12n
0017
(K12n
0017
)
A knot diagram
1
Linearized knot diagam
3 5 6 7 2 9 5 11 6 12 8 10
Solving Sequence
2,6
5 3
1,10
9 7 8 4 12 11
c
5
c
2
c
1
c
9
c
6
c
7
c
4
c
12
c
11
c
3
, c
8
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.18594 × 10
34
u
52
− 2.07414 × 10
35
u
51
+ ··· + 1.22009 × 10
34
b + 4.27515 × 10
34
,
− 5.11228 × 10
32
u
52
− 1.97357 × 10
33
u
51
+ ··· + 1.82103 × 10
32
a − 9.15657 × 10
32
, u
53
+ 5u
52
+ ··· − 9u − 1i
I
u
2
= h−a
3
u − a
3
− 3a
2
− au + 3b + 2a + u + 4, a
4
− a
3
u + 3a
3
− a
2
u + a
2
− 4a − u − 3, u
2
− u + 1i
* 2 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
= h−4.19×10
34
u
52
−2.07×10
35
u
51
+· · ·+1.22×10
34
b+4.28×10
34
, −5.11×
10
32
u
52
−1.97×10
33
u
51
+· · ·+1.82×10
32
a−9.16×10
32
, u
53
+5u
52
+· · ·−9u−1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u
2
a
3
=
u
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
10
=
2.80735u
52
+ 10.8376u
51
+ ··· − 0.444267u + 5.02822
3.43084u
52
+ 16.9999u
51
+ ··· − 34.1145u − 3.50395
a
9
=
−0.623488u
52
− 6.16226u
51
+ ··· + 33.6702u + 8.53217
3.43084u
52
+ 16.9999u
51
+ ··· − 34.1145u − 3.50395
a
7
=
−1.75032u
52
− 0.890320u
51
+ ··· − 10.7679u − 3.13567
−6.83122u
52
− 35.1862u
51
+ ··· + 71.7880u + 8.58154
a
8
=
1.59554u
52
+ 9.62066u
51
+ ··· − 7.98101u − 2.41540
−1.76578u
52
− 8.80291u
51
+ ··· + 19.1693u + 2.36325
a
4
=
−u
3
u
3
+ u
a
12
=
4.55627u
52
+ 20.9187u
51
+ ··· − 49.1860u − 2.25218
1.76578u
52
+ 8.80291u
51
+ ··· − 19.1693u − 2.36325
a
11
=
1.71105u
52
+ 5.75864u
51
+ ··· − 19.5378u + 3.68527
2.74059u
52
+ 13.6878u
51
+ ··· − 30.0115u − 3.36198
(ii) Obstruction class = −1
(iii) Cusp Shapes = −5.35104u
52
− 25.5532u
51
+ ··· + 78.3747u + 11.0743
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
53
+ 15u
52
+ ··· − 9u − 1
c
2
, c
5
u
53
+ 5u
52
+ ··· − 9u − 1
c
3
u
53
− 5u
52
+ ··· − 2302791u − 148289
c
4
, c
7
u
53
+ 5u
52
+ ··· − 1664u − 256
c
6
, c
9
u
53
+ 3u
52
+ ··· − 3u − 1
c
8
, c
11
u
53
− 3u
52
+ ··· + 5u − 1
c
10
, c
12
u
53
− 21u
52
+ ··· − u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
53
+ 51y
52
+ ··· − 4269y −1
c
2
, c
5
y
53
+ 15y
52
+ ··· − 9y −1
c
3
y
53
+ 87y
52
+ ··· − 708900293913y −21989627521
c
4
, c
7
y
53
− 45y
52
+ ··· − 606208y −65536
c
6
, c
9
y
53
+ 5y
52
+ ··· − y −1
c
8
, c
11
y
53
+ 21y
52
+ ··· − y −1
c
10
, c
12
y
53
+ 25y
52
+ ··· − 77y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.530308 + 0.891641I
a = −1.41610 − 2.34002I
b = −0.227413 + 0.365967I
0.156968 + 0.305979I −9.1267 + 31.8061I
u = 0.530308 − 0.891641I
a = −1.41610 + 2.34002I
b = −0.227413 − 0.365967I
0.156968 − 0.305979I −9.1267 − 31.8061I
u = 0.550027 + 0.789290I
a = 0.66997 + 2.28557I
b = 0.074147 − 0.510318I
0.47806 + 4.00723I −10.14274 − 8.52943I
u = 0.550027 − 0.789290I
a = 0.66997 − 2.28557I
b = 0.074147 + 0.510318I
0.47806 − 4.00723I −10.14274 + 8.52943I
u = 0.290660 + 0.872671I
