12a
0512
(K12a
0512
)
A knot diagram
1
Linearized knot diagam
3 7 8 9 11 2 1 4 6 12 5 10
Solving Sequence
5,11
6 12 10 1 9 4 8 3 7 2
c
5
c
11
c
10
c
12
c
9
c
4
c
8
c
3
c
7
c
2
c
1
, c
6
Ideals for irreducible components
2
of X
par
I
u
1
= hu
75
+ u
74
+ ··· + u
2
− 1i
* 1 irreducible components of dim
C
= 0, with total 75 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
75
+ u
74
+ · · · + u
2
− 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
6
=
1
−u
2
a
12
=
u
u
a
10
=
u
3
u
3
+ u
a
1
=
u
5
+ u
u
5
+ u
3
+ u
a
9
=
−u
5
− u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
−u
12
− u
10
− 3u
8
− 2u
6
− 2u
4
− u
2
+ 1
u
14
+ 2u
12
+ 5u
10
+ 6u
8
+ 6u
6
+ 4u
4
+ u
2
a
8
=
u
19
+ 2u
17
+ 6u
15
+ 8u
13
+ 11u
11
+ 10u
9
+ 6u
7
+ 2u
5
− u
3
− 2u
−u
21
− 3u
19
+ ··· + u
3
+ u
a
3
=
u
26
+ 3u
24
+ ··· − 3u
2
+ 1
−u
28
− 4u
26
+ ··· + 7u
4
+ 2u
2
a
7
=
u
31
+ 4u
29
+ ··· − 4u
3
− 2u
u
31
+ 5u
29
+ ··· − 2u
3
+ u
a
2
=
−u
59
− 8u
57
+ ··· + 12u
5
+ 7u
3
u
61
+ 9u
59
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = 4u
73
+ 4u
72
+ ··· + 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
75
+ 33u
74
+ ··· + 2u + 1
c
2
, c
6
u
75
− u
74
+ ··· + u
2
− 1
c
3
, c
4
, c
8
u
75
+ u
74
+ ··· − 110u − 25
c
5
, c
11
u
75
+ u
74
+ ··· + u
2
− 1
c
7
u
75
− 3u
74
+ ··· − 8u + 3
c
9
u
75
− 5u
74
+ ··· + 21044u − 3477
c
10
, c
12
u
75
+ 23u
74
+ ··· + 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
75
+ 19y
74
+ ··· − 10y −1
c
2
, c
6
y
75
− 33y
74
+ ··· + 2y −1
c
3
, c
4
, c
8
y
75
− 81y
74
+ ··· + 28950y −625
c
5
, c
11
y
75
+ 23y
74
+ ··· + 2y −1
c
7
y
75
− 5y
74
+ ··· + 562y −9
c
9
y
75
− 29y
74
+ ··· + 182318326y −12089529
c
10
, c
12
y
75
+ 59y
74
+ ··· + 22y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.682193 + 0.732664I
−0.302285 + 0.979820I 0
u = 0.682193 − 0.732664I
−0.302285 − 0.979820I 0
u = −0.101406 + 0.992248I
−4.21065 − 6.07424I −4.70014 + 8.18701I
u = −0.101406 − 0.992248I
−4.21065 + 6.07424I −4.70014 − 8.18701I
u = −0.044728 + 0.980361I
−5.29212 + 0.73505I −7.97312 + 0.I
u = −0.044728 − 0.980361I
−5.29212 − 0.73505I −7.97312 + 0.I
u = 0.231455 + 1.000170I
−0.58521 + 2.91346I 0
u = 0.231455 − 1.000170I
−0.58521 − 2.91346I 0
u = 0.748094 + 0.708104I
1.49916 − 5.73552I 0
u = 0.748094 − 0.708104I
1.49916 + 5.73552I 0
u = 0.277622 + 1.006300I
3.26637 − 3.71880I 0
u = 0.277622 − 1.006300I
3.26637 + 3.71880I 0
u = 0.099815 + 0.950570I
−2.03163 + 1.90280I −1.00812 − 4.53925I
u = 0.099815 − 0.950570I
−2.03163 − 1.90280I −1.00812 + 4.53925I
u = −0.265572 + 1.012460I
4.96981 − 1.56282I 0
u = −0.265572 − 1.012460I
4.96981 + 1.56282I 0
u = −0.586679 + 0.867149I
−1.77126 + 1.03509I 0
u = −0.586679 − 0.867149I
−1.77126 − 1.03509I 0
u = −0.746947 + 0.736867I
3.53722 + 1.18244I 0
u = −0.746947 − 0.736867I
3.53722 − 1.18244I 0
u = −0.242468 + 1.028110I
4.79959 − 4.64962I 0
u = −0.242468 − 1.028110I
4.79959 + 4.64962I 0
u = 0.234800 + 1.034640I
2.95579 + 9.94979I 0
u = 0.234800 − 1.034640I
2.95579 − 9.94979I 0
u = 0.647448 + 0.875979I
0.73242 + 2.51663I 0
u = 0.647448 − 0.875979I
0.73242 − 2.51663I 0
u = −0.758459 + 0.794993I
4.55012 − 0.14668I 0
u = −0.758459 − 0.794993I
