12a
0733
(K12a
0733
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 12 11 1 2 4 7 6 5
Solving Sequence
2,9
8 3 4 10 5 1 7 11 6 12
c
8
c
2
c
3
c
9
c
4
c
1
c
7
c
10
c
6
c
12
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
− u
35
+ ··· + u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 36 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
36
− u
35
+ · · · + u
2
− 1i
(i) Arc colorings
a
2
=
0
u
a
9
=
1
0
a
8
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
10
=
−u
6
− u
4
+ 1
u
6
+ 2u
4
+ u
2
a
5
=
u
9
+ 2u
7
+ u
5
− 2u
3
− u
−u
9
− 3u
7
− 3u
5
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
7
=
−u
6
− u
4
+ 1
−u
8
− 2u
6
− 2u
4
a
11
=
−u
20
− 5u
18
− 11u
16
− 10u
14
+ 2u
12
+ 13u
10
+ 9u
8
− 2u
6
− 5u
4
− u
2
+ 1
−u
22
− 6u
20
− 17u
18
− 26u
16
− 20u
14
+ 13u
10
+ 10u
8
+ 3u
6
+ 2u
4
+ u
2
a
6
=
−u
34
− 9u
32
+ ··· − u
2
+ 1
−u
35
+ u
34
+ ··· + u
2
− 1
a
12
=
u
23
+ 6u
21
+ ··· + 6u
5
+ 2u
3
−u
23
− 7u
21
+ ··· − 3u
5
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes =
4u
35
−4u
34
+40u
33
−36u
32
+188u
31
−156u
30
+524u
29
−408u
28
+908u
27
−688u
26
+880u
25
−
720u
24
+124u
23
−340u
22
−868u
21
+236u
20
−1120u
19
+600u
18
−444u
17
+592u
16
+280u
15
+
332u
14
+360u
13
+20u
12
+84u
11
−172u
10
−60u
9
−156u
8
−24u
7
−52u
6
+16u
5
+4u
4
+20u
3
−10
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
36
+ 21u
35
+ ··· − 2u + 1
c
2
, c
8
u
36
− u
35
+ ··· + u
2
− 1
c
3
, c
4
, c
7
c
9
u
36
+ u
35
+ ··· − 6u − 5
c
5
, c
6
, c
10
c
11
, c
12
u
36
+ u
35
+ ··· − 4u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
− 11y
35
+ ··· − 30y + 1
c
2
, c
8
y
36
+ 21y
35
+ ··· − 2y + 1
c
3
, c
4
, c
7
c
9
y
36
− 43y
35
+ ··· − 166y + 25
c
5
, c
6
, c
10
c
11
, c
12
y
36
+ 45y
35
+ ··· − 2y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.282875 + 1.062700I
−1.68586 + 0.53085I −10.75192 + 0.82754I
u = 0.282875 − 1.062700I
−1.68586 − 0.53085I −10.75192 − 0.82754I
u = 0.891515 + 0.048885I
2.90046 − 5.74969I −5.68594 + 2.68814I
u = 0.891515 − 0.048885I
2.90046 + 5.74969I −5.68594 − 2.68814I
u = 0.890163
−8.32989 −11.7240
u = −0.888293 + 0.024901I
−5.76957 + 3.65801I −7.50646 − 3.88825I
u = −0.888293 − 0.024901I
−5.76957 − 3.65801I −7.50646 + 3.88825I
u = 0.498093 + 0.734304I
12.00850 + 2.05861I −1.12178 − 3.75231I
u = 0.498093 − 0.734304I
12.00850 − 2.05861I −1.12178 + 3.75231I
u = −0.375034 + 1.064500I
−3.45066 − 3.25878I −14.9165 + 5.6693I
u = −0.375034 − 1.064500I
−3.45066 + 3.25878I −14.9165 − 5.6693I
u = −0.210685 + 1.118540I
6.42157 + 0.49356I −9.63907 + 0.32963I
u = −0.210685 − 1.118540I
6.42157 − 0.49356I −9.63907 − 0.32963I
u = 0.444121 + 1.051070I
−0.51949 + 5.89850I −7.49197 − 8.58873I
u = 0.444121 − 1.051070I
−0.51949 − 5.89850I −7.49197 + 8.58873I
u = −0.490379 + 1.047610I
8.45002 − 7.20201I −5.83680 + 6.79259I
u = −0.490379 − 1.047610I
8.45002 + 7.20201I −5.83680 − 6.79259I
u = −0.405042 + 0.735070I
2.86862 − 1.80232I −0.91103 + 4.87236I
u = −0.405042 − 0.735070I
2.86862 + 1.80232I −0.91103 − 4.87236I
u = 0.149662 + 0.790037I
−0.605604 + 0.932135I −9.94128 − 6.89796I
u = 0.149662 − 0.790037I
−0.605604 − 0.932135I −9.94128 + 6.89796I
u = −0.622331 + 0.303894I
10.53390 + 2.88470I −2.43200 − 2.46197I
u = −0.622331 − 0.303894I
10.53390 − 2.88470I −2.43200 + 2.46197I
u = 0.439815 + 1.266880I
−1.13178 − 1.06458I −9.26896 − 0.31777I
u = 0.439815 − 1.266880I
−1.13178 + 1.06458I −9.26896 + 0.31777I
u = −0.454338 + 1.261880I
−9.69160 − 1.09254I −10.99035 − 0.80742I
u = −0.454338 − 1.261880I
−9.69160 + 1.09254I −10.99035 + 0.80742I
u = −0.481098 + 1.254150I
−9.49472 − 8.55149I −10.56405 + 6.84602I
u = −0.481098 − 1.254150I
−9.49472 + 8.55149I −10.56405 − 6.84602I
u = 0.468539 + 1.259380I
−12.15810 + 4.83267I −14.8489 − 3.1819I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.468539 − 1.259380I
−12.15810 − 4.83267I −14.8489 + 3.1819I
u = 0.493269 + 1.250710I
−0.73827 + 10.71510I −8.69637 − 5.67492I
u = 0.493269 − 1.250710I
−0.73827 − 10.71510I −8.69637 + 5.67492I
u = 0.539657 + 0.237187I
1.69494 − 1.97215I −3.23018 + 4.60396I
u = 0.539657 − 0.237187I
1.69494 + 1.97215I −3.23018 − 4.60396I
u = −0.450859
−0.804226 −12.6090
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
36
+ 21u
35
+ ··· − 2u + 1
c
2
, c
8
u
36
− u
35
+ ··· + u
2
− 1
c
3
, c
4
, c
7
c
9
u
36
+ u
35
+ ··· − 6u − 5
c
5
, c
6
, c
10
c
11
, c
12
u
36
+ u
35
+ ··· − 4u − 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
36
− 11y
35
+ ··· − 30y + 1
c
2
, c
8
y
36
+ 21y
35
+ ··· − 2y + 1
c
3
, c
4
, c
7
c
9
y
36
− 43y
35
+ ··· − 166y + 25
c
5
, c
6
, c
10
c
11
, c
12
y
36
+ 45y
35
+ ··· − 2y + 1
8