a = −1.38678 − 1.24113I
b = −0.646642 + 0.233451I
−0.90313 + 4.01726I 5.20804 − 5.06978I
u = 0.290660 − 0.872671I
a = −1.38678 + 1.24113I
b = −0.646642 − 0.233451I
−0.90313 − 4.01726I 5.20804 + 5.06978I
u = 1.056180 + 0.236014I
a = −0.594933 − 0.033166I
b = −0.768107 − 0.046948I
3.64081 + 3.04661I 13.4424 − 4.7932I
u = 1.056180 − 0.236014I
a = −0.594933 + 0.033166I
b = −0.768107 + 0.046948I
3.64081 − 3.04661I 13.4424 + 4.7932I
u = 0.657790 + 0.921515I
a = −1.023740 + 0.420502I
b = −0.553170 − 0.255009I
0.62571 + 2.57123I 0
u = 0.657790 − 0.921515I
a = −1.023740 − 0.420502I
b = −0.553170 + 0.255009I
0.62571 − 2.57123I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.169703 + 0.847189I
a = −0.573410 − 1.128960I
b = 0.220478 + 0.766514I
−1.59631 + 1.76854I −2.74640 − 4.48451I
u = 0.169703 − 0.847189I
a = −0.573410 + 1.128960I
b = 0.220478 − 0.766514I
−1.59631 − 1.76854I −2.74640 + 4.48451I
u = −0.359167 + 0.783757I
a = −1.60327 + 0.04327I
b = −0.01818 + 1.50451I
−7.06670 + 1.57178I −4.33706 − 7.74502I
u = −0.359167 − 0.783757I
a = −1.60327 − 0.04327I
b = −0.01818 − 1.50451I
−7.06670 − 1.57178I −4.33706 + 7.74502I
u = −0.409008 + 0.741183I
a = 1.80767 − 0.00417I
b = 0.22475 − 1.53329I
−6.87601 − 4.70786I −1.13106 − 3.85165I
u = −0.409008 − 0.741183I
a = 1.80767 + 0.00417I
b = 0.22475 + 1.53329I
−6.87601 + 4.70786I −1.13106 + 3.85165I
u = −0.923392 + 0.708125I
a = 0.826229 + 0.812255I
b = 1.15258 + 0.92886I
4.90426 + 3.27952I 0
u = −0.923392 − 0.708125I
a = 0.826229 − 0.812255I
b = 1.15258 − 0.92886I
4.90426 − 3.27952I 0
u = −0.809353 + 0.881663I
a = 0.531942 + 0.908624I
b = 1.20306 + 1.02356I
4.15839 − 1.32183I 0
u = −0.809353 − 0.881663I
a = 0.531942 − 0.908624I
b = 1.20306 − 1.02356I
4.15839 + 1.32183I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.963077 + 0.716560I
a = 0.748110 − 0.046980I
b = 0.724122 + 0.163979I
3.13131 + 0.47040I 0
u = 0.963077 − 0.716560I
a = 0.748110 + 0.046980I
b = 0.724122 − 0.163979I
3.13131 − 0.47040I 0
u = −0.848949 + 0.856511I
a = −1.69721 − 0.38788I
b = −0.99863 + 1.18800I
6.21091 + 1.13505I 0
u = −0.848949 − 0.856511I
a = −1.69721 + 0.38788I
b = −0.99863 − 1.18800I
6.21091 − 1.13505I 0
u = −0.997021 + 0.686901I
a = −0.854814 − 0.725692I
b = −1.12564 − 0.93321I
7.01799 + 8.93611I 0
u = −0.997021 − 0.686901I
a = −0.854814 + 0.725692I
b = −1.12564 + 0.93321I
7.01799 − 8.93611I 0
u = −0.800905 + 0.909129I
a = 1.72367 + 0.46790I
b = 1.04239 − 1.19652I
4.07249 − 4.71363I 0
u = −0.800905 − 0.909129I
a = 1.72367 − 0.46790I
b = 1.04239 + 1.19652I
4.07249 + 4.71363I 0
u = 0.190036 + 1.206100I
a = −0.014657 − 0.532586I
b = 0.543932 + 0.735641I
−2.94216 + 2.73108I 0
u = 0.190036 − 1.206100I
a = −0.014657 + 0.532586I
b = 0.543932 − 0.735641I
−2.94216 − 2.73108I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.167242 + 0.748310I
a = 1.20707 + 1.23679I
b = 0.772219 − 0.132719I
