12a
0912
(K12a
0912
)
A knot diagram
1
Linearized knot diagam
4 6 9 2 10 1 12 11 5 3 8 7
Solving Sequence
8,12
7 1
3,6
2 11 9 4 10 5
c
7
c
12
c
6
c
2
c
11
c
8
c
3
c
10
c
5
c
1
, c
4
, c
9
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.53538 × 10
34
u
61
− 7.35524 × 10
34
u
60
+ ··· + 5.78589 × 10
34
b − 5.61888 × 10
34
,
− 4.09242 × 10
34
u
61
− 8.12080 × 10
34
u
60
+ ··· + 5.78589 × 10
34
a − 5.99085 × 10
34
, u
62
+ 2u
61
+ ··· + 3u + 1i
I
u
2
= h−5u
3
+ 2u
2
+ 8b − 9u + 3, −5u
3
+ 2u
2
+ 8a − 9u + 3, u
4
− u
3
+ 3u
2
− 2u + 1i
* 2 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−3.54×10
34
u
61
−7.36×10
34
u
60
+· · ·+5.79×10
34
b−5.62×10
34
, −4.09×
10
34
u
61
−8.12×10
34
u
60
+· · ·+5.79×10
34
a−5.99×10
34
, u
62
+2u
61
+· · ·+3u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
0.707309u
61
+ 1.40355u
60
+ ··· − 3.00845u + 1.03542
0.611035u
61
+ 1.27124u
60
+ ··· + 3.64899u + 0.971135
a
6
=
u
2
+ 1
−u
4
− 2u
2
a
2
=
0.977767u
61
+ 2.00250u
60
+ ··· − 1.39856u + 1.95121
0.326563u
61
+ 0.628916u
60
+ ··· + 4.36630u + 1.06259
a
11
=
u
u
a
9
=
u
2
+ 1
u
2
a
4
=
1.05259u
61
+ 2.11420u
60
+ ··· − 0.201565u + 1.91539
0.291426u
61
+ 0.621179u
60
+ ··· + 2.89131u + 0.940203
a
10
=
−0.272512u
61
− 0.378181u
60
+ ··· − 1.40685u − 0.0919374
−0.0260682u
61
− 0.0324778u
60
+ ··· − 2.18207u − 0.262833
a
5
=
−0.272512u
61
− 0.378181u
60
+ ··· − 1.40685u − 0.0919374
0.193930u
61
+ 0.304148u
60
+ ··· + 2.41008u + 0.429675
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0309280u
61
+ 0.299984u
60
+ ··· + 28.0488u + 1.88545
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
u
62
− 5u
61
+ ··· − 321u + 64
c
2
8(8u
62
− 57u
61
+ ··· − 5508u + 7609)
c
3
8(8u
62
− 21u
61
+ ··· + 2370u + 179)
c
5
, c
9
u
62
+ 2u
61
+ ··· + 3u + 1
c
6
, c
7
, c
8
c
11
, c
12
u
62
− 2u
61
+ ··· − 3u + 1
c
10
u
62
+ 3u
61
+ ··· + 2496u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
62
− 31y
61
+ ··· + 34687y + 4096
c
2
64(64y
62
+ 223y
61
+ ··· + 7.95786 × 10
8
y + 5.78969 × 10
7
)
c
3
64(64y
62
− 2857y
61
+ ··· − 2988464y + 32041)
c
5
, c
9
y
62
− 34y
61
+ ··· − 5y + 1
c
6
, c
7
, c
8
c
11
, c
12
y
62
+ 82y
61
+ ··· − 5y + 1
c
10
y
62
− 27y
61
+ ··· − 9949184y + 1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.070453 + 1.008300I
a = 2.41201 − 2.05029I
b = 1.89323 − 2.09210I
3.75467 + 0.00521I 0
u = 0.070453 − 1.008300I
a = 2.41201 + 2.05029I
b = 1.89323 + 2.09210I
3.75467 − 0.00521I 0
u = 0.181790 + 0.945505I
a = 0.482726 − 0.006483I
b = −1.190670 − 0.035089I
2.30320 − 4.63639I 0
u = 0.181790 − 0.945505I
a = 0.482726 + 0.006483I
b = −1.190670 + 0.035089I
2.30320 + 4.63639I 0
u = −0.329924 + 1.002430I
a = 0.681675 + 0.062269I
b = 0.920280 + 1.043650I
7.11283 + 2.06836I 0
u = −0.329924 − 1.002430I
a = 0.681675 − 0.062269I
b = 0.920280 − 1.043650I
7.11283 − 2.06836I 0
u = −0.110698 + 0.915218I
a = −0.906019 + 0.382288I
b = 0.097013 + 0.988332I
0.59146 + 1.40911I 0
u = −0.110698 − 0.915218I
a = −0.906019 − 0.382288I
b = 0.097013 − 0.988332I
0.59146 − 1.40911I 0
u = −0.241171 + 1.079550I
a = −0.263274 − 0.708351I
b = 0.13064 − 2.22317I
8.23800 + 6.15877I 0
u = −0.241171 − 1.079550I
a = −0.263274 + 0.708351I
b = 0.13064 + 2.22317I
8.23800 − 6.15877I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.173893 + 1.094910I
a = 0.307305 − 0.647520I
b = −0.05498 − 1.49102I
4.39365 − 2.33302I 0
u = 0.173893 − 1.094910I
a = 0.307305 + 0.647520I
b = −0.05498 + 1.49102I
4.39365 + 2.33302I 0
u = 0.382128 + 1.060710I
a = −0.283114 + 0.498733I
b = −0.05935 + 1.53726I
