12a
0854
(K12a
0854
)
A knot diagram
1
Linearized knot diagam
4 5 9 10 3 12 11 1 2 8 7 6
Solving Sequence
7,12
6
1,3
5 2 11 8 9 10 4
c
6
c
12
c
5
c
2
c
11
c
7
c
8
c
10
c
4
c
1
, c
3
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−4.18772 × 10
18
u
65
+ 6.44102 × 10
20
u
64
+ ··· + 7.93709 × 10
20
b − 6.29281 × 10
16
,
− 2.93073 × 10
19
u
65
+ 4.50916 × 10
21
u
64
+ ··· + 5.55596 × 10
21
a − 5.64900 × 10
21
, u
66
+ u
65
+ ··· + 3u + 1i
* 1 irreducible components of dim
C
= 0, with total 66 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
18
u
65
+6.44×10
20
u
64
+· · ·+7.94×10
20
b−6.29×10
16
, −2.93×
10
19
u
65
+4.51×10
21
u
64
+· · ·+5.56×10
21
a−5.65×10
21
, u
66
+u
65
+· · ·+3u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
6
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
0.00527494u
65
− 0.811590u
64
+ ··· + 3.23371u + 1.01675
0.00527615u
65
− 0.811510u
64
+ ··· − 3.18309u + 0.0000792836
a
5
=
−0.00442903u
65
− 0.736691u
64
+ ··· + 2.32738u + 1.74996
−0.00442982u
65
− 0.736731u
64
+ ··· − 3.25012u − 0.0000393662
a
2
=
−0.00273721u
65
− 0.833252u
64
+ ··· + 1.44957u − 0.716626
−0.00273716u
65
− 0.833212u
64
+ ··· − 0.116545u + 0.0000404686
a
11
=
u
u
a
8
=
u
2
+ 1
u
2
a
9
=
−u
6
− 3u
4
+ 1
u
8
+ 4u
6
+ 4u
4
+ 2u
2
a
10
=
u
3
+ 2u
u
3
+ u
a
4
=
−0.000766897u
65
− 0.0917424u
64
+ ··· + 2.32749u + 1.75000
−0.000767003u
65
− 0.0917456u
64
+ ··· − 3.25001u − 3.08525 × 10
−6
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
17667926048719462539416
5555960082374174168269
u
65
−
1888758008650562826900
793708583196310595467
u
64
+ ··· +
30639294781679213832508
5555960082374174168269
u +
25448149131766158381870
5555960082374174168269
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
66
− 11u
65
+ ··· − u + 1
c
2
, c
5
u
66
+ u
65
+ ··· + 11u + 1
c
3
u
66
− u
65
+ ··· + 116u − 8
c
4
u
66
+ u
65
+ ··· − 39u + 19
c
6
, c
7
, c
10
c
11
, c
12
u
66
− u
65
+ ··· − 3u + 1
c
8
u
66
− u
65
+ ··· − 1149u + 1069
c
9
u
66
+ 3u
65
+ ··· + u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
66
− 3y
65
+ ··· − 11y + 1
c
2
, c
5
y
66
− 43y
65
+ ··· − 11y + 1
c
3
y
66
+ 53y
65
+ ··· − 18384y + 64
c
4
y
66
+ 69y
65
+ ··· + 17213y + 361
c
6
, c
7
, c
10
c
11
, c
12
y
66
+ 85y
65
+ ··· − 3y + 1
c
8
y
66
− 3y
65
+ ··· + 10590597y + 1142761
c
9
y
66
− 11y
65
+ ··· − 3y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.320550 + 0.945885I
a = −1.063260 − 0.335944I
b = −0.685686 + 0.247428I
0.80470 + 7.26585I 0