−1.23355 − 0.85670I 1.99397 + 0.77147I
u = 0.167242 − 0.748310I
a = 1.20707 − 1.23679I
b = 0.772219 + 0.132719I
−1.23355 + 0.85670I 1.99397 − 0.77147I
u = 0.593122 + 1.098860I
a = −0.640887 + 0.592926I
b = −0.568895 − 0.414061I
0.79815 + 2.64733I 0
u = 0.593122 − 1.098860I
a = −0.640887 − 0.592926I
b = −0.568895 + 0.414061I
0.79815 − 2.64733I 0
u = −0.816554 + 0.945782I
a = −0.448825 − 0.835890I
b = −1.17212 − 1.05145I
5.93083 − 7.33894I 0
u = −0.816554 − 0.945782I
a = −0.448825 + 0.835890I
b = −1.17212 + 1.05145I
5.93083 + 7.33894I 0
u = −0.938500 + 0.838979I
a = −0.667637 − 0.761297I
b = −1.15180 − 0.97924I
11.01260 + 0.70068I 0
u = −0.938500 − 0.838979I
a = −0.667637 + 0.761297I
b = −1.15180 + 0.97924I
11.01260 − 0.70068I 0
u = −0.781108 + 1.058600I
a = 1.62355 + 0.62236I
b = 1.09267 − 1.11554I
3.80915 − 9.57151I 0
u = −0.781108 − 1.058600I
a = 1.62355 − 0.62236I
b = 1.09267 + 1.11554I
3.80915 + 9.57151I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.855619 + 1.002320I
a = −1.61140 − 0.52084I
b = −1.04937 + 1.13619I
10.48550 − 7.29514I 0
u = −0.855619 − 1.002320I
a = −1.61140 + 0.52084I
b = −1.04937 − 1.13619I
10.48550 + 7.29514I 0
u = 0.276293 + 1.310550I
a = −0.145590 + 0.459150I
b = −0.617657 − 0.677073I
−1.79792 + 7.60628I 0
u = 0.276293 − 1.310550I
a = −0.145590 − 0.459150I
b = −0.617657 + 0.677073I
−1.79792 − 7.60628I 0
u = 0.651246
a = 0.347416
b = 0.701762
1.38715 7.24480
u = −0.797265 + 1.097860I
a = −1.57835 − 0.63310I
b = −1.08229 + 1.09516I
5.7123 − 15.4835I 0
u = −0.797265 − 1.097860I
a = −1.57835 + 0.63310I
b = −1.08229 − 1.09516I
5.7123 + 15.4835I 0
u = 0.884439 + 1.048670I
a = 0.701048 − 0.259116I
b = 0.705424 + 0.300411I
2.15584 + 6.28914I 0
u = 0.884439 − 1.048670I
a = 0.701048 + 0.259116I
b = 0.705424 − 0.300411I
2.15584 − 6.28914I 0
u = 0.289494 + 0.414333I
a = 1.16272 + 2.27371I
b = 0.033058 − 0.698327I
0.54607 − 1.46734I 1.60005 + 1.62915I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.289494 − 0.414333I
a = 1.16272 − 2.27371I
b = 0.033058 + 0.698327I
0.54607 + 1.46734I 1.60005 − 1.62915I
u = −0.107152 + 0.100700I
a = 5.08191 + 0.12392I
b = 0.340195 − 0.558279I
0.33530 − 1.50733I 2.98224 + 4.24130I
u = −0.107152 − 0.100700I
a = 5.08191 − 0.12392I
b = 0.340195 + 0.558279I
0.33530 + 1.50733I 2.98224 − 4.24130I
10
II. I
u
2
= h−a
3
u − a
3
− 3a
2
− au + 3b + 2a + u + 4, a
4
− a
3
u + 3a
3
− a
2
u +
a
2
− 4a − u − 3, u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
6
=
1
0
a
5
=
1
u − 1
a
3
=
u
u − 1
a
1
=
−1
0
a
10
=
a
1
3
a
3
u +
1
3
au + ··· −
2
3
a −
4
3
a
9
=
−
1
3
a
3
u −
1
3
au + ··· +
5
3
a +
4
3
1
3
a
3
u +
1
3
au + ··· −
2
3
a −
4
3
a
7
=
−
1
3
a
3
u −
4
3
a
2
u + ··· − a −
4
3
2
3
a
3
u +
2
3
a
2
u + ··· + a +
5
3
a
8
=
−
1
3
a
3
u −
4
3
a
2
u + ··· − a −
4
3
2
3
a
3
u +
2
3
a
2
u + ··· + a +
5
3
a
4
=
1
u − 1
a
12
=
1
3
a
3
u −
2
3
a
2
u + ··· +
4
3
a
2
−
5
3
2
3
a
3
u +
2
3
a
2
u + ··· + a +
