12n
0117
(K12n
0117
)
A knot diagram
1
Linearized knot diagam
3 5 6 2 10 3 11 12 1 6 9 8
Solving Sequence
5,10 3,6
7 11 8 2 1 4 9 12
c
5
c
6
c
10
c
7
c
2
c
1
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−1.31243 × 10
79
u
53
+ 2.52611 × 10
79
u
52
+ ··· + 3.89056 × 10
79
b + 3.47087 × 10
79
,
− 6.05548 × 10
79
u
53
+ 8.73883 × 10
79
u
52
+ ··· + 3.89056 × 10
79
a + 1.31119 × 10
80
, u
54
− 2u
53
+ ··· − u + 1i
I
u
2
= hb + 1, u
5
− 4u
3
− u
2
+ a + 4u + 3, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 60 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
= h−1.31×10
79
u
53
+2.53×10
79
u
52
+· · ·+3.89×10
79
b+3.47×10
79
, −6.06×
10
79
u
53
+8.74×10
79
u
52
+· · ·+3.89×10
79
a+1.31×10
80
, u
54
−2u
53
+· · ·−u+1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
1.55645u
53
− 2.24616u
52
+ ··· − 5.64280u − 3.37019
0.337337u
53
− 0.649292u
52
+ ··· − 1.00166u − 0.892127
a
6
=
1
u
2
a
7
=
0.494692u
53
− 0.863004u
52
+ ··· − 1.15347u − 0.702997
0.0990880u
53
− 0.268680u
52
+ ··· − 0.626964u − 0.0224128
a
11
=
−u
−u
3
+ u
a
8
=
0.356510u
53
− 0.587357u
52
+ ··· − 0.776606u − 0.657794
0.241891u
53
− 0.521606u
52
+ ··· − 0.866363u − 0.0668977
a
2
=
1.89379u
53
− 2.89546u
52
+ ··· − 6.64447u − 4.26232
0.337337u
53
− 0.649292u
52
+ ··· − 1.00166u − 0.892127
a
1
=
0.422066u
53
− 0.798929u
52
+ ··· − 1.41212u − 0.599029
0.0726263u
53
− 0.0640750u
52
+ ··· + 0.258652u − 0.103967
a
4
=
1.61205u
53
− 2.39082u
52
+ ··· − 5.95476u − 3.39557
0.312040u
53
− 0.627049u
52
+ ··· − 1.09072u − 0.858664
a
9
=
0.224414u
53
− 0.297818u
52
+ ··· + 1.50104u − 0.620789
−0.00237699u
53
− 0.0155895u
52
+ ··· + 0.993052u − 0.0916897
a
12
=
−0.0386938u
53
+ 0.107824u
52
+ ··· − 0.761082u − 0.0321440
0.281009u
53
− 0.285348u
52
+ ··· + 1.09523u − 0.220603
(ii) Obstruction class = −1
(iii) Cusp Shapes = −7.59111u
53
+ 13.1261u
52
+ ··· + 13.3633u − 0.108982
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
54
+ 21u
53
+ ··· + 622u + 1
c
2
, c
4
u
54
− 7u
53
+ ··· − 26u + 1
c
3
, c
6
u
54
+ 7u
53
+ ··· + 768u + 64
c
5
, c
10
u
54
− 2u
53
+ ··· − u + 1
c
7
, c
9
u
54
+ 2u
53
+ ··· + 141u + 17
c
8
, c
11
, c
12
u
54
− 2u
53
+ ··· + 5u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
54
+ 31y
53
+ ··· − 394862y + 1
c
2
, c
4
y
54
− 21y
53
+ ··· − 622y + 1
c
3
, c
6
y
54
− 39y
53
+ ··· − 147456y + 4096
c
5
, c
10
y
54
− 14y
53
+ ··· − 13y + 1
c
7
, c
9
y
54
− 26y
53
+ ··· − 1997y + 289
c
8
, c
11
, c
12
y
54
+ 46y
53
+ ··· − 13y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.768246 + 0.418674I
a = 0.229316 − 1.287030I
b = −0.920583 + 0.946817I
0.59137 + 6.88514I −9.74374 − 8.93563I
u = −0.768246 − 0.418674I
a = 0.229316 + 1.287030I
b = −0.920583 − 0.946817I