u = −0.320550 − 0.945885I
a = −1.063260 + 0.335944I
b = −0.685686 − 0.247428I
0.80470 − 7.26585I 0
u = −0.259011 + 0.962168I
a = −2.13062 + 1.40357I
b = −1.20371 + 0.85170I
5.56803 + 4.96269I 0
u = −0.259011 − 0.962168I
a = −2.13062 − 1.40357I
b = −1.20371 − 0.85170I
5.56803 − 4.96269I 0
u = −0.191816 + 0.964958I
a = −1.81489 + 1.32945I
b = −0.589613 + 0.207069I
6.29804 + 1.24184I 0
u = −0.191816 − 0.964958I
a = −1.81489 − 1.32945I
b = −0.589613 − 0.207069I
6.29804 − 1.24184I 0
u = 0.238535 + 0.917340I
a = −3.28193 − 3.26906I
b = −2.96619 − 1.22505I
3.70547 − 2.54918I 0
u = 0.238535 − 0.917340I
a = −3.28193 + 3.26906I
b = −2.96619 + 1.22505I
3.70547 + 2.54918I 0
u = −0.365061 + 0.991459I
a = 2.00582 − 1.50902I
b = 1.44867 − 0.39349I
4.89146 + 13.26630I 0
u = −0.365061 − 0.991459I
a = 2.00582 + 1.50902I
b = 1.44867 + 0.39349I
4.89146 − 13.26630I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.303217 + 0.885615I
a = 0.315243 − 0.014355I
b = 0.100769 − 0.435003I
1.36354 − 2.78002I 0
u = 0.303217 − 0.885615I
a = 0.315243 + 0.014355I
b = 0.100769 + 0.435003I
1.36354 + 2.78002I 0
u = −0.063187 + 0.925648I
a = 0.363461 + 0.619325I
b = 0.744300 − 0.157815I
3.48184 − 1.42801I 0
u = −0.063187 − 0.925648I
a = 0.363461 − 0.619325I
b = 0.744300 + 0.157815I
3.48184 + 1.42801I 0
u = 0.363535 + 1.037990I
a = 1.60954 + 0.96579I
b = 1.224800 − 0.068819I
3.57327 − 5.06511I 0
u = 0.363535 − 1.037990I
a = 1.60954 − 0.96579I
b = 1.224800 + 0.068819I
3.57327 + 5.06511I 0
u = 0.167951 + 0.857359I
a = 0.465621 + 1.190710I
b = 1.40004 + 0.77822I
2.98373 − 1.62353I 4.86404 + 6.61880I
u = 0.167951 − 0.857359I
a = 0.465621 − 1.190710I
b = 1.40004 − 0.77822I
2.98373 + 1.62353I 4.86404 − 6.61880I
u = 0.457424 + 0.731064I
a = 0.725928 + 0.706575I
b = −0.201103 − 0.033272I
1.12406 − 3.70601I 0. + 11.51127I
u = 0.457424 − 0.731064I
a = 0.725928 − 0.706575I
b = −0.201103 + 0.033272I
1.12406 + 3.70601I 0. − 11.51127I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.061425 + 1.191140I
a = 1.84871 − 0.38837I
b = 1.41998 + 0.05717I
8.29302 − 4.76690I 0
u = −0.061425 − 1.191140I
a = 1.84871 + 0.38837I
b = 1.41998 − 0.05717I
8.29302 + 4.76690I 0
u = −0.458535 + 0.561466I
a = 0.255118 − 0.554018I
b = −0.941274 + 0.566973I
2.41285 − 6.45141I −0.54002 + 2.68736I
u = −0.458535 − 0.561466I
a = 0.255118 + 0.554018I
b = −0.941274 − 0.566973I
2.41285 + 6.45141I −0.54002 − 2.68736I
u = −0.290297 + 0.626646I
a = 1.205330 − 0.394635I
b = 0.339995 − 0.557211I
