12a
0984
(K12a
0984
)
A knot diagram
1
Linearized knot diagam
4 6 11 9 10 3 12 1 5 2 7 8
Solving Sequence
7,12
8
1,4
2 9 5 11 3 6 10
c
7
c
12
c
1
c
8
c
4
c
11
c
3
c
6
c
10
c
2
, c
5
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−5.50090 × 10
58
u
64
+ 1.26323 × 10
59
u
63
+ ··· + 2.01207 × 10
58
b − 1.19889 × 10
59
,
− 8.05777 × 10
57
u
64
− 9.65753 × 10
57
u
63
+ ··· + 2.01207 × 10
58
a + 2.45376 × 10
59
, u
65
− u
64
+ ··· + 15u + 1i
I
u
2
= h−u
12
+ 8u
10
− u
9
− 24u
8
+ 6u
7
+ 34u
6
− 12u
5
− 24u
4
+ 9u
3
+ 8u
2
+ b − 2u − 1,
u
13
− 10u
11
+ 2u
10
+ 39u
9
− 15u
8
− 74u
7
+ 40u
6
+ 70u
5
− 46u
4
− 31u
3
+ 24u
2
+ a + 5u − 6,
u
14
− 10u
12
+ u
11
+ 39u
10
− 8u
9
− 75u
8
+ 23u
7
+ 75u
6
− 29u
5
− 39u
4
+ 17u
3
+ 10u
2
− 5u − 1i
* 2 irreducible components of dim
C
= 0, with total 79 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−5.50×10
58
u
64
+1.26×10
59
u
63
+· · ·+2.01×10
58
b−1.20×10
59
, −8.06×
10
57
u
64
−9.66×10
57
u
63
+· · ·+2.01×10
58
a+2.45×10
59
, u
65
−u
64
+· · ·+15u+1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
0.400471u
64
+ 0.479979u
63
+ ··· − 6.74840u − 12.1952
2.73394u
64
− 6.27826u
63
+ ··· + 62.2065u + 5.95850
a
2
=
−1.62795u
64
+ 0.503503u
63
+ ··· − 247.503u − 7.75301
1.78903u
64
− 2.08762u
63
+ ··· + 55.9693u + 3.12673
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
0.863498u
64
− 0.649790u
63
+ ··· − 2.52825u − 10.4084
1.54027u
64
− 4.04431u
63
+ ··· + 38.9849u + 4.28279
a
11
=
−u
u
a
3
=
1.78938u
64
− 2.87215u
63
+ ··· + 30.0752u − 9.53132
1.34504u
64
− 2.92613u
63
+ ··· + 25.3829u + 3.29464
a
6
=
0.633467u
64
+ 0.762597u
63
+ ··· + 99.1976u − 8.80979
−0.359097u
64
− 0.374796u
63
+ ··· − 20.0580u + 0.472607
a
10
=
0.648781u
64
− 2.39549u
63
+ ··· + 0.850744u + 17.0104
2.20379u
64
− 2.48811u
63
+ ··· + 37.1721u + 0.459690
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.12410u
64
− 3.19508u
63
+ ··· − 2.97273u + 13.0445
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
65
− 10u
64
+ ··· − 646157u + 15851
c
2
, c
6
u
65
− 31u
63
+ ··· + 4u + 1
c
3
u
65
− 2u
64
+ ··· + 1806u − 14929
c
4
, c
5
, c
9
u
65
+ 2u
64
+ ··· + 81u − 1
c
7
, c
8
, c
11
c
12
u
65
+ u
64
+ ··· + 15u − 1
c
10
u
65
+ 3u
64
+ ··· − 18311u + 5039
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
65
+ 42y
64
+ ··· + 350419778635y −251254201
c
2
, c
6
y
65
− 62y
64
+ ··· − 446y −1
c
3
y
65
+ 34y
64
+ ··· + 1425607182y −222875041
c
4
, c
5
, c
9
y
65
− 74y
64
+ ··· + 6515y −1
c
7
, c
8
, c
11
c
12
y
65
− 85y
64
+ ··· − 125y −1
c
10
y
65
+ 27y
64
+ ··· + 94761095y −25391521
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.889757 + 0.433062I