4.55012 + 0.14668I 0
u = −0.628084 + 0.921139I
−2.04419 − 5.77241I 0
u = −0.628084 − 0.921139I
−2.04419 + 5.77241I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.835257 + 0.742674I
6.35107 + 2.04623I 0
u = −0.835257 − 0.742674I
6.35107 − 2.04623I 0
u = 0.758172 + 0.825776I
3.58561 + 4.71802I 0
u = 0.758172 − 0.825776I
3.58561 − 4.71802I 0
u = −0.847393 + 0.734484I
10.08040 + 9.29957I 0
u = −0.847393 − 0.734484I
10.08040 − 9.29957I 0
u = 0.846821 + 0.739280I
11.94220 − 3.91143I 0
u = 0.846821 − 0.739280I
11.94220 + 3.91143I 0
u = 0.845301 + 0.751762I
12.17070 − 0.58717I 0
u = 0.845301 − 0.751762I
12.17070 + 0.58717I 0
u = −0.844440 + 0.757264I
10.49740 − 4.80557I 0
u = −0.844440 − 0.757264I
10.49740 + 4.80557I 0
u = 0.738716 + 0.913060I
3.31838 + 0.95336I 0
u = 0.738716 − 0.913060I
3.31838 − 0.95336I 0
u = 0.682106 + 0.959266I
−0.98202 + 4.31584I 0
u = 0.682106 − 0.959266I
−0.98202 − 4.31584I 0
u = −0.731393 + 0.936292I
4.12042 − 5.50383I 0
u = −0.731393 − 0.936292I
4.12042 + 5.50383I 0
u = 0.158699 + 0.795794I
−0.93723 + 1.74811I 1.58765 − 5.17968I
u = 0.158699 − 0.795794I
−0.93723 − 1.74811I 1.58765 + 5.17968I
u = −0.709189 + 0.967062I
2.84545 − 6.72964I 0
u = −0.709189 − 0.967062I
2.84545 + 6.72964I 0
u = 0.702838 + 0.980436I
0.68737 + 11.26350I 0
u = 0.702838 − 0.980436I
0.68737 − 11.26350I 0
u = −0.753756 + 0.996096I
5.57098 − 7.98818I 0
u = −0.753756 − 0.996096I
5.57098 + 7.98818I 0
u = −0.765394 + 0.991927I
9.77291 − 1.20159I 0
u = −0.765394 − 0.991927I
9.77291 + 1.20159I 0
u = 0.763313 + 0.995423I
11.41870 + 6.58981I 0
u = 0.763313 − 0.995423I
11.41870 − 6.58981I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.758437 + 1.002770I
11.1297 + 9.9017I 0
u = 0.758437 − 1.002770I
11.1297 − 9.9017I 0
u = −0.756608 + 1.005470I
9.2451 − 15.2850I 0
u = −0.756608 − 1.005470I
9.2451 + 15.2850I 0
u = 0.686093 + 0.028981I
6.40339 + 6.93089I 7.58937 − 5.03714I
u = 0.686093 − 0.028981I
6.40339 − 6.93089I 7.58937 + 5.03714I
u = −0.685171 + 0.015873I
8.17683 − 1.59594I 10.20433 + 0.32100I
u = −0.685171 − 0.015873I
8.17683 + 1.59594I 10.20433 − 0.32100I
u = 0.652464
2.61478 4.37850
u = −0.334129 + 0.411688I
−1.50019 + 1.55713I 0.650340 − 0.272682I
u = −0.334129 − 0.411688I
−1.50019 − 1.55713I 0.650340 + 0.272682I
u = −0.480157 + 0.207491I
−0.60976 − 4.42214I 4.50486 + 7.49216I
u = −0.480157 − 0.207491I
−0.60976 + 4.42214I 4.50486 − 7.49216I
u = 0.429074 + 0.095570I
1.039040 + 0.315096I 9.75730 − 1.79361I
u = 0.429074 − 0.095570I
1.039040 − 0.315096I 9.75730 + 1.79361I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
75
+ 33u
74
+ ··· + 2u + 1
c
2
, c
6
u
75
− u
74
+ ··· + u
2
− 1
c
3
, c
4
, c
8
u
75
+ u
74
+ ··· − 110u − 25
c
5
, c
11
u
75
+ u
74
+ ··· + u
2
− 1
c
7
u
75
− 3u
74
+ ··· − 8u + 3
c
9
u
75
− 5u
74
+ ··· + 21044u − 3477
c
10
, c
12
u
75
+ 23u
74
+ ··· + 2u − 1
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
75
+ 19y
74
+ ··· − 10y −1
c
2
, c
6
y
75
− 33y
74
+ ··· + 2y −1
c
3
, c
4
, c
8
y
75
− 81y
74
+ ··· + 28950y −625
c
5
, c
11
y
75
+ 23y
74
+ ··· + 2y −1
c
7
y
75
− 5y
74
+ ··· + 562y −9
c
9
y
75
− 29y
74
+ ··· + 182318326y −12089529
c
10
, c
12
y
75
+ 59y
74
+ ··· + 22y −1
9
