12a
0713
(K12a
0713
)
A knot diagram
1
Linearized knot diagam
3 8 9 10 11 12 2 7 4 1 6 5
Solving Sequence
2,7
8 3 9 4 10 5 1 11 12 6
c
7
c
2
c
8
c
3
c
9
c
4
c
1
c
10
c
12
c
6
c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
69
+ u
68
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 69 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
69
+ u
68
+ · · · + u + 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
4
=
u
7
− 2u
5
+ 2u
3
− 2u
−u
7
+ u
5
− 2u
3
+ u
a
10
=
u
12
− 3u
10
+ 5u
8
− 6u
6
+ 4u
4
− 3u
2
+ 1
−u
12
+ 2u
10
− 4u
8
+ 4u
6
− 3u
4
+ 2u
2
a
5
=
−u
17
+ 4u
15
− 9u
13
+ 14u
11
− 15u
9
+ 14u
7
− 10u
5
+ 6u
3
− 3u
u
17
− 3u
15
+ 7u
13
− 10u
11
+ 11u
9
− 10u
7
+ 6u
5
− 4u
3
+ u
a
1
=
u
3
u
5
− u
3
+ u
a
11
=
u
20
− 3u
18
+ ··· − 3u
2
+ 1
u
22
− 4u
20
+ ··· − 8u
4
+ 3u
2
a
12
=
−u
39
+ 8u
37
+ ··· + 42u
5
− 8u
3
u
39
− 7u
37
+ ··· + 2u
3
+ u
a
6
=
u
59
− 10u
57
+ ··· + 5u
3
− 2u
u
61
− 11u
59
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
68
+ 52u
66
+ ··· − 4u − 6
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
69
+ 25u
68
+ ··· − u + 1
c
2
, c
7
u
69
+ u
68
+ ··· + u + 1
c
3
, c
4
, c
9
u
69
− u
68
+ ··· − 15u + 1
c
5
, c
6
, c
11
u
69
+ u
68
+ ··· + u + 1
c
10
u
69
− 17u
68
+ ··· + 49u − 1
c
12
u
69
− 3u
68
+ ··· − 15u + 5
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
69
+ 39y
68
+ ··· + 3y −1
c
2
, c
7
y
69
− 25y
68
+ ··· − y −1
c
3
, c
4
, c
9
y
69
− 69y
68
+ ··· + 31y −1
c
5
, c
6
, c
11
y
69
− 61y
68
+ ··· − y −1
c
10
y
69
+ 3y
68
+ ··· + 959y −1
c
12
y
69
+ 7y
68
+ ··· + 535y −25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.561535 + 0.801719I
0.59754 − 9.28056I −1.67855 + 4.92481I
u = −0.561535 − 0.801719I
0.59754 + 9.28056I −1.67855 − 4.92481I
u = −0.741260 + 0.705629I
2.07770 − 1.55952I 0. + 4.24575I
u = −0.741260 − 0.705629I
2.07770 + 1.55952I 0. − 4.24575I
u = 0.858174 + 0.460652I
3.02036 + 0.76922I −4.00000 + 0.63988I
u = 0.858174 − 0.460652I
3.02036 − 0.76922I −4.00000 − 0.63988I
u = 0.552904 + 0.795056I
−4.60768 + 5.51677I −6.32456 − 4.07554I
u = 0.552904 − 0.795056I
−4.60768 − 5.51677I −6.32456 + 4.07554I
u = 0.787073 + 0.683095I
2.73226 − 1.63418I 0
u = 0.787073 − 0.683095I
2.73226 + 1.63418I 0
u = 0.744206 + 0.732824I
7.48690 + 4.59797I 0
u = 0.744206 − 0.732824I
7.48690 − 4.59797I 0
u = −0.891875 + 0.548288I
−1.16815 + 2.14250I 0
u = −0.891875 − 0.548288I
−1.16815 − 2.14250I 0
u = −0.540612 + 0.778681I
−2.67823 − 1.59684I −3.63668 − 0.69772I
u = −0.540612 − 0.778681I
−2.67823 + 1.59684I −3.63668 + 0.69772I
u = −0.923734 + 0.200980I
1.85137 + 5.82041I −6.32686 − 6.94483I
u = −0.923734 − 0.200980I
1.85137 − 5.82041I −6.32686 + 6.94483I
u = 0.582842 + 0.744201I
3.93389 + 1.07116I 0.776477 − 0.457625I
u = 0.582842 − 0.744201I
3.93389 − 1.07116I 0.776477 + 0.457625I
u = −0.930462
−0.771769 −9.37220
u = −0.519198 + 0.768041I
−2.80848 − 1.33304I −4.00000 + 1.12385I
u = −0.519198 − 0.768041I
−2.80848 + 1.33304I −4.00000 − 1.12385I
u = −0.805040 + 0.718870I
