12a
0146
(K12a
0146
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 11 12 1 4 6 7 8
Solving Sequence
5,10
6 11 7
3,12
2 1 4 9 8
c
5
c
10
c
6
c
11
c
2
c
1
c
4
c
9
c
8
c
3
, c
7
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= hu
29
− u
28
+ ··· + b + 1, −u
29
+ u
28
+ ··· + a + 6u, u
30
− 2u
29
+ ··· − 36u
3
− 1i
I
u
2
= hb + 1, a, u
3
+ u
2
− 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 33 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
29
−u
28
+· · ·+b+1, −u
29
+u
28
+· · ·+a+6u, u
30
−2u
29
+· · ·−36u
3
−1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
u
−u
3
+ u
a
7
=
−u
2
+ 1
u
4
− 2u
2
a
3
=
u
29
− u
28
+ ··· − 8u
2
− 6u
−u
29
+ u
28
+ ··· − 2u − 1
a
12
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
2
=
−u
14
+ 11u
12
+ ··· − 8u − 1
−u
29
+ u
28
+ ··· − 2u − 1
a
1
=
−u
5
+ 4u
3
− 3u
u
7
− 5u
5
+ 6u
3
− u
a
4
=
−u
29
+ u
28
+ ··· − 6u − 1
−u
29
+ u
28
+ ··· − u − 1
a
9
=
−u
6
+ 5u
4
− 6u
2
+ 1
u
8
− 6u
6
+ 10u
4
− 4u
2
a
8
=
u
4
− 3u
2
+ 1
−u
6
+ 4u
4
− 3u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −3u
29
+ 4u
28
+ 62u
27
− 82u
26
− 561u
25
+ 739u
24
+ 2918u
23
−
3849u
22
− 9630u
21
+ 12801u
20
+ 21006u
19
− 28320u
18
− 30675u
17
+ 42061u
16
+
30044u
15
− 41342u
14
− 20264u
13
+ 26026u
12
+ 10788u
11
− 10222u
10
− 5598u
9
+
2750u
8
+ 2538u
7
− 619u
6
− 778u
5
+ 21u
4
+ 168u
3
+ 52u
2
− 25u + 7
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 12u
29
+ ··· + 97u + 1
c
2
, c
4
u
30
− 4u
29
+ ··· + 13u − 1
c
3
, c
9
u
30
− u
29
+ ··· − 28u + 8
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
u
30
+ 2u
29
+ ··· + 36u
3
− 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
+ 16y
29
+ ··· − 7313y + 1
c
2
, c
4
y
30
− 12y
29
+ ··· − 97y + 1
c
3
, c
9
y
30
− 21y
29
+ ··· − 1104y + 64
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y
30
− 46y
29
+ ··· + 40y
2
+ 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.900406 + 0.238240I
a = −0.659304 − 0.413832I
b = 0.605232 + 0.768254I
5.67065 + 1.25696I 15.5737 − 1.7388I
u = 0.900406 − 0.238240I
a = −0.659304 + 0.413832I
b = 0.605232 − 0.768254I
5.67065 − 1.25696I 15.5737 + 1.7388I
u = 0.814325 + 0.340165I
a = 0.69999 + 1.77618I
b = 1.030380 − 0.688639I
4.42916 + 6.78890I 12.9792 − 7.4265I
u = 0.814325 − 0.340165I
a = 0.69999 − 1.77618I
b = 1.030380 + 0.688639I
4.42916 − 6.78890I 12.9792 + 7.4265I
u = 1.18737
a = 0.321529
b = 0.549343
5.59474 18.0870
u = −0.736617 + 0.129687I
a = 0.52614 + 2.05833I
b = −0.816371 − 0.432342I
0.97252 − 1.81198I 11.73549 + 4.66948I
u = −0.736617 − 0.129687I
a = 0.52614 − 2.05833I
b = −0.816371 + 0.432342I
0.97252 + 1.81198I 11.73549 − 4.66948I
u = 0.654424
a = −0.551259
b = −1.18483
−0.312115 16.4990
u = −1.37237
a = 0.0265788
b = −1.33306
6.56541 13.9410
u = 1.393080 + 0.049142I
a = 0.62086 − 1.75059I
b = −0.838747 + 0.622252I
8.15659 + 2.43505I 13.02410 − 2.90794I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.393080 − 0.049142I
a = 0.62086 + 1.75059I
b = −0.838747 − 0.622252I
8.15659 − 2.43505I 13.02410 + 2.90794I
u = −1.41889 + 0.15784I
a = 0.01368 − 1.73786I
b = 1.114240 + 0.728134I
11.8944 − 8.6308I 14.0718 + 5.7224I
u = −1.41889 − 0.15784I
a = 0.01368 + 1.73786I