0.59137 − 6.88514I −9.74374 + 8.93563I
u = 0.607809 + 0.618855I
a = 0.260894 + 0.992870I
b = −0.199900 − 0.710236I
3.57906 − 1.48496I −4.05718 + 4.03244I
u = 0.607809 − 0.618855I
a = 0.260894 − 0.992870I
b = −0.199900 + 0.710236I
3.57906 + 1.48496I −4.05718 − 4.03244I
u = −0.764967 + 0.849835I
a = −0.290324 − 0.846955I
b = 0.429432 + 1.086500I
1.86993 + 4.42374I 0
u = −0.764967 − 0.849835I
a = −0.290324 + 0.846955I
b = 0.429432 − 1.086500I
1.86993 − 4.42374I 0
u = 0.704848 + 0.923652I
a = −0.256437 + 0.652141I
b = 0.534153 − 0.864717I
3.77813 − 0.69821I 0
u = 0.704848 − 0.923652I
a = −0.256437 − 0.652141I
b = 0.534153 + 0.864717I
3.77813 + 0.69821I 0
u = 0.746032 + 0.376084I
a = 0.208695 + 1.272420I
b = −1.000010 − 0.815508I
−3.84826 − 3.29989I −15.7501 + 7.0561I
u = 0.746032 − 0.376084I
a = 0.208695 − 1.272420I
b = −1.000010 + 0.815508I
−3.84826 + 3.29989I −15.7501 − 7.0561I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.803876 + 0.851386I
a = −0.369782 + 0.893548I
b = 0.480584 − 1.193560I
6.92007 − 8.14255I 0
u = 0.803876 − 0.851386I
a = −0.369782 − 0.893548I
b = 0.480584 + 1.193560I
6.92007 + 8.14255I 0
u = −0.741661 + 0.299782I
a = 0.129845 − 1.191170I
b = −1.173070 + 0.667650I
−0.523210 − 0.060545I −12.38307 − 2.35064I
u = −0.741661 − 0.299782I
a = 0.129845 + 1.191170I
b = −1.173070 − 0.667650I
−0.523210 + 0.060545I −12.38307 + 2.35064I
u = 0.773740 + 0.056042I
a = −0.048323 + 0.281192I
b = −1.57214 − 0.14784I
−1.63990 − 3.52551I −13.9655 + 3.9216I
u = 0.773740 − 0.056042I
a = −0.048323 − 0.281192I
b = −1.57214 + 0.14784I
−1.63990 + 3.52551I −13.9655 − 3.9216I
u = −0.761194
a = −0.126584
b = −1.55203
−5.56883 −19.2640
u = −0.801458 + 0.970429I
a = −0.477469 − 0.628269I
b = 0.772246 + 0.988987I
10.54700 + 0.04212I 0
u = −0.801458 − 0.970429I
a = −0.477469 + 0.628269I
b = 0.772246 − 0.988987I
10.54700 − 0.04212I 0
u = 1.029720 + 0.727275I
a = 0.864484 − 1.045500I
b = 0.745526 + 0.764163I
6.18806 + 2.15434I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.029720 − 0.727275I
a = 0.864484 + 1.045500I
b = 0.745526 − 0.764163I
6.18806 − 2.15434I 0
u = 0.680095 + 1.079720I
a = −0.295388 + 0.394253I
b = 0.744693 − 0.637616I
3.23226 − 0.56101I 0
u = 0.680095 − 1.079720I
a = −0.295388 − 0.394253I
b = 0.744693 + 0.637616I
3.23226 + 0.56101I 0
u = −1.094030 + 0.729061I
a = 0.716084 + 0.962560I
b = 0.826123 − 0.670841I
0.83207 + 1.55401I 0
u = −1.094030 − 0.729061I
a = 0.716084 − 0.962560I
b = 0.826123 + 0.670841I
0.83207 − 1.55401I 0
u = 0.545482 + 0.387512I
a = 1.49627 + 0.17225I
b = −0.109480 + 0.221560I
3.26577 − 2.10907I −4.57255 + 4.21158I
u = 0.545482 − 0.387512I
a = 1.49627 − 0.17225I
b = −0.109480 − 0.221560I
3.26577 + 2.10907I −4.57255 − 4.21158I