a = 0.595422 − 0.198986I
b = 0.281933 + 0.547527I
7.58885 + 1.40904I 0
u = 0.889757 − 0.433062I
a = 0.595422 + 0.198986I
b = 0.281933 − 0.547527I
7.58885 − 1.40904I 0
u = 0.935679 + 0.430142I
a = −0.133556 + 0.252790I
b = 0.002645 + 1.300830I
5.78424 + 7.60090I 0
u = 0.935679 − 0.430142I
a = −0.133556 − 0.252790I
b = 0.002645 − 1.300830I
5.78424 − 7.60090I 0
u = −0.868051 + 0.564459I
a = −0.220898 − 0.124404I
b = 0.568115 − 0.720158I
4.84341 − 0.52476I 0
u = −0.868051 − 0.564459I
a = −0.220898 + 0.124404I
b = 0.568115 + 0.720158I
4.84341 + 0.52476I 0
u = 0.157396 + 0.936252I
a = −0.718874 − 0.451433I
b = −0.314810 − 0.120327I
9.74575 + 6.14975I 0
u = 0.157396 − 0.936252I
a = −0.718874 + 0.451433I
b = −0.314810 + 0.120327I
9.74575 − 6.14975I 0
u = −0.866334 + 0.387041I
a = 0.177626 + 0.667924I
b = −0.38134 − 1.60962I
7.62669 − 5.64553I 0
u = −0.866334 − 0.387041I
a = 0.177626 − 0.667924I
b = −0.38134 + 1.60962I
7.62669 + 5.64553I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.936520 + 0.039908I
a = −1.58250 − 0.14580I
b = 0.084560 − 1.007070I
11.75260 + 2.96607I 0
u = 0.936520 − 0.039908I
a = −1.58250 + 0.14580I
b = 0.084560 + 1.007070I
11.75260 − 2.96607I 0
u = −0.891446 + 0.041272I
a = −1.76473 − 0.50188I
b = 1.41399 + 1.40674I
11.30310 + 2.13802I 18.7856 − 3.2914I
u = −0.891446 − 0.041272I
a = −1.76473 + 0.50188I
b = 1.41399 − 1.40674I
11.30310 − 2.13802I 18.7856 + 3.2914I
u = −0.863593 + 0.206273I
a = 0.735499 + 0.727785I
b = −0.004341 + 1.321520I
4.72318 − 1.99911I 16.8500 + 4.6466I
u = −0.863593 − 0.206273I
a = 0.735499 − 0.727785I
b = −0.004341 − 1.321520I
4.72318 + 1.99911I 16.8500 − 4.6466I
u = 0.825189 + 0.164350I
a = 1.109760 − 0.001937I
b = −0.97431 − 1.02822I
4.60530 + 1.62841I 19.0869 − 5.0351I
u = 0.825189 − 0.164350I
a = 1.109760 + 0.001937I
b = −0.97431 + 1.02822I
4.60530 − 1.62841I 19.0869 + 5.0351I
u = 0.782280 + 0.256564I
a = −0.067172 + 0.264192I
b = 0.419229 − 1.239770I
1.05736 + 3.42824I 9.38737 − 8.82437I
u = 0.782280 − 0.256564I
a = −0.067172 − 0.264192I
b = 0.419229 + 1.239770I
1.05736 − 3.42824I 9.38737 + 8.82437I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.049540 + 0.559169I
a = −0.0045583 − 0.0656234I
b = 0.073399 + 1.340640I
13.4741 − 11.0913I 0
u = −1.049540 − 0.559169I
a = −0.0045583 + 0.0656234I
b = 0.073399 − 1.340640I
13.4741 + 11.0913I 0
u = −1.22679
a = −0.270827
b = −0.374892
2.39981 0
u = 0.952627 + 0.791056I
a = −0.0432079 + 0.0247757I
b = −0.402011 − 0.728715I
12.00730 − 0.38636I 0
u = 0.952627 − 0.791056I
a = −0.0432079 − 0.0247757I
b = −0.402011 + 0.728715I
12.00730 + 0.38636I 0
u = −0.096388 + 0.710673I
a = 0.837011 − 0.685506I
b = 0.488500 − 0.029172I