b = 1.114240 − 0.728134I
11.8944 + 8.6308I 14.0718 − 5.7224I
u = −0.348859 + 0.441668I
a = 0.229073 − 0.720707I
b = 0.785869 − 0.632862I
1.73384 + 0.97008I 10.55280 + 0.95390I
u = −0.348859 − 0.441668I
a = 0.229073 + 0.720707I
b = 0.785869 + 0.632862I
1.73384 − 0.97008I 10.55280 − 0.95390I
u = −1.45263 + 0.10165I
a = −0.661962 + 1.037750I
b = 0.546899 − 0.940788I
13.61630 − 2.52281I 16.2553 + 0.I
u = −1.45263 − 0.10165I
a = −0.661962 − 1.037750I
b = 0.546899 + 0.940788I
13.61630 + 2.52281I 16.2553 + 0.I
u = −0.206383 + 0.495565I
a = 1.71927 − 0.54217I
b = 0.926515 + 0.641729I
1.28497 − 4.02644I 8.41488 + 6.42284I
u = −0.206383 − 0.495565I
a = 1.71927 + 0.54217I
b = 0.926515 − 0.641729I
1.28497 + 4.02644I 8.41488 − 6.42284I
u = −0.362782
a = 0.804898
b = 0.108164
0.561369 17.6530
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.118463 + 0.232287I
a = −1.31174 − 2.44567I
b = −0.912796 + 0.166074I
−1.60535 + 0.58110I −1.83750 − 2.62782I
u = 0.118463 − 0.232287I
a = −1.31174 + 2.44567I
b = −0.912796 − 0.166074I
−1.60535 − 0.58110I −1.83750 + 2.62782I
u = −1.79109
a = 0.214755
b = 0.718711
16.5830 0
u = 1.83755
a = 0.242340
b = −1.40717
18.6422 0
u = −1.84184 + 0.01166I
a = 0.64542 + 1.69046I
b = −0.867094 − 0.716132I
−19.1326 − 2.7360I 0
u = −1.84184 − 0.01166I
a = 0.64542 − 1.69046I
b = −0.867094 + 0.716132I
−19.1326 + 2.7360I 0
u = 1.84728 + 0.04017I
a = −0.22651 + 1.65159I
b = 1.166510 − 0.750722I
−15.2987 + 9.6434I 0
u = 1.84728 − 0.04017I
a = −0.22651 − 1.65159I
b = 1.166510 + 0.750722I
−15.2987 − 9.6434I 0
u = 1.85511 + 0.02516I
a = −0.624328 − 1.260080I
b = 0.533783 + 1.034720I
−13.33250 + 3.18487I 0
u = 1.85511 − 0.02516I
a = −0.624328 + 1.260080I
b = 0.533783 − 1.034720I
−13.33250 − 3.18487I 0
7
II. I
u
2
= hb + 1, a, u
3
+ u
2
− 2u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
6
=
1
−u
2
a
11
=
u
u
2
− u − 1
a
7
=
−u
2
+ 1
u
2
− u − 1
a
3
=
0
−1
a
12
=
u
2
− 1
−u
2
a
2
=
−1
−1
a
1
=
−1
0
a
4
=
0
−1
a
9
=
0
u
a
8
=
−u
u
(ii) Obstruction class = 1
(iii) Cusp Shapes = u
2
+ u + 5
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
3
c
3
, c
9
u
3
c
4
(u + 1)
3
c
5
, c
6
, c
7
c
8
u
3
+ u
2
− 2u − 1
c
10
, c
11
, c
12
u
3
− u
2
− 2u + 1
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
3
c
3
, c
9
y
3
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
y
3
− 5y
2
+ 6y −1
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.24698
a = 0
b = −1.00000
4.69981 7.80190
u = −0.445042
a = 0
b = −1.00000
−0.939962 4.75300
u = −1.80194
a = 0
b = −1.00000
15.9794 6.44500
11
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
3
)(u
30
+ 12u
29
+ ··· + 97u + 1)
c
2
((u − 1)
3
)(u
30
− 4u
29
+ ··· + 13u − 1)
c
3
, c
9
u
3
(u
30
− u
29
+ ··· − 28u + 8)
c
4
((u + 1)
3
)(u
30
− 4u
29
+ ··· + 13u − 1)
c
5
, c
6
, c
7
c
8
(u
3
+ u
2
− 2u − 1)(u
30
+ 2u
29
+ ··· + 36u
3
− 1)
c
10
, c
11
, c
12
(u
3
− u
2
− 2u + 1)(u
30
+ 2u
29
+ ··· + 36u
3
− 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
3
)(y
30
+ 16y
29
+ ··· − 7313y + 1)
c
2
, c
4
((y −1)
3
)(y
30
− 12y
29
+ ··· − 97y + 1)
c
3
, c
9
y
3
(y
30
− 21y
29
+ ··· − 1104y + 64)
c
5
, c
6
, c
7
c
8
, c
10
, c
11
c
12
(y
3
− 5y
2
+ 6y −1)(y
30
− 46y
29
+ ··· + 40y
2
+ 1)
13