−1.00030 − 1.44920I −4.20313 + 0.51290I
u = −0.290297 − 0.626646I
a = 1.205330 + 0.394635I
b = 0.339995 + 0.557211I
−1.00030 + 1.44920I −4.20313 − 0.51290I
u = 0.583780 + 0.292413I
a = 0.586657 + 0.798318I
b = −0.733275 − 0.248558I
−0.52146 − 1.81812I −11.1036 + 9.5392I
u = 0.583780 − 0.292413I
a = 0.586657 − 0.798318I
b = −0.733275 + 0.248558I
−0.52146 + 1.81812I −11.1036 − 9.5392I
u = 0.651823
a = −0.176116
b = −0.723296
−1.07816 −15.1890
u = −0.600823 + 0.187862I
a = 0.18260 − 1.64994I
b = −0.988132 + 0.036198I
1.26055 + 9.99441I −3.17960 − 8.12625I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.600823 − 0.187862I
a = 0.18260 + 1.64994I
b = −0.988132 − 0.036198I
1.26055 − 9.99441I −3.17960 + 8.12625I
u = −0.533895 + 0.131590I
a = −0.533306 + 1.262460I
b = −0.136821 + 0.638790I
−2.49763 + 4.35833I −7.38425 − 7.01489I
u = −0.533895 − 0.131590I
a = −0.533306 − 1.262460I
b = −0.136821 − 0.638790I
−2.49763 − 4.35833I −7.38425 + 7.01489I
u = 0.513633
a = 0.361156
b = −0.284384
−1.34771 −8.70160
u = −0.431584 + 0.169963I
a = 0.27177 + 2.35884I
b = 0.813624 + 0.264792I
2.09817 + 2.58100I −0.10269 − 8.35821I
u = −0.431584 − 0.169963I
a = 0.27177 − 2.35884I
b = 0.813624 − 0.264792I
2.09817 − 2.58100I −0.10269 + 8.35821I
u = 0.258905 + 0.380359I
a = 0.834851 + 0.121731I
b = −0.074634 − 0.484044I
−0.402527 − 1.133020I −5.71641 + 5.32128I
u = 0.258905 − 0.380359I
a = 0.834851 − 0.121731I
b = −0.074634 + 0.484044I
−0.402527 + 1.133020I −5.71641 − 5.32128I
u = 0.410014 + 0.063112I
a = 0.31651 − 4.71230I
b = 0.659200 + 0.694375I
0.701377 − 0.322381I 4.5634 − 19.7316I
u = 0.410014 − 0.063112I
a = 0.31651 + 4.71230I
b = 0.659200 − 0.694375I
0.701377 + 0.322381I 4.5634 + 19.7316I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04843 + 1.59433I
a = 1.042930 + 0.100093I
b = 1.64649 + 0.53314I
8.81067 − 5.43936I 0
u = 0.04843 − 1.59433I
a = 1.042930 − 0.100093I
b = 1.64649 − 0.53314I
8.81067 + 5.43936I 0
u = −0.261393 + 0.254743I
a = 0.680829 + 1.108350I
b = 1.102630 − 0.201893I
2.68024 − 0.40653I 3.06802 − 3.24326I
u = −0.261393 − 0.254743I
a = 0.680829 − 1.108350I
b = 1.102630 + 0.201893I
2.68024 + 0.40653I 3.06802 + 3.24326I
u = −0.02226 + 1.64012I
a = 0.931045 + 0.007675I
b = 2.06715 − 0.75388I
6.95676 − 0.72964I 0
u = −0.02226 − 1.64012I
a = 0.931045 − 0.007675I
b = 2.06715 + 0.75388I
6.95676 + 0.72964I 0
u = 0.04369 + 1.69093I
a = −0.088591 + 0.936388I
b = 0.56172 + 2.91859I
12.08540 − 2.44069I 0
u = 0.04369 − 1.69093I
a = −0.088591 − 0.936388I