2.61549 − 3.79888I 9.89337 + 6.78663I
u = −0.096388 − 0.710673I
a = 0.837011 + 0.685506I
b = 0.488500 + 0.029172I
2.61549 + 3.79888I 9.89337 − 6.78663I
u = −0.706625 + 0.004243I
a = −0.326615 + 0.075243I
b = −0.438772 + 0.728388I
1.114370 + 0.096093I 9.80971 + 0.48102I
u = −0.706625 − 0.004243I
a = −0.326615 − 0.075243I
b = −0.438772 − 0.728388I
1.114370 − 0.096093I 9.80971 − 0.48102I
u = 1.30205
a = 0.756337
b = −0.949659
5.71531 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.011225 + 0.631699I
a = 1.173430 + 0.684067I
b = −0.243702 + 0.396416I
4.95418 + 2.21427I 8.45324 − 3.11503I
u = 0.011225 − 0.631699I
a = 1.173430 − 0.684067I
b = −0.243702 − 0.396416I
4.95418 − 2.21427I 8.45324 + 3.11503I
u = 1.46845
a = −0.187024
b = 1.14204
6.49904 0
u = −0.414265
a = 3.15526
b = −0.0379566
0.0573235 19.4200
u = 0.050717 + 0.407384I
a = −0.98626 + 1.37309I
b = 0.106234 + 0.222035I
−1.10170 − 1.06626I −0.72797 + 3.75877I
u = 0.050717 − 0.407384I
a = −0.98626 − 1.37309I
b = 0.106234 − 0.222035I
−1.10170 + 1.06626I −0.72797 − 3.75877I
u = −0.002304 + 0.351380I
a = −1.95027 − 1.37104I
b = −0.824432 + 0.186984I
2.13526 + 0.06396I 7.70510 + 0.30032I
u = −0.002304 − 0.351380I
a = −1.95027 + 1.37104I
b = −0.824432 − 0.186984I
2.13526 − 0.06396I 7.70510 − 0.30032I
u = −0.350174
a = −0.614828
b = −0.463481
0.719899 14.9890
u = 1.65272 + 0.01145I
a = 0.47953 + 1.86610I
b = −0.77556 − 2.58159I
9.51546 + 0.03244I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.65272 − 0.01145I
a = 0.47953 − 1.86610I
b = −0.77556 + 2.58159I
9.51546 − 0.03244I 0
u = −1.65709 + 0.05434I
a = −0.25689 − 2.19662I
b = 0.48205 + 2.85246I
9.61848 − 4.52679I 0
u = −1.65709 − 0.05434I
a = −0.25689 + 2.19662I
b = 0.48205 − 2.85246I
9.61848 + 4.52679I 0
u = −1.66991 + 0.04242I
a = 0.76197 − 1.61866I
b = −0.36741 + 2.21521I
13.41440 − 2.40644I 0
u = −1.66991 − 0.04242I
a = 0.76197 + 1.61866I
b = −0.36741 − 2.21521I
13.41440 + 2.40644I 0
u = 1.67767 + 0.09570I
a = 0.05955 − 2.48218I
b = −0.26406 + 3.07470I
16.5146 + 7.4665I 0
u = 1.67767 − 0.09570I
a = 0.05955 + 2.48218I
b = −0.26406 − 3.07470I
16.5146 − 7.4665I 0
u = 1.68402 + 0.05115I
a = −0.52918 + 2.34990I
b = 1.42152 − 3.59158I
13.74990 + 2.97652I 0
u = 1.68402 − 0.05115I
a = −0.52918 − 2.34990I
b = 1.42152 + 3.59158I
13.74990 − 2.97652I 0
u = 1.69185 + 0.00973I
a = −1.06345 + 1.76949I
b = 0.64856 − 2.29976I
−18.9704 − 1.9445I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.69185 − 0.00973I
a = −1.06345 − 1.76949I
b = 0.64856 + 2.29976I
−18.9704 + 1.9445I 0
u = −1.69453 + 0.10643I
a = −0.47342 + 1.38437I
b = 0.84199 − 2.02585I
16.6703 − 3.4851I 0