5
3
a
11
=
4
3
a
3
u +
4
3
a
2
u + ··· +
1
3
a
2
+
1
3
−
1
3
a
3
u −
1
3
a
2
u + ··· + a +
2
3
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
1
3
a
3
u +
5
3
a
3
− 3a
2
u + 4a
2
+
5
3
au −
7
3
a −
17
3
u +
4
3
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
(u
2
− u + 1)
4
c
2
(u
2
+ u + 1)
4
c
4
, c
7
u
8
c
6
, c
10
(u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
c
8
(u
4
+ u
3
+ u
2
+ 1)
2
c
9
, c
12
(u
4
− u
3
+ 3u
2
− 2u + 1)
2
c
11
(u
4
− u
3
+ u
2
+ 1)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
(y
2
+ y + 1)
4
c
4
, c
7
y
8
c
6
, c
9
, c
10
c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
c
8
, c
11
(y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = −0.715307 − 0.631577I
b = −0.395123 + 0.506844I
0.211005 + 0.614778I 3.64182 − 4.24446I
u = 0.500000 + 0.866025I
a = 1.248740 + 0.225872I
b = −0.10488 + 1.55249I
−6.79074 − 1.13408I 4.47320 − 4.89165I
u = 0.500000 + 0.866025I
a = −1.44025 − 0.04422I
b = −0.10488 − 1.55249I
−6.79074 + 5.19385I 1.68800 − 11.53835I
u = 0.500000 + 0.866025I
a = −1.59319 + 1.31595I
b = −0.395123 − 0.506844I
0.21101 + 3.44499I −1.30302 − 11.36848I
u = 0.500000 − 0.866025I
a = −0.715307 + 0.631577I
b = −0.395123 − 0.506844I
0.211005 − 0.614778I 3.64182 + 4.24446I
u = 0.500000 − 0.866025I
a = 1.248740 − 0.225872I
b = −0.10488 − 1.55249I
−6.79074 + 1.13408I 4.47320 + 4.89165I
u = 0.500000 − 0.866025I
a = −1.44025 + 0.04422I
b = −0.10488 + 1.55249I
−6.79074 − 5.19385I 1.68800 + 11.53835I
u = 0.500000 − 0.866025I
a = −1.59319 − 1.31595I
b = −0.395123 + 0.506844I
0.21101 − 3.44499I −1.30302 + 11.36848I
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u
2
− u + 1)
4
)(u
53
+ 15u
52
+ ··· − 9u − 1)
c
2
((u
2
+ u + 1)
4
)(u
53
+ 5u
52
+ ··· − 9u − 1)
c
3
((u
2
− u + 1)
4
)(u
53
− 5u
52
+ ··· − 2302791u − 148289)
c
4
, c
7
u
8
(u
53
+ 5u
52
+ ··· − 1664u − 256)
c
5
((u
2
− u + 1)
4
)(u
53
+ 5u
52
+ ··· − 9u − 1)
c
6
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
53
+ 3u
52
+ ··· − 3u − 1)
c
8
((u
4
+ u
3
+ u
2
+ 1)
2
)(u
53
− 3u
52
+ ··· + 5u − 1)
c
9
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
53
+ 3u
52
+ ··· − 3u − 1)
c
10
((u
4
+ u
3
+ 3u
2
+ 2u + 1)
2
)(u
53
− 21u
52
+ ··· − u + 1)
c
11
((u
4
− u
3
+ u
2
+ 1)
2
)(u
53
− 3u
52
+ ··· + 5u − 1)
c
12
((u
4
− u
3
+ 3u
2
− 2u + 1)
2
)(u
53
− 21u
52
+ ··· − u + 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y
2
+ y + 1)
4
)(y
53
+ 51y
52
+ ··· − 4269y −1)
c
2
, c
5
((y
2
+ y + 1)
4
)(y
53
+ 15y
52
+ ··· − 9y −1)
c
3
((y
2
+ y + 1)
4
)(y
53
+ 87y
52
+ ··· − 7.08900 × 10
11
y −2.19896 × 10
10
)
c
4
, c
7
y
8
(y
53
− 45y
52
+ ··· − 606208y −65536)
c
6
, c
9
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
53
+ 5y
52
+ ··· − y −1)
c
8
, c
11
((y
4
+ y
3
+ 3y
2
+ 2y + 1)
2
)(y
53
+ 21y
52
+ ··· − y −1)
c
10
, c
12
((y
4
+ 5y
3
+ 7y
2
+ 2y + 1)
2
)(y
53
+ 25y
52
+ ··· − 77y −1)
16
