12a
0791
(K12a
0791
)
A knot diagram
1
Linearized knot diagam
3 8 11 12 10 9 2 7 6 1 4 5
Solving Sequence
2,7
8 3 9 1 6 10 11 4 5 12
c
7
c
2
c
8
c
1
c
6
c
9
c
10
c
3
c
5
c
12
c
4
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
31
− u
30
+ ··· − 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 31 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
31
− u
30
+ · · · − 2u
2
+ 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
8
=
1
u
2
a
3
=
−u
−u
3
+ u
a
9
=
−u
2
+ 1
u
2
a
1
=
u
3
u
5
− u
3
+ u
a
6
=
u
4
− u
2
+ 1
−u
4
a
10
=
−u
6
+ u
4
− 2u
2
+ 1
u
6
+ u
2
a
11
=
u
14
− u
12
+ 4u
10
− 3u
8
+ 2u
6
− 2u
2
+ 1
u
16
− 2u
14
+ 6u
12
− 8u
10
+ 10u
8
− 6u
6
+ 4u
4
a
4
=
u
27
− 2u
25
+ ··· + 12u
5
− 5u
3
u
29
− 3u
27
+ ··· − u
3
+ u
a
5
=
u
8
− u
6
+ 3u
4
− 2u
2
+ 1
−u
8
− 2u
4
a
12
=
−u
21
+ 2u
19
+ ··· + 6u
3
− u
u
21
− u
19
+ 7u
17
− 6u
15
+ 16u
13
− 11u
11
+ 13u
9
− 6u
7
+ 3u
5
− u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
30
− 12u
28
+ 4u
27
+ 60u
26
− 8u
25
− 136u
24
+ 44u
23
+ 344u
22
− 72u
21
− 592u
20
+
184u
19
+ 960u
18
−240u
17
−1232u
16
+ 372u
15
+ 1356u
14
−376u
13
−1232u
12
+ 388u
11
+
896u
10
− 300u
9
− 504u
8
+ 204u
7
+ 204u
6
− 112u
5
− 40u
4
+ 40u
3
− 12u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
8
, c
9
u
31
+ 5u
30
+ ··· + 4u + 1
c
2
, c
7
u
31
+ u
30
+ ··· + 2u
2
− 1
c
3
, c
4
, c
11
c
12
u
31
− u
30
+ ··· − 2u − 1
c
10
u
31
+ 11u
30
+ ··· + 904u + 329
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
8
, c
9
y
31
+ 43y
30
+ ··· − 32y −1
c
2
, c
7
y
31
− 5y
30
+ ··· + 4y −1
c
3
, c
4
, c
11
c
12
y
31
− 37y
30
+ ··· + 4y −1
c
10
y
31
− 25y
30
+ ··· − 9232y −108241
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.791350 + 0.665692I
2.77292 + 2.49031I 0.70638 − 3.36912I
u = −0.791350 − 0.665692I
2.77292 − 2.49031I 0.70638 + 3.36912I
u = 0.734968 + 0.730997I
5.22440 + 0.49349I 6.40243 − 1.42889I
u = 0.734968 − 0.730997I
5.22440 − 0.49349I 6.40243 + 1.42889I
u = 0.862163 + 0.360448I
6.88853 − 4.31158I 1.70139 + 6.75618I
u = 0.862163 − 0.360448I
6.88853 + 4.31158I 1.70139 − 6.75618I
u = −0.720478 + 0.790919I
13.50980 − 2.17197I 7.93260 + 0.27794I
u = −0.720478 − 0.790919I
13.50980 + 2.17197I 7.93260 − 0.27794I
u = 0.861511 + 0.679212I
4.80823 − 5.72178I 4.77645 + 8.09118I
u = 0.861511 − 0.679212I
4.80823 + 5.72178I 4.77645 − 8.09118I
u = −0.906594 + 0.698694I
12.8848 + 7.6593I 6.39810 − 6.24102I
u = −0.906594 − 0.698694I
12.8848 − 7.6593I 6.39810 + 6.24102I
u = −0.853762
5.04240 −2.72190
u = −0.778513 + 0.296852I
−0.36181 + 2.94393I −1.66820 − 9.97564I
u = −0.778513 − 0.296852I
−0.36181 − 2.94393I −1.66820 + 9.97564I
u = 0.704905 + 0.147061I
−1.148080 − 0.379484I −7.32750 + 0.54568I
u = 0.704905 − 0.147061I
−1.148080 + 0.379484I −7.32750 − 0.54568I
u = 0.946436 + 0.923716I
12.91130 − 3.39712I 2.13967 + 2.24704I
u = 0.946436 − 0.923716I
12.91130 + 3.39712I 2.13967 − 2.24704I
u = −0.937373 + 0.934900I
15.4949 − 0.4280I 6.07033 + 1.46342I
u = −0.937373 − 0.934900I
15.4949 + 0.4280I 6.07033 − 1.46342I
u = 0.933748 + 0.947021I
−15.3696 + 2.7248I 7.83122 − 0.36082I
u = 0.933748 − 0.947021I
−15.3696 − 2.7248I 7.83122 + 0.36082I
u = −0.960199 + 0.921928I
15.4193 + 7.2526I 5.88050 − 5.99908I
u = −0.960199 − 0.921928I
15.4193 − 7.2526I 5.88050 + 5.99908I
u = 0.971666 + 0.924478I
−15.4964 − 9.5974I 7.61372 + 4.81531I
u = 0.971666 − 0.924478I
−15.4964 + 9.5974I 7.61372 − 4.81531I
u = 0.286578 + 0.593109I
8.74676 + 0.94916I 8.06495 − 0.10527I
u = 0.286578 − 0.593109I
8.74676 − 0.94916I 8.06495 + 0.10527I
u = −0.280590 + 0.401102I
1.103510 − 0.348173I 7.83889 + 1.08782I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.280590 − 0.401102I
1.103510 + 0.348173I 7.83889 − 1.08782I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
, c
6
c
8
, c
9
u
31
+ 5u
30
+ ··· + 4u + 1
c
2
, c
7
u
31
+ u
30
+ ··· + 2u
2
− 1
c
3
, c
4
, c
11
c
12
u
31
− u
30
+ ··· − 2u − 1
c
10
u
31
+ 11u
30
+ ··· + 904u + 329
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
5
, c
6
c
8
, c
9
y
31
+ 43y
30
+ ··· − 32y −1
c
2
, c
7
y
31
− 5y
30
+ ··· + 4y −1
c
3
, c
4
, c
11
c
12
y
31
− 37y
30
+ ··· + 4y −1
c
10
y
31
− 25y
30
+ ··· − 9232y −108241
8
