12a
0597
(K12a
0597
)
A knot diagram
1
Linearized knot diagam
3 7 9 11 10 8 2 1 12 5 4 6
Solving Sequence
3,7
2 8 1 9 4 6 12 10 5 11
c
2
c
7
c
1
c
8
c
3
c
6
c
12
c
9
c
5
c
11
c
4
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= hu
61
− u
60
+ ··· + u + 1i
* 1 irreducible components of dim
C
= 0, with total 61 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
61
− u
60
+ · · · + u + 1i
(i) Arc colorings
a
3
=
1
0
a
7
=
0
u
a
2
=
1
u
2
a
8
=
u
u
3
+ u
a
1
=
u
2
+ 1
u
2
a
9
=
u
7
+ 2u
5
+ 2u
3
+ 2u
u
7
+ u
5
+ 2u
3
+ u
a
4
=
−u
14
− 3u
12
− 6u
10
− 9u
8
− 8u
6
− 6u
4
− 2u
2
+ 1
−u
14
− 2u
12
− 5u
10
− 6u
8
− 6u
6
− 4u
4
− u
2
a
6
=
u
3
u
5
+ u
3
+ u
a
12
=
u
10
+ u
8
+ 2u
6
+ u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 4u
8
+ 4u
6
+ 3u
4
+ 2u
2
a
10
=
−u
29
− 4u
27
+ ··· + 2u
3
+ 3u
−u
31
− 5u
29
+ ··· + 4u
3
+ u
a
5
=
u
55
+ 8u
53
+ ··· + 18u
5
+ 10u
3
u
57
+ 9u
55
+ ··· + 4u
3
+ u
a
11
=
u
40
+ 7u
38
+ ··· + 4u
2
+ 1
u
40
+ 6u
38
+ ··· − 12u
6
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
59
+ 4u
58
+ ··· + 12u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
6
u
61
+ 19u
60
+ ··· − 5u − 1
c
2
, c
7
u
61
+ u
60
+ ··· + u − 1
c
3
, c
12
u
61
+ u
60
+ ··· − 39u − 5
c
4
, c
5
, c
10
c
11
u
61
+ u
60
+ ··· − 3u − 1
c
8
u
61
− 5u
60
+ ··· + 861u − 259
c
9
u
61
+ 19u
60
+ ··· + 42053u + 4523
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
61
+ 47y
60
+ ··· − 57y −1
c
2
, c
7
y
61
+ 19y
60
+ ··· − 5y −1
c
3
, c
12
y
61
− 53y
60
+ ··· − 1749y −25
c
4
, c
5
, c
10
c
11
y
61
+ 71y
60
+ ··· − 5y −1
c
8
y
61
− 17y
60
+ ··· − 237181y −67081
c
9
y
61
− 29y
60
+ ··· + 159849859y −20457529
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.198222 + 0.979758I
−0.89670 − 2.63312I −3.63978 + 3.74927I
u = −0.198222 − 0.979758I
−0.89670 + 2.63312I −3.63978 − 3.74927I
u = 0.069123 + 1.009000I
3.02018 + 3.11542I −2.16036 − 3.84044I
u = 0.069123 − 1.009000I
3.02018 − 3.11542I −2.16036 + 3.84044I
u = −0.716119 + 0.680098I
8.47263 + 3.12456I 5.89203 − 2.57979I
u = −0.716119 − 0.680098I
8.47263 − 3.12456I 5.89203 + 2.57979I
u = −0.626262 + 0.796421I
0.48829 − 1.58753I −1.44496 + 3.51896I
u = −0.626262 − 0.796421I
0.48829 + 1.58753I −1.44496 − 3.51896I
u = 0.257675 + 0.950012I
1.57037 − 0.31655I 2.17444 + 0.48608I
u = 0.257675 − 0.950012I
1.57037 + 0.31655I 2.17444 − 0.48608I
u = 0.667956 + 0.719080I
1.32938 − 1.40534I 2.56264 + 4.66576I
u = 0.667956 − 0.719080I
1.32938 + 1.40534I 2.56264 − 4.66576I
u = −0.294395 + 0.976008I
9.73503 + 2.12680I 3.77784 + 0.86173I
u = −0.294395 − 0.976008I
9.73503 − 2.12680I 3.77784 − 0.86173I
u = −0.026838 + 0.978454I
−3.53400 − 1.53833I −6.81314 + 5.04627I
u = −0.026838 − 0.978454I
−3.53400 + 1.53833I −6.81314 − 5.04627I
u = 0.206301 + 1.015650I
1.05887 + 6.04063I 0.60481 − 8.09978I
u = 0.206301 − 1.015650I
1.05887 − 6.04063I 0.60481 + 8.09978I
u = −0.214262 + 1.034720I
9.14721 − 8.20432I 2.64600 + 6.28027I