8.37556 + 3.79820I 0
u = −0.805040 − 0.718870I
8.37556 − 3.79820I 0
u = 0.900653 + 0.146018I
−3.07880 − 2.61927I −12.21002 + 6.26526I
u = 0.900653 − 0.146018I
−3.07880 + 2.61927I −12.21002 − 6.26526I
u = 0.493368 + 0.760092I
−4.98673 − 2.50951I −7.03178 + 3.70440I
u = 0.493368 − 0.760092I
−4.98673 + 2.50951I −7.03178 − 3.70440I
u = −1.09692
−1.56890 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.476518 + 0.754332I
0.06794 + 6.25168I −2.30141 − 4.86494I
u = −0.476518 − 0.754332I
0.06794 − 6.25168I −2.30141 + 4.86494I
u = 0.945924 + 0.588557I
2.32478 − 5.03042I 0
u = 0.945924 − 0.588557I
2.32478 + 5.03042I 0
u = 0.911304 + 0.669367I
2.35185 − 3.58854I 0
u = 0.911304 − 0.669367I
2.35185 + 3.58854I 0
u = 1.132630 + 0.007821I
−8.44892 − 0.18975I 0
u = 1.132630 − 0.007821I
−8.44892 + 0.18975I 0
u = −1.135870 + 0.021393I
−10.52510 + 4.16744I 0
u = −1.135870 − 0.021393I
−10.52510 − 4.16744I 0
u = 1.136010 + 0.030089I
−5.39627 − 7.98412I 0
u = 1.136010 − 0.030089I
−5.39627 + 7.98412I 0
u = −0.900087 + 0.702148I
8.08679 + 1.63035I 0
u = −0.900087 − 0.702148I
8.08679 − 1.63035I 0
u = −0.943327 + 0.681204I
1.46972 + 6.88966I 0
u = −0.943327 − 0.681204I
1.46972 − 6.88966I 0
u = 0.947298 + 0.697651I
6.87547 − 10.05570I 0
u = 0.947298 − 0.697651I
6.87547 + 10.05570I 0
u = 1.033920 + 0.660350I
2.60685 − 6.43711I 0
u = 1.033920 − 0.660350I
2.60685 + 6.43711I 0
u = −1.057090 + 0.628994I
−1.60252 − 1.02909I 0
u = −1.057090 − 0.628994I
−1.60252 + 1.02909I 0
u = −0.769541
−1.25215 −7.16180
u = 1.057010 + 0.636565I
−6.61719 − 2.76776I 0
u = 1.057010 − 0.636565I
−6.61719 + 2.76776I 0
u = −1.055470 + 0.647367I
−4.37317 + 6.68516I 0
u = −1.055470 − 0.647367I
−4.37317 − 6.68516I 0
u = −1.054270 + 0.658260I
−4.18744 + 7.02467I 0
u = −1.054270 − 0.658260I
−4.18744 − 7.02467I 0
u = 1.056900 + 0.666631I
−6.10164 − 11.02080I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.056900 − 0.666631I
−6.10164 + 11.02080I 0
u = −1.056820 + 0.671674I
−0.8759 + 14.8224I 0
u = −1.056820 − 0.671674I
−0.8759 − 14.8224I 0
u = 0.461695 + 0.473110I
3.31546 + 0.65994I −1.10722 + 1.03109I
u = 0.461695 − 0.473110I
3.31546 − 0.65994I −1.10722 − 1.03109I
u = 0.101930 + 0.482846I
4.82799 − 3.72475I 2.55800 + 4.45689I
u = 0.101930 − 0.482846I
4.82799 + 3.72475I 2.55800 − 4.45689I
u = −0.142678 + 0.371599I
−0.151965 + 1.056310I −2.64659 − 6.18313I
u = −0.142678 − 0.371599I
−0.151965 − 1.056310I −2.64659 + 6.18313I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
69
+ 25u
68
+ ··· − u + 1
c
2
, c
7
u
69
+ u
68
+ ··· + u + 1
c
3
, c
4
, c
9
u
69
− u
68
+ ··· − 15u + 1
c
5
, c
6
, c
11
u
69
+ u
68
+ ··· + u + 1
c
10
u
69
− 17u
68
+ ··· + 49u − 1
c
12
u
69
− 3u
68
+ ··· − 15u + 5
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
69
+ 39y
68
+ ··· + 3y −1
c
2
, c
7
y
69
− 25y
68
+ ··· − y −1
c
3
, c
4
, c
9
y
69
− 69y
68
+ ··· + 31y −1
c
5
, c
6
, c
11
y
69
− 61y
68
+ ··· − y −1
c
10
y
69
+ 3y
68
+ ··· + 959y −1
c
12
y
69
+ 7y
68
+ ··· + 535y −25
9