b = 0.56172 − 2.91859I
12.08540 + 2.44069I 0
u = 0.07604 + 1.68991I
a = 0.257142 + 0.020404I
b = 0.672101 − 0.399751I
10.45740 − 4.23214I 0
u = 0.07604 − 1.68991I
a = 0.257142 − 0.020404I
b = 0.672101 + 0.399751I
10.45740 + 4.23214I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.06014 + 1.69901I
a = −3.27791 − 2.08492I
b = −8.79298 − 5.45875I
12.99110 − 3.71015I 0
u = 0.06014 − 1.69901I
a = −3.27791 + 2.08492I
b = −8.79298 + 5.45875I
12.99110 + 3.71015I 0
u = −0.02854 + 1.70099I
a = −0.082212 + 0.726413I
b = 0.298235 + 1.131330I
12.84170 − 0.97443I 0
u = −0.02854 − 1.70099I
a = −0.082212 − 0.726413I
b = 0.298235 − 1.131330I
12.84170 + 0.97443I 0
u = −0.08226 + 1.70288I
a = −0.697707 − 0.726127I
b = −1.83993 − 1.06056I
10.15510 + 8.84894I 0
u = −0.08226 − 1.70288I
a = −0.697707 + 0.726127I
b = −1.83993 + 1.06056I
10.15510 − 8.84894I 0
u = −0.06632 + 1.70870I
a = −2.25962 + 0.63483I
b = −5.34135 + 2.11063I
15.0454 + 6.2521I 0
u = −0.06632 − 1.70870I
a = −2.25962 − 0.63483I
b = −5.34135 − 2.11063I
15.0454 − 6.2521I 0
u = −0.05073 + 1.70963I
a = −2.20674 + 0.93195I
b = −4.97480 + 1.99997I
15.8171 + 2.2173I 0
u = −0.05073 − 1.70963I
a = −2.20674 − 0.93195I
b = −4.97480 − 1.99997I
15.8171 − 2.2173I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.09749 + 1.71480I
a = 2.26743 − 0.89318I
b = 5.56296 − 2.43902I
14.4372 + 15.1298I 0
u = −0.09749 − 1.71480I
a = 2.26743 + 0.89318I
b = 5.56296 + 2.43902I
14.4372 − 15.1298I 0
u = 0.09880 + 1.72557I
a = 1.89713 + 0.66588I
b = 4.74145 + 1.60013I
13.3360 − 6.9684I 0
u = 0.09880 − 1.72557I
a = 1.89713 − 0.66588I
b = 4.74145 − 1.60013I
13.3360 + 6.9684I 0
u = −0.00801 + 1.75235I
a = 2.28061 − 0.30206I
b = 5.66923 − 0.58870I
18.8528 − 4.5341I 0
u = −0.00801 − 1.75235I
a = 2.28061 + 0.30206I
b = 5.66923 + 0.58870I
18.8528 + 4.5341I 0
11
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u
66
− 11u
65
+ ··· − u + 1
c
2
, c
5
u
66
+ u
65
+ ··· + 11u + 1
c
3
u
66
− u
65
+ ··· + 116u − 8
c
4
u
66
+ u
65
+ ··· − 39u + 19
c
6
, c
7
, c
10
c
11
, c
12
u
66
− u
65
+ ··· − 3u + 1
c
8
u
66
− u
65
+ ··· − 1149u + 1069
c
9
u
66
+ 3u
65
+ ··· + u + 1
12
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y
66
− 3y
65
+ ··· − 11y + 1
c
2
, c
5
y
66
− 43y
65
+ ··· − 11y + 1
c
3
y
66
+ 53y
65
+ ··· − 18384y + 64
c
4
y
66
+ 69y
65
+ ··· + 17213y + 361
c
6
, c
7
, c
10
c
11
, c
12
y
66
+ 85y
65
+ ··· − 3y + 1
c
8
y
66
− 3y
65
+ ··· + 10590597y + 1142761
c
9
y
66
− 11y
65
+ ··· − 3y + 1
13
