12a
1145
(K12a
1145
)
A knot diagram
1
Linearized knot diagam
4 8 9 11 12 1 10 3 2 7 5 6
Solving Sequence
5,12
6 1 7 11 4 2 10 8 9 3
c
5
c
12
c
6
c
11
c
4
c
1
c
10
c
7
c
9
c
3
c
2
, c
8
Ideals for irreducible components
2
of X
par
I
u
1
= hu
39
− u
38
+ ··· + 2u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 39 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
39
− u
38
+ · · · + 2u
2
+ 1i
(i) Arc colorings
a
5
=
1
0
a
12
=
0
u
a
6
=
1
u
2
a
1
=
−u
−u
3
+ u
a
7
=
−u
2
+ 1
−u
4
+ 2u
2
a
11
=
u
u
a
4
=
−u
2
+ 1
−u
2
a
2
=
u
7
− 4u
5
+ 4u
3
− 2u
u
7
− 3u
5
+ u
a
10
=
−u
7
+ 4u
5
− 4u
3
+ 2u
−u
9
+ 5u
7
− 7u
5
+ 2u
3
+ u
a
8
=
−u
12
+ 7u
10
− 17u
8
+ 18u
6
− 10u
4
+ u
2
+ 1
−u
14
+ 8u
12
− 23u
10
+ 28u
8
− 12u
6
− 2u
4
+ 3u
2
a
9
=
u
23
− 14u
21
+ ··· − 12u
3
+ 2u
u
23
− 13u
21
+ ··· + 6u
3
+ u
a
3
=
−u
33
+ 20u
31
+ ··· + 12u
3
− u
−u
35
+ 21u
33
+ ··· + 3u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
35
+ 88u
33
− 864u
31
+ 4u
30
+ 4992u
29
− 76u
28
− 18852u
27
+ 632u
26
+ 48892u
25
−
3020u
24
− 89008u
23
+ 9160u
22
+ 113828u
21
− 18396u
20
− 99164u
19
+ 24724u
18
+
52076u
17
−21696u
16
−6724u
15
+ 11000u
14
−12088u
13
−1160u
12
+ 9184u
11
−2344u
10
−
2088u
9
+ 1456u
8
− 600u
7
− 192u
6
+ 400u
5
− 112u
4
− 36u
3
+ 32u
2
− 8u − 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
39
− 5u
38
+ ··· + 8u + 1
c
2
, c
3
, c
8
u
39
− u
38
+ ··· + 2u
2
+ 1
c
4
, c
5
, c
6
c
11
, c
12
u
39
− u
38
+ ··· + 2u
2
+ 1
c
9
u
39
+ 3u
38
+ ··· − 64u − 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
39
+ 39y
38
+ ··· + 244y −1
c
2
, c
3
, c
8
y
39
− 37y
38
+ ··· − 4y −1
c
4
, c
5
, c
6
c
11
, c
12
y
39
− 49y
38
+ ··· − 4y −1
c
9
y
39
− 17y
38
+ ··· + 8716y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.873826 + 0.423613I
8.93364 + 8.89763I −1.22130 − 6.83170I
u = −0.873826 − 0.423613I
8.93364 − 8.89763I −1.22130 + 6.83170I
u = −0.922435 + 0.227714I
1.26466 + 5.08177I −5.39049 − 6.97758I
u = −0.922435 − 0.227714I
1.26466 − 5.08177I −5.39049 + 6.97758I
u = 0.857810 + 0.404783I
2.75689 − 5.58258I −4.65603 + 7.15219I
u = 0.857810 − 0.404783I
2.75689 + 5.58258I −4.65603 − 7.15219I
u = −0.947855
−0.837000 −8.85130
u = −0.823526 + 0.404955I
2.96787 + 1.34141I −3.94883 − 0.93763I
u = −0.823526 − 0.404955I
2.96787 − 1.34141I −3.94883 + 0.93763I
u = 0.808094 + 0.433795I
9.33527 + 1.68479I −0.469786 + 0.991725I
u = 0.808094 − 0.433795I
9.33527 − 1.68479I −0.469786 − 0.991725I
u = 0.903789 + 0.146741I
−3.37051 − 2.28297I −12.10756 + 6.07427I
u = 0.903789 − 0.146741I
−3.37051 + 2.28297I −12.10756 − 6.07427I
u = −0.782444
−1.49310 −5.17370
u = 0.031226 + 0.642633I
11.68140 − 5.30733I 3.41369 + 3.29432I
u = 0.031226 − 0.642633I
11.68140 + 5.30733I 3.41369 − 3.29432I
u = −0.016307 + 0.620475I
5.40670 + 2.12189I 0.27996 − 3.35368I
u = −0.016307 − 0.620475I
5.40670 − 2.12189I 0.27996 + 3.35368I
u = 0.511980 + 0.260557I
3.56308 + 0.25388I −1.48569 + 2.19421I
u = 0.511980 − 0.260557I
3.56308 − 0.25388I −1.48569 − 2.19421I
u = 0.169814 + 0.447108I
4.60381 − 2.81067I 2.08372 + 5.83272I
u = 0.169814 − 0.447108I
4.60381 + 2.81067I 2.08372 − 5.83272I
u = −1.62352
−3.95660 0
u = −1.64697 + 0.10692I
0.881433 + 0.320859I 0
u = −1.64697 − 0.10692I
0.881433 − 0.320859I 0
u = 1.65839 + 0.09920I
−5.63467 − 3.21417I 0
u = 1.65839 − 0.09920I
−5.63467 + 3.21417I 0
u = −0.168097 + 0.288654I
−0.147703 + 0.791971I −4.18696 − 8.61927I
u = −0.168097 − 0.288654I
−0.147703 − 0.791971I −4.18696 + 8.61927I
u = 1.67155
−10.2526 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.66956 + 0.10417I
−6.02842 + 7.51655I 0
u = −1.66956 − 0.10417I
−6.02842 − 7.51655I 0
u = 1.67324 + 0.11206I
0.08852 − 10.95580I 0
u = 1.67324 − 0.11206I
0.08852 + 10.95580I 0
u = −1.68686 + 0.03375I
−12.53770 + 2.95947I 0
u = −1.68686 − 0.03375I
−12.53770 − 2.95947I 0
u = 1.68924
−10.1491 0
u = 1.68974 + 0.05249I
−7.95265 − 6.13840I 0
u = 1.68974 − 0.05249I
−7.95265 + 6.13840I 0
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
, c
10
u
39
− 5u
38
+ ··· + 8u + 1
c
2
, c
3
, c
8
u
39
− u
38
+ ··· + 2u
2
+ 1
c
4
, c
5
, c
6
c
11
, c
12
u
39
− u
38
+ ··· + 2u
2
+ 1
c
9
u
39
+ 3u
38
+ ··· − 64u − 11
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
, c
10
y
39
+ 39y
38
+ ··· + 244y −1
c
2
, c
3
, c
8
y
39
− 37y
38
+ ··· − 4y −1
c
4
, c
5
, c
6
c
11
, c
12
y
39
− 49y
38
+ ··· − 4y −1
c
9
y
39
− 17y
38
+ ··· + 8716y −121
8