u = −0.549686 + 0.379087I
a = 0.41820 − 1.65690I
b = −0.756383 + 0.350743I
−0.98992 + 1.28097I −8.23381 − 4.95312I
u = −0.549686 − 0.379087I
a = 0.41820 + 1.65690I
b = −0.756383 − 0.350743I
−0.98992 − 1.28097I −8.23381 + 4.95312I
u = −0.765980 + 1.114890I
a = −0.423959 − 0.343278I
b = 0.903717 + 0.672502I
0.58680 − 3.64832I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.765980 − 1.114890I
a = −0.423959 + 0.343278I
b = 0.903717 − 0.672502I
0.58680 + 3.64832I 0
u = −1.072810 + 0.850554I
a = 0.521225 + 1.271540I
b = 1.038160 − 0.833697I
9.68000 + 6.67132I 0
u = −1.072810 − 0.850554I
a = 0.521225 − 1.271540I
b = 1.038160 + 0.833697I
9.68000 − 6.67132I 0
u = 0.809181 + 1.110190I
a = −0.498165 + 0.338281I
b = 0.978433 − 0.715727I
5.47300 + 7.77762I 0
u = 0.809181 − 1.110190I
a = −0.498165 − 0.338281I
b = 0.978433 + 0.715727I
5.47300 − 7.77762I 0
u = −0.355157 + 0.506837I
a = 3.09166 − 1.48155I
b = −0.790878 − 0.242839I
1.75113 − 3.66412I −7.58424 − 2.09874I
u = −0.355157 − 0.506837I
a = 3.09166 + 1.48155I
b = −0.790878 + 0.242839I
1.75113 + 3.66412I −7.58424 + 2.09874I
u = 1.127980 + 0.801217I
a = 0.525545 − 1.040990I
b = 0.975741 + 0.675989I
2.46104 − 5.73021I 0
u = 1.127980 − 0.801217I
a = 0.525545 + 1.040990I
b = 0.975741 − 0.675989I
2.46104 + 5.73021I 0
u = 1.13900 + 0.87943I
a = 0.314802 − 1.138340I
b = 1.146120 + 0.686785I
1.85511 − 6.51126I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.13900 − 0.87943I
a = 0.314802 + 1.138340I
b = 1.146120 − 0.686785I
1.85511 + 6.51126I 0
u = 1.11062 + 0.91730I
a = 0.232119 − 1.286790I
b = 1.24453 + 0.76770I
4.4865 − 15.0788I 0
u = 1.11062 − 0.91730I
a = 0.232119 + 1.286790I
b = 1.24453 − 0.76770I
4.4865 + 15.0788I 0
u = −1.12423 + 0.90674I
a = 0.249320 + 1.222810I
b = 1.21483 − 0.72751I
−0.55203 + 10.91430I 0
u = −1.12423 − 0.90674I
a = 0.249320 − 1.222810I
b = 1.21483 + 0.72751I
−0.55203 − 10.91430I 0
u = 0.298615 + 0.438132I
a = 3.44332 + 2.65285I
b = −0.886190 + 0.122203I
−2.63664 + 0.46428I −17.5611 + 8.2084I
u = 0.298615 − 0.438132I
a = 3.44332 − 2.65285I
b = −0.886190 − 0.122203I
−2.63664 − 0.46428I −17.5611 − 8.2084I
u = −0.158468 + 0.454530I
a = 5.77902 − 2.31620I
b = −1.028880 − 0.101463I
1.11313 + 2.46535I 1.5488 − 21.3906I
u = −0.158468 − 0.454530I
a = 5.77902 + 2.31620I
b = −1.028880 + 0.101463I
1.11313 − 2.46535I 1.5488 + 21.3906I
u = −0.455910
a = 1.15202
b = 0.0398888
−0.785514 −12.5200
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.453888
a = −3.16883
b = −1.08168
−2.16763 5.07630
u = −1.61778 + 0.14927I
a = 0.501712 + 0.090012I
b = 0.800121 − 0.055050I
−4.90969 + 4.71375I 0
u = −1.61778 − 0.14927I
a = 0.501712 − 0.090012I
b = 0.800121 + 0.055050I
−4.90969 − 4.71375I 0