u = −1.69453 − 0.10643I
a = −0.47342 − 1.38437I
b = 0.84199 + 2.02585I
16.6703 + 3.4851I 0
u = −1.69423 + 0.11190I
a = 0.06318 + 2.21599I
b = −0.64443 − 3.30761I
14.9626 − 9.7162I 0
u = −1.69423 − 0.11190I
a = 0.06318 − 2.21599I
b = −0.64443 + 3.30761I
14.9626 + 9.7162I 0
u = 1.69496 + 0.13798I
a = −0.387962 − 1.341050I
b = 0.04223 + 2.01775I
13.8035 + 3.2283I 0
u = 1.69496 − 0.13798I
a = −0.387962 + 1.341050I
b = 0.04223 − 2.01775I
13.8035 − 3.2283I 0
u = −1.70249 + 0.00913I
a = 0.76510 − 1.62903I
b = −1.89492 + 2.45435I
−18.3078 − 3.1530I 0
u = −1.70249 − 0.00913I
a = 0.76510 + 1.62903I
b = −1.89492 − 2.45435I
−18.3078 + 3.1530I 0
u = 1.73019 + 0.15438I
a = 0.02330 + 2.05733I
b = 0.51225 − 3.00877I
−16.3366 + 14.0024I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.73019 − 0.15438I
a = 0.02330 − 2.05733I
b = 0.51225 + 3.00877I
−16.3366 − 14.0024I 0
u = −1.75668 + 0.21779I
a = 0.222757 − 1.210750I
b = 0.07750 + 1.91022I
−18.1051 − 3.7291I 0
u = −1.75668 − 0.21779I
a = 0.222757 + 1.210750I
b = 0.07750 − 1.91022I
−18.1051 + 3.7291I 0
u = −0.0432217 + 0.0807555I
a = −11.91410 − 0.09743I
b = 1.40737 − 0.33426I
8.63685 − 2.55255I 12.94052 − 1.53049I
u = −0.0432217 − 0.0807555I
a = −11.91410 + 0.09743I
b = 1.40737 + 0.33426I
8.63685 + 2.55255I 12.94052 + 1.53049I
11
II.
I
u
2
= h−u
12
+8u
10
+· · ·+b−1, u
13
−10u
11
+· · ·+a−6, u
14
−10u
12
+· · ·−5u−1i
(i) Arc colorings
a
7
=
1
0
a
12
=
0
u
a
8
=
1
−u
2
a
1
=
u
−u
3
+ u
a
4
=
−u
13
+ 10u
11
+ ··· − 5u + 6
u
12
− 8u
10
+ ··· + 2u + 1
a
2
=
−u
13
+ 10u
11
+ ··· − 5u + 5
−u
9
+ 6u
7
− 12u
5
+ 9u
3
− 2u
a
9
=
−u
2
+ 1
u
4
− 2u
2
a
5
=
−u
13
+ u
12
+ ··· − 5u + 7
u
11
− 7u
9
+ 17u
7
− 17u
5
+ 8u
3
− 3u
a
11
=
−u
u
a
3
=
−u
13
+ u
12
+ ··· − u + 7
u
3
− 2u
a
6
=
−u
13
+ 10u
11
+ ··· − 3u + 3
u
6
− 4u
4
+ 4u
2
a
10
=
−u
11
+ u
10
+ ··· + u − 5
u
13
− 9u
11
+ 31u
9
− 51u
7
+ 41u
5
− 15u
3
+ 3u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
3u
13
−u
12
−31u
11
+12u
10
+123u
9
−54u
8
−234u
7
+113u
6
+222u
5
−112u
4
−107u
3
+53u
2
+23u
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
14
+ 3u
13
+ ··· − u − 1
c
2
u
14
− 3u
13
+ ··· − 4u + 1
c
3
u
14
+ u
13
+ ··· − 2u + 1
c
4
, c
5
u
14
+ u
13
+ ··· + u − 1
c
6
u
14
+ 3u
13
+ ··· + 4u + 1
c
7
, c
8
u
14
− 10u
12
+ ··· − 5u − 1
c
9
u
14
− u
13
+ ··· − u − 1
c
10
u
14
+ 2u
13
+ ··· − u + 1
c
11
, c
12
u
14
− 10u
12
+ ··· + 5u − 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
14
+ 3y
13
+ ··· − 9y + 1
c
2
, c
6
y
14
− 17y
13
+ ··· − 60y + 1
c
3
y
14
+ 3y
13
+ ··· + 4y
3
+ 1
c
4
, c
5
, c
9
y
14
− 17y
13
+ ··· − y + 1
c
7
, c
8
, c
11
c
12
y
14
− 20y
13
+ ··· − 45y + 1
c
10
y
14
+ 4y
11
+ ··· + 3y + 1
