12a
0379
(K12a
0379
)
A knot diagram
1
Linearized knot diagam
3 6 9 10 2 1 12 11 4 5 8 7
Solving Sequence
5,11
10 4 9 3 8 12 7 1 2 6
c
10
c
4
c
9
c
3
c
8
c
11
c
7
c
12
c
1
c
6
c
2
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
− u
34
+ ··· + 3u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 35 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
35
− u
34
+ · · · + 3u
2
− 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
0
a
10
=
1
u
2
a
4
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
−u
4
+ 2u
2
a
3
=
u
3
− 2u
u
5
− 3u
3
+ u
a
8
=
u
4
− 3u
2
+ 1
−u
4
+ 2u
2
a
12
=
u
8
− 5u
6
+ 7u
4
− 2u
2
+ 1
−u
8
+ 4u
6
− 4u
4
a
7
=
u
12
− 7u
10
+ 17u
8
− 16u
6
+ 6u
4
− 5u
2
+ 1
−u
12
+ 6u
10
− 12u
8
+ 8u
6
− u
4
+ 2u
2
a
1
=
u
16
− 9u
14
+ 31u
12
− 50u
10
+ 39u
8
− 22u
6
+ 18u
4
− 4u
2
+ 1
−u
16
+ 8u
14
− 24u
12
+ 32u
10
− 18u
8
+ 8u
6
− 8u
4
a
2
=
u
24
− 13u
22
+ ··· − 6u
2
+ 1
u
26
− 14u
24
+ ··· − 18u
4
+ u
2
a
6
=
u
20
− 11u
18
+ ··· − 7u
2
+ 1
−u
20
+ 10u
18
+ ··· − u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
32
+ 68u
30
+ 4u
29
− 508u
28
− 64u
27
+ 2184u
26
+ 444u
25
−
5960u
24
− 1744u
23
+ 10836u
22
+ 4264u
21
− 13756u
20
− 6804u
19
+ 13416u
18
+ 7508u
17
−
11532u
16
− 6528u
15
+ 8700u
14
+ 5128u
13
− 5028u
12
− 3288u
11
+ 2552u
10
+ 1528u
9
−
1288u
8
− 704u
7
+ 328u
6
+ 240u
5
− 120u
4
− 44u
3
+ 16u
2
+ 20u + 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 21u
34
+ ··· + 6u + 1
c
2
, c
5
u
35
+ u
34
+ ··· + 3u
2
− 1
c
3
, c
4
, c
9
c
10
u
35
− u
34
+ ··· + 3u
2
− 1
c
6
, c
7
, c
8
c
11
, c
12
u
35
+ 3u
34
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
− 13y
34
+ ··· + 10y −1
c
2
, c
5
y
35
− 21y
34
+ ··· + 6y −1
c
3
, c
4
, c
9
c
10
y
35
− 37y
34
+ ··· + 6y −1
c
6
, c
7
, c
8
c
11
, c
12
y
35
+ 47y
34
+ ··· + 90y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.525071 + 0.695031I
−15.9587 − 7.3230I −0.50203 + 5.74720I
u = −0.525071 − 0.695031I
−15.9587 + 7.3230I −0.50203 − 5.74720I
u = −0.503644 + 0.700836I
−16.0231 + 2.6486I −0.693389 − 0.151455I
u = −0.503644 − 0.700836I
−16.0231 − 2.6486I −0.693389 + 0.151455I
u = 0.512719 + 0.691106I
−12.06160 + 2.31682I 2.54987 − 2.83092I
u = 0.512719 − 0.691106I
−12.06160 − 2.31682I 2.54987 + 2.83092I
u = 0.522839 + 0.541402I
−5.47274 + 5.77937I 0.47146 − 7.85052I
u = 0.522839 − 0.541402I
−5.47274 − 5.77937I 0.47146 + 7.85052I
u = 0.408454 + 0.569281I
−5.82031 − 1.98611I −1.101715 + 0.333068I
u = 0.408454 − 0.569281I
−5.82031 + 1.98611I −1.101715 − 0.333068I
u = −0.459588 + 0.502405I
−2.40665 − 1.73767I 3.44724 + 4.36626I
u = −0.459588 − 0.502405I
−2.40665 + 1.73767I 3.44724 − 4.36626I
u = −0.549002 + 0.276756I
−0.34953 − 3.08643I 6.48319 + 9.61199I
u = −0.549002 − 0.276756I
−0.34953 + 3.08643I 6.48319 − 9.61199I
u = 1.43209
3.32584 2.08830
u = −1.46088 + 0.14870I
0.217823 − 0.520687I 0
u = −1.46088 − 0.14870I
0.217823 + 0.520687I 0
u = 0.495921 + 0.057416I
0.779355 + 0.040720I 13.22367 − 0.76931I
u = 0.495921 − 0.057416I
0.779355 − 0.040720I 13.22367 + 0.76931I
u = 1.49978 + 0.13102I
4.04258 + 3.93448I 6.00000 + 0.I
u = 1.49978 − 0.13102I
4.04258 − 3.93448I 6.00000 + 0.I
u = −1.51928 + 0.02326I
7.54181 − 0.38720I 12.42967 + 0.I
u = −1.51928 − 0.02326I
7.54181 + 0.38720I 12.42967 + 0.I
u = −1.51926 + 0.15290I
1.26876 − 8.24991I 0. + 7.12333I
u = −1.51926 − 0.15290I
1.26876 + 8.24991I 0. − 7.12333I
u = 1.52643 + 0.06311I
6.56659 + 4.22789I 0. − 6.71857I
u = 1.52643 − 0.06311I
6.56659 − 4.22789I 0. + 6.71857I
u = 1.50999 + 0.23245I
−9.45605 + 0.74325I 0
u = 1.50999 − 0.23245I
−9.45605 − 0.74325I 0
u = −1.51605 + 0.22648I
−5.43016 − 5.65254I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.51605 − 0.22648I
−5.43016 + 5.65254I 0
u = 1.52333 + 0.22907I
−9.25340 + 10.69110I 0
u = 1.52333 − 0.22907I
−9.25340 − 10.69110I 0
u = −0.162727 + 0.381338I
−1.53270 + 0.77833I −1.99796 − 0.53208I
u = −0.162727 − 0.381338I
−1.53270 − 0.77833I −1.99796 + 0.53208I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
35
+ 21u
34
+ ··· + 6u + 1
c
2
, c
5
u
35
+ u
34
+ ··· + 3u
2
− 1
c
3
, c
4
, c
9
c
10
u
35
− u
34
+ ··· + 3u
2
− 1
c
6
, c
7
, c
8
c
11
, c
12
u
35
+ 3u
34
+ ··· + 12u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
35
− 13y
34
+ ··· + 10y −1
c
2
, c
5
y
35
− 21y
34
+ ··· + 6y −1
c
3
, c
4
, c
9
c
10
y
35
− 37y
34
+ ··· + 6y −1
c
6
, c
7
, c
8
c
11
, c
12
y
35
+ 47y
34
+ ··· + 90y −1
8
