
a
6
=
0
u
a
11
=
1
0
a
12
=
1
u
2
a
5
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
4
+ 2u
2
a
7
=
−u
5
− 2u
3
− u
−u
7
− 3u
5
− 2u
3
+ u
a
4
=
u
3
+ 2u
u
3
+ u
a
10
=
−u
6
− 3u
4
− 2u
2
+ 1
−u
6
− 2u
4
− u
2
a
3
=
−u
9
− 4u
7
− 5u
5
+ 3u
−u
9
− 3u
7
− 3u
5
+ u
a
2
=
−u
22
− 9u
20
+ ··· + 4u
2
+ 1
−u
22
− 8u
20
+ ··· − 4u
4
+ 3u
2
a
9
=
u
18
+ 7u
16
+ 20u
14
+ 27u
12
+ 11u
10
− 13u
8
− 16u
6
− 6u
4
− u
2
+ 1
u
20
+ 8u
18
+ 26u
16
+ 40u
14
+ 19u
12
− 24u
10
− 30u
8
− 2u
6
+ 5u
4
− 2u
2
a
8
=
−u
31
− 12u
29
+ ··· + 4u
3
− 2u
−u
33
− 13u
31
+ ··· − 18u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
47
+ 4u
46
+ ··· − 40u − 18
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
48
+ 13u
47
+ ··· − 20u
2
+ 1
c
2
, c
8
u
48
− u
47
+ ··· − 4u
3
− 1
c
3
, c
4
, c
6
c
10
u
48
− u
47
+ ··· − 8u − 1
c
5
, c
11
, c
12
u
48
+ u
47
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
48
+ 45y
47
+ ··· − 40y + 1
c
2
, c
8
y
48
+ 13y
47
+ ··· − 20y
2
+ 1
c
3
, c
4
, c
6
c
10
y
48
− 55y
47
+ ··· + 16y + 1
c
5
, c
11
, c
12
y
48
+ 37y
47
+ ··· + 40y
2
+ 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.902489 + 0.013088I
−11.82170 + 3.20969I −16.0349 − 3.5979I
u = −0.902489 − 0.013088I
−11.82170 − 3.20969I −16.0349 + 3.5979I
u = −0.896963 + 0.039791I
−5.15426 + 8.27036I −11.18543 − 5.30830I
u = −0.896963 − 0.039791I
−5.15426 − 8.27036I −11.18543 + 5.30830I
u = 0.106016 + 0.890046I
4.71074 + 2.89935I −6.28054 − 2.45278I
u = 0.106016 − 0.890046I
4.71074 − 2.89935I −6.28054 + 2.45278I
u = 0.888507 + 0.037659I
−4.44635 − 2.20706I −10.05242 + 0.41932I
u = 0.888507 − 0.037659I
−4.44635 + 2.20706I −10.05242 − 0.41932I
u = 0.888170
−8.51708 −10.0950
u = 0.208888 + 1.136380I
−0.286683 − 0.633763I −12.86737 + 0.I
u = 0.208888 − 1.136380I
−0.286683 + 0.633763I −12.86737 + 0.I
u = −0.055446 + 1.242230I
3.87211 + 1.66687I −8.00000 + 0.I
u = −0.055446 − 1.242230I
3.87211 − 1.66687I −8.00000 + 0.I
u = −0.172886 + 1.232050I
2.76935 + 2.33914I 0
u = −0.172886 − 1.232050I
2.76935 − 2.33914I 0
u = 0.237255 + 1.249610I
0.73776 − 5.42844I 0
u = 0.237255 − 1.249610I
0.73776 + 5.42844I 0
u = 0.429212 + 1.245610I
−0.71161 − 2.50358I 0
u = 0.429212 − 1.245610I
−0.71161 + 2.50358I 0
u = −0.438389 + 1.246210I
−1.42518 − 3.50108I 0
u = −0.438389 − 1.246210I
−1.42518 + 3.50108I 0
u = −0.100503 + 0.671222I
4.73942 + 2.93301I −5.08982 − 3.47848I
u = −0.100503 − 0.671222I
4.73942 − 2.93301I −5.08982 + 3.47848I
u = −0.206929 + 1.315630I
7.95747 + 2.83644I 0
u = −0.206929 − 1.315630I
7.95747 − 2.83644I 0
u = −0.006952 + 1.332280I
10.37430 + 3.07654I 0
u = −0.006952 − 1.332280I
10.37430 − 3.07654I 0
u = 0.220070 + 1.316800I
7.61366 − 8.95984I 0
u = 0.220070 − 1.316800I
7.61366 + 8.95984I 0
u = −0.435687 + 1.271790I
−7.91815 + 1.57073I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.435687 − 1.271790I
−7.91815 − 1.57073I 0
u = 0.420722 + 1.279510I
−4.54259 − 4.68294I 0
u = 0.420722 − 1.279510I
−4.54259 + 4.68294I 0
u = 0.601719 + 0.218980I
2.84333 − 6.05138I −9.37196 + 7.32890I
u = 0.601719 − 0.218980I
2.84333 + 6.05138I −9.37196 − 7.32890I
u = −0.429025 + 1.292620I
−7.75996 + 7.96966I 0
u = −0.429025 − 1.292620I
−7.75996 − 7.96966I 0
u = 0.413817 + 1.307110I
−0.25199 − 6.87039I 0
u = 0.413817 − 1.307110I
−0.25199 + 6.87039I 0
u = −0.418825 + 1.310300I
−0.94233 + 12.97910I 0
u = −0.418825 − 1.310300I
−0.94233 − 12.97910I 0
u = −0.571774 + 0.231822I
3.16611 + 0.08411I −8.52562 − 2.22903I
u = −0.571774 − 0.231822I
3.16611 − 0.08411I −8.52562 + 2.22903I
u = 0.606213 + 0.082718I
−3.31656 − 2.39276I −16.3721 + 5.8805I
u = 0.606213 − 0.082718I
−3.31656 + 2.39276I −16.3721 − 5.8805I
u = −0.476571
−0.944117 −10.2930
u = −0.202351 + 0.264057I
−0.411106 + 0.845422I −8.88692 − 7.79987I
u = −0.202351 − 0.264057I
−0.411106 − 0.845422I −8.88692 + 7.79987I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
9
u
48
+ 13u
47
+ ··· − 20u
2
+ 1
c
2
, c
8
u
48
− u
47
+ ··· − 4u
3
− 1
c
3
, c
4
, c
6
c
10
u
48
− u
47
+ ··· − 8u − 1
c
5
, c
11
, c
12
u
48
+ u
47
+ ··· − 4u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
9
y
48
+ 45y
47
+ ··· − 40y + 1
c
2
, c
8
y
48
+ 13y
47
+ ··· − 20y
2
+ 1
c
3
, c
4
, c
6
c
10
y
48
− 55y
47
+ ··· + 16y + 1
c
5
, c
11
, c
12
y
48
+ 37y
47
+ ··· + 40y
2
+ 1
8