u = 1.63817
a = 0.498085
b = 0.800035
−8.87320 0
10
II. I
u
2
= hb + 1, u
5
− 4u
3
− u
2
+ a + 4u + 3, u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1i
(i) Arc colorings
a
5
=
1
0
a
10
=
0
u
a
3
=
−u
5
+ 4u
3
+ u
2
− 4u − 3
−1
a
6
=
1
u
2
a
7
=
1
u
2
a
11
=
−u
−u
3
+ u
a
8
=
−u
2
+ 1
−u
4
+ 2u
2
a
2
=
−u
5
+ 4u
3
+ u
2
− 4u − 4
−1
a
1
=
−1
0
a
4
=
−u
5
+ 4u
3
+ u
2
− 4u − 3
−1
a
9
=
u
u
a
12
=
u
5
− 2u
3
− u
u
5
− 3u
3
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes = −7u
5
+ 3u
4
+ 27u
3
− 5u
2
− 24u − 26
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
6
c
3
, c
6
u
6
c
4
(u + 1)
6
c
5
, c
7
, c
9
u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
8
u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1
c
10
u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1
c
11
, c
12
u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y −1)
6
c
3
, c
6
y
6
c
5
, c
7
, c
9
c
10
y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1
c
8
, c
11
, c
12
y
6
+ 5y
5
+ 9y
4
+ 4y
3
− 6y
2
− 5y + 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493180 + 0.575288I
a = 0.26610 − 1.72116I
b = −1.00000
1.31531 + 1.97241I −5.36986 − 2.86834I
u = −0.493180 − 0.575288I
a = 0.26610 + 1.72116I
b = −1.00000
1.31531 − 1.97241I −5.36986 + 2.86834I
u = 0.483672
a = −4.27462
b = −1.00000
−2.38379 −35.7440
u = 1.52087 + 0.16310I
a = −0.417699 + 0.090629I
b = −1.00000
−5.34051 − 4.59213I −17.7291 + 1.0120I
u = 1.52087 − 0.16310I
a = −0.417699 − 0.090629I
b = −1.00000
−5.34051 + 4.59213I −17.7291 − 1.0120I
u = −1.53904
a = −0.422181
b = −1.00000
−9.30502 −22.0580
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
6
)(u
54
+ 21u
53
+ ··· + 622u + 1)
c
2
((u − 1)
6
)(u
54
− 7u
53
+ ··· − 26u + 1)
c
3
, c
6
u
6
(u
54
+ 7u
53
+ ··· + 768u + 64)
c
4
((u + 1)
6
)(u
54
− 7u
53
+ ··· − 26u + 1)
c
5
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
54
− 2u
53
+ ··· − u + 1)
c
7
, c
9
(u
6
− u
5
− 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
54
+ 2u
53
+ ··· + 141u + 17)
c
8
(u
6
+ u
5
+ 3u
4
+ 2u
3
+ 2u
2
+ u − 1)(u
54
− 2u
53
+ ··· + 5u + 1)
c
10
(u
6
+ u
5
− 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
54
− 2u
53
+ ··· − u + 1)
c
11
, c
12
(u
6
− u
5
+ 3u
4
− 2u
3
+ 2u
2
− u − 1)(u
54
− 2u
53
+ ··· + 5u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
6
)(y
54
+ 31y
53
+ ··· − 394862y + 1)
c
2
, c
4
((y −1)
6
)(y
54
− 21y
53
+ ··· − 622y + 1)
c
3
, c
6
y
6
(y
54
− 39y
53
+ ··· − 147456y + 4096)
c
5
, c
10
(y
6
− 7y
5
+ ··· − 5y + 1)(y
54
− 14y
53
+ ··· − 13y + 1)
c
7
, c
9
(y
6
− 7y
5
+ 17y
4
− 16y
3
+ 6y
2
− 5y + 1)
· (y
54
− 26y
53
+ ··· − 1997y + 289)
c
8
, c
11
, c
12
(y
6
+ 5y
5
+ ··· − 5y + 1)(y
54
+ 46y
53
+ ··· − 13y + 1)
16