u = −0.214262 − 1.034720I
9.14721 + 8.20432I 2.64600 − 6.28027I
u = 0.591025 + 0.917591I
5.89659 + 2.23149I 0. − 2.95980I
u = 0.591025 − 0.917591I
5.89659 − 2.23149I 0. + 2.95980I
u = 0.820314 + 0.739466I
5.73172 − 1.77173I 0
u = 0.820314 − 0.739466I
5.73172 + 1.77173I 0
u = −0.831181 + 0.729794I
7.87844 + 5.39756I 7.24983 − 4.52597I
u = −0.831181 − 0.729794I
7.87844 − 5.39756I 7.24983 + 4.52597I
u = 0.840697 + 0.726055I
16.1180 − 7.6640I 9.08437 + 0.I
u = 0.840697 − 0.726055I
16.1180 + 7.6640I 9.08437 + 0.I
u = −0.823878 + 0.757079I
8.38019 − 1.56812I 8.32978 + 0.I
u = −0.823878 − 0.757079I
8.38019 + 1.56812I 8.32978 + 0.I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.712977 + 0.865338I
3.82340 + 2.72723I 8.74224 + 0.I
u = 0.712977 − 0.865338I
3.82340 − 2.72723I 8.74224 + 0.I
u = 0.833971 + 0.766158I
16.8468 + 3.4795I 0
u = 0.833971 − 0.766158I
16.8468 − 3.4795I 0
u = −0.653737 + 0.933662I
0.02925 − 3.43744I 0
u = −0.653737 − 0.933662I
0.02925 + 3.43744I 0
u = −0.755724 + 0.871667I
11.89910 − 2.85751I 0
u = −0.755724 − 0.871667I
11.89910 + 2.85751I 0
u = 0.672779 + 0.960113I
0.61376 + 6.63166I 0
u = 0.672779 − 0.960113I
0.61376 − 6.63166I 0
u = −0.683815 + 0.982225I
7.58853 − 8.50302I 0
u = −0.683815 − 0.982225I
7.58853 + 8.50302I 0
u = −0.753356 + 0.982783I
7.68554 − 4.33983I 0
u = −0.753356 − 0.982783I
7.68554 + 4.33983I 0
u = 0.744405 + 0.991746I
4.95753 + 7.64010I 0
u = 0.744405 − 0.991746I
4.95753 − 7.64010I 0
u = 0.763531 + 0.981755I
16.1819 + 2.4910I 0
u = 0.763531 − 0.981755I
16.1819 − 2.4910I 0
u = −0.746432 + 1.000940I
7.04607 − 11.30270I 0
u = −0.746432 − 1.000940I
7.04607 + 11.30270I 0
u = 0.749645 + 1.006720I
15.2551 + 13.6064I 0
u = 0.749645 − 1.006720I
15.2551 − 13.6064I 0
u = −0.668707 + 0.053438I
12.66400 − 5.34174I 9.57934 + 3.17709I
u = −0.668707 − 0.053438I
12.66400 + 5.34174I 9.57934 − 3.17709I
u = 0.638982 + 0.042408I
4.44397 + 3.29723I 8.06395 − 4.69300I
u = 0.638982 − 0.042408I
4.44397 − 3.29723I 8.06395 + 4.69300I
u = −0.605215
2.19284 3.85720
u = 0.485051 + 0.321167I
6.99050 + 1.74446I 6.06464 − 3.55680I
u = 0.485051 − 0.321167I
6.99050 − 1.74446I 6.06464 + 3.55680I
u = −0.258895 + 0.323692I
0.116836 − 0.908570I 2.53961 + 7.56880I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.258895 − 0.323692I
0.116836 + 0.908570I 2.53961 − 7.56880I
7
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
6
u
61
+ 19u
60
+ ··· − 5u − 1
c
2
, c
7
u
61
+ u
60
+ ··· + u − 1
c
3
, c
12
u
61
+ u
60
+ ··· − 39u − 5
c
4
, c
5
, c
10
c
11
u
61
+ u
60
+ ··· − 3u − 1
c
8
u
61
− 5u
60
+ ··· + 861u − 259
c
9
u
61
+ 19u
60
+ ··· + 42053u + 4523
8
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
6
y
61
+ 47y
60
+ ··· − 57y −1
c
2
, c
7
y
61
+ 19y
60
+ ··· − 5y −1
c
3
, c
12
y
61
− 53y
60
+ ··· − 1749y −25
c
4
, c
5
, c
10
c
11
y
61
+ 71y
60
+ ··· − 5y −1
c
8
y
61
− 17y
60
+ ··· − 237181y −67081
c
9
y
61
− 29y
60
+ ··· + 159849859y −20457529
9