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.968017 + 0.337938I
a = 1.078150 − 0.571014I
b = −0.709305 + 0.039438I
10.20040 − 0.82211I 14.2370 − 0.6203I
u = 0.968017 − 0.337938I
a = 1.078150 + 0.571014I
b = −0.709305 − 0.039438I
10.20040 + 0.82211I 14.2370 + 0.6203I
u = −1.14545
a = −0.563709
b = −0.155012
2.82868 18.6140
u = −0.720462 + 0.270481I
a = −0.628432 − 0.675348I
b = 0.656755 − 0.815273I
3.73792 − 1.01626I 11.08062 + 0.61543I
u = −0.720462 − 0.270481I
a = −0.628432 + 0.675348I
b = 0.656755 + 0.815273I
3.73792 + 1.01626I 11.08062 − 0.61543I
u = 0.558487 + 0.398529I
a = 0.112815 + 0.298362I
b = −1.03491 − 1.00628I
8.88600 + 3.51593I 15.2342 − 5.4123I
u = 0.558487 − 0.398529I
a = 0.112815 − 0.298362I
b = −1.03491 + 1.00628I
8.88600 − 3.51593I 15.2342 + 5.4123I
u = 1.37496
a = −0.439623
b = 1.10231
4.87233 7.57420
u = −1.64578 + 0.11762I
a = 0.89070 − 1.83826I
b = −0.91793 + 2.49252I
16.7686 − 5.4927I 16.7104 + 3.4526I
u = −1.64578 − 0.11762I
a = 0.89070 + 1.83826I
b = −0.91793 − 2.49252I
16.7686 + 5.4927I 16.7104 − 3.4526I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.66941 + 0.05921I
a = −0.19583 − 1.71092I
b = −0.33171 + 2.51769I
12.32760 + 2.20627I 11.06041 − 0.00050I
u = 1.66941 − 0.05921I
a = −0.19583 + 1.71092I
b = −0.33171 − 2.51769I
12.32760 − 2.20627I 11.06041 + 0.00050I
u = −1.72337
a = 0.416712
b = 0.220318
−19.0939 17.1450
u = −0.165484
a = 6.07182
b = 0.506584
−0.331903 −1.97830
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
14
+ 3u
13
+ ··· − u − 1)(u
65
− 10u
64
+ ··· − 646157u + 15851)
c
2
(u
14
− 3u
13
+ ··· − 4u + 1)(u
65
− 31u
63
+ ··· + 4u + 1)
c
3
(u
14
+ u
13
+ ··· − 2u + 1)(u
65
− 2u
64
+ ··· + 1806u − 14929)
c
4
, c
5
(u
14
+ u
13
+ ··· + u − 1)(u
65
+ 2u
64
+ ··· + 81u − 1)
c
6
(u
14
+ 3u
13
+ ··· + 4u + 1)(u
65
− 31u
63
+ ··· + 4u + 1)
c
7
, c
8
(u
14
− 10u
12
+ ··· − 5u − 1)(u
65
+ u
64
+ ··· + 15u − 1)
c
9
(u
14
− u
13
+ ··· − u − 1)(u
65
+ 2u
64
+ ··· + 81u − 1)
c
10
(u
14
+ 2u
13
+ ··· − u + 1)(u
65
+ 3u
64
+ ··· − 18311u + 5039)
c
11
, c
12
(u
14
− 10u
12
+ ··· + 5u − 1)(u
65
+ u
64
+ ··· + 15u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
14
+ 3y
13
+ ··· − 9y + 1)
· (y
65
+ 42y
64
+ ··· + 350419778635y −251254201)
c
2
, c
6
(y
14
− 17y
13
+ ··· − 60y + 1)(y
65
− 62y
64
+ ··· − 446y −1)
c
3
(y
14
+ 3y
13
+ ··· + 4y
3
+ 1)
· (y
65
+ 34y
64
+ ··· + 1425607182y −222875041)
c
4
, c
5
, c
9
(y
14
− 17y
13
+ ··· − y + 1)(y
65
− 74y
64
+ ··· + 6515y −1)
c
7
, c
8
, c
11
c
12
(y
14
− 20y
13
+ ··· − 45y + 1)(y
65
− 85y
64
+ ··· − 125y −1)
c
10
(y
14
+ 4y
11
+ ··· + 3y + 1)
· (y
65
+ 27y
64
+ ··· + 94761095y −25391521)
18
