12a
0038
(K12a
0038
)
A knot diagram
1
Linearized knot diagam
3 5 6 10 2 1 12 11 4 9 8 7
Solving Sequence
4,9
10 5 11 8 12 7 1 6 3 2
c
9
c
4
c
10
c
8
c
11
c
7
c
12
c
6
c
3
c
2
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
35
− u
34
+ ··· + 2u − 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
+ · · · + 2u − 1i
(i) Arc colorings
a
4
=
0
u
a
9
=
1
0
a
10
=
1
u
2
a
5
=
−u
−u
3
+ u
a
11
=
−u
2
+ 1
u
2
a
8
=
u
4
− u
2
+ 1
−u
4
a
12
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
7
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
8
− 2u
4
a
1
=
−u
10
+ u
8
− 4u
6
+ 3u
4
− 3u
2
+ 1
u
10
+ 3u
6
+ u
2
a
6
=
u
12
− u
10
+ 5u
8
− 4u
6
+ 6u
4
− 3u
2
+ 1
−u
12
− 4u
8
− 3u
4
a
3
=
u
25
− 2u
23
+ ··· − 6u
3
+ u
−u
25
+ u
23
+ ··· − 3u
5
+ u
a
2
=
u
29
− 2u
27
+ ··· − 8u
3
+ u
u
31
− 3u
29
+ ··· + 2u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
34
+ 12u
32
− 4u
31
− 68u
30
+ 8u
29
+ 160u
28
− 52u
27
−
460u
26
+ 88u
25
+ 852u
24
− 268u
23
− 1596u
22
+ 376u
21
+ 2304u
20
− 704u
19
− 3032u
18
+
800u
17
+ 3316u
16
− 1020u
15
− 3092u
14
+ 920u
13
+ 2408u
12
− 836u
11
− 1512u
10
+
588u
9
+ 728u
8
− 372u
7
− 256u
6
+ 192u
5
+ 48u
4
− 64u
3
+ 12u − 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
35
+ 15u
34
+ ··· + 2u − 1
c
2
, c
5
u
35
+ u
34
+ ··· + 4u + 1
c
3
u
35
− u
34
+ ··· − 8u + 1
c
4
, c
9
u
35
+ u
34
+ ··· + 2u + 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
35
+ 5u
34
+ ··· + 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 11y
34
+ ··· + 50y −1
c
2
, c
5
y
35
+ 15y
34
+ ··· + 2y −1
c
3
y
35
+ 7y
34
+ ··· − 30y −1
c
4
, c
9
y
35
− 5y
34
+ ··· + 2y −1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
35
+ 51y
34
+ ··· + 10y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.827985 + 0.442924I
−0.41301 − 6.75076I −7.52201 + 10.31083I
u = 0.827985 − 0.442924I
−0.41301 + 6.75076I −7.52201 − 10.31083I
u = −0.819369 + 0.722392I
3.00560 + 2.68433I −6.38966 − 3.26103I
u = −0.819369 − 0.722392I
3.00560 − 2.68433I −6.38966 + 3.26103I
u = −0.748025 + 0.473052I
1.37372 + 2.37460I −2.95509 − 5.64025I
u = −0.748025 − 0.473052I
1.37372 − 2.37460I −2.95509 + 5.64025I
u = −0.781691 + 0.815109I
6.78620 − 3.64652I −2.24620 + 2.51117I
u = −0.781691 − 0.815109I
6.78620 + 3.64652I −2.24620 − 2.51117I
u = 0.812484 + 0.804258I
8.37825 − 1.52833I 0.15922 + 2.57141I
u = 0.812484 − 0.804258I
8.37825 + 1.52833I 0.15922 − 2.57141I
u = 0.876029 + 0.769070I
8.16101 − 4.25998I −0.39518 + 3.37976I
u = 0.876029 − 0.769070I
8.16101 + 4.25998I −0.39518 − 3.37976I
u = −0.899548 + 0.751693I
6.38574 + 9.40965I −3.35814 − 8.21027I
u = −0.899548 − 0.751693I
6.38574 − 9.40965I −3.35814 + 8.21027I
u = 0.764387 + 0.291862I
−2.05998 − 0.57416I −12.32788 + 4.08784I
u = 0.764387 − 0.291862I
−2.05998 + 0.57416I −12.32788 − 4.08784I
u = −0.796033 + 0.081424I
−3.02472 + 3.09558I −15.0272 − 5.6835I
u = −0.796033 − 0.081424I
−3.02472 − 3.09558I −15.0272 + 5.6835I
u = −0.569720 + 0.552671I
1.96860 + 1.39447I −0.18894 − 3.96327I
u = −0.569720 − 0.552671I
1.96860 − 1.39447I −0.18894 + 3.96327I
u = 0.446314 + 0.583151I
0.82978 + 3.00776I −2.26446 − 2.93479I
u = 0.446314 − 0.583151I
0.82978 − 3.00776I −2.26446 + 2.93479I
u = 0.954730 + 0.937736I
13.9541 − 3.4440I −5.66125 + 2.21477I
u = 0.954730 − 0.937736I
13.9541 + 3.4440I −5.66125 − 2.21477I
u = 0.947637 + 0.954402I
18.2191 + 3.9502I −2.24732 − 2.32186I
u = 0.947637 − 0.954402I
18.2191 − 3.9502I −2.24732 + 2.32186I
u = −0.953750 + 0.951945I
−19.4865 + 1.6085I 0. − 2.11449I
u = −0.953750 − 0.951945I
−19.4865 − 1.6085I 0. + 2.11449I
u = −0.967443 + 0.943280I
−19.5330 + 5.3455I 0. − 2.28570I
u = −0.967443 − 0.943280I
−19.5330 − 5.3455I 0. + 2.28570I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.972104 + 0.939042I
18.1363 − 10.8977I −2.41433 + 6.69442I
u = 0.972104 − 0.939042I
18.1363 + 10.8977I −2.41433 − 6.69442I
u = 0.628123
−0.861815 −11.7130
u = 0.119848 + 0.450363I
−0.30459 − 1.79271I −2.31417 + 3.71994I
u = 0.119848 − 0.450363I
−0.30459 + 1.79271I −2.31417 − 3.71994I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
35
+ 15u
34
+ ··· + 2u − 1
c
2
, c
5
u
35
+ u
34
+ ··· + 4u + 1
c
3
u
35
− u
34
+ ··· − 8u + 1
c
4
, c
9
u
35
+ u
34
+ ··· + 2u + 1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
u
35
+ 5u
34
+ ··· + 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 11y
34
+ ··· + 50y −1
c
2
, c
5
y
35
+ 15y
34
+ ··· + 2y −1
c
3
y
35
+ 7y
34
+ ··· − 30y −1
c
4
, c
9
y
35
− 5y
34
+ ··· + 2y −1
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y
35
+ 51y
34
+ ··· + 10y −1
8