1.82629 − 6.88277I 0
u = 0.382128 − 1.060710I
a = −0.283114 − 0.498733I
b = −0.05935 − 1.53726I
1.82629 + 6.88277I 0
u = −0.360863 + 1.083000I
a = 0.340097 + 0.839627I
b = 0.00161 + 2.17450I
5.31778 + 12.69260I 0
u = −0.360863 − 1.083000I
a = 0.340097 − 0.839627I
b = 0.00161 − 2.17450I
5.31778 − 12.69260I 0
u = −0.069609 + 0.834401I
a = −0.397322 + 0.616061I
b = 0.22387 + 2.04792I
0.09233 + 1.48715I −2.19079 − 3.99799I
u = −0.069609 − 0.834401I
a = −0.397322 − 0.616061I
b = 0.22387 − 2.04792I
0.09233 − 1.48715I −2.19079 + 3.99799I
u = 0.563401 + 0.581571I
a = 0.434752 − 0.199850I
b = −0.325684 + 0.214730I
−1.30352 − 0.70213I 1.08488 − 2.08211I
u = 0.563401 − 0.581571I
a = 0.434752 + 0.199850I
b = −0.325684 − 0.214730I
−1.30352 + 0.70213I 1.08488 + 2.08211I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.255043 + 1.200940I
a = −0.401233 − 0.467101I
b = −0.76852 − 1.23254I
6.76138 − 2.45433I 0
u = −0.255043 − 1.200940I
a = −0.401233 + 0.467101I
b = −0.76852 + 1.23254I
6.76138 + 2.45433I 0
u = −0.583913 + 0.454618I
a = −1.048110 − 0.044724I
b = 0.526648 + 0.216745I
1.44700 − 5.36748I −1.39491 + 3.36000I
u = −0.583913 − 0.454618I
a = −1.048110 + 0.044724I
b = 0.526648 − 0.216745I
1.44700 + 5.36748I −1.39491 − 3.36000I
u = 0.658726 + 0.253626I
a = −0.656410 + 0.567952I
b = 0.180230 − 0.443043I
−2.25995 − 3.35953I −4.38672 + 6.99367I
u = 0.658726 − 0.253626I
a = −0.656410 − 0.567952I
b = 0.180230 + 0.443043I
−2.25995 + 3.35953I −4.38672 − 6.99367I
u = −0.627368 + 0.304568I
a = 0.877042 + 0.926675I
b = −0.155103 − 0.758475I
0.99678 + 9.33410I −2.66606 − 8.39608I
u = −0.627368 − 0.304568I
a = 0.877042 − 0.926675I
b = −0.155103 + 0.758475I
0.99678 − 9.33410I −2.66606 + 8.39608I
u = −0.448611 + 0.353688I
a = −0.63018 − 1.63885I
b = 0.263806 + 0.539972I
3.76404 + 3.80466I 0.97266 − 6.48808I
u = −0.448611 − 0.353688I
a = −0.63018 + 1.63885I
b = 0.263806 − 0.539972I
3.76404 − 3.80466I 0.97266 + 6.48808I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.497757 + 0.225969I
a = 1.063150 + 0.042781I
b = −0.742489 − 0.206163I
3.37167 − 0.77892I 0.45056 − 2.40505I
u = −0.497757 − 0.225969I
a = 1.063150 − 0.042781I
b = −0.742489 + 0.206163I
3.37167 + 0.77892I 0.45056 + 2.40505I
u = 0.14026 + 1.52029I
a = 0.109842 − 0.293520I
b = 0.136239 − 0.648021I
5.58374 − 3.21684I 0
u = 0.14026 − 1.52029I
a = 0.109842 + 0.293520I
b = 0.136239 + 0.648021I
5.58374 + 3.21684I 0
u = 0.382370 + 0.144909I
a = −2.29821 − 1.74988I
b = −0.105131 + 0.442226I
−1.00840 − 2.70031I −7.30327 + 8.03455I
u = 0.382370 − 0.144909I
a = −2.29821 + 1.74988I
b = −0.105131 − 0.442226I
−1.00840 + 2.70031I −7.30327 − 8.03455I
u = 0.257995 + 0.303118I
a = −0.360406 − 0.861445I
b = −0.005399 + 0.393666I
−0.107004 − 0.841367I −2.66690 + 7.99137I
u = 0.257995 − 0.303118I
a = −0.360406 + 0.861445I
b = −0.005399 − 0.393666I
−0.107004 + 0.841367I −2.66690 − 7.99137I
u = 0.171710 + 0.316302I
a = −0.600051 − 0.117965I
b = 0.29575 + 1.66039I
−0.194780 + 0.812413I 0.93566 + 8.09045I
u = 0.171710 − 0.316302I
a = −0.600051 + 0.117965I
b = 0.29575 − 1.66039I
−0.194780 − 0.812413I 0.93566 − 8.09045I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.324588 + 0.004379I
a = 2.89984 − 0.03792I
b = 0.408718 + 0.019164I
−2.18849 + 0.0001I −8.36748 + 0.29865I
u = −0.324588 − 0.004379I
a = 2.89984 + 0.03792I
b = 0.408718 − 0.019164I
−2.18849 − 0.0001I −8.36748 − 0.29865I
u = −0.00897 + 1.69781I
a = −0.39272 − 3.11626I
b = −0.72887 − 4.08987I
9.22742 + 1.71660I 0
u = −0.00897 − 1.69781I
a = −0.39272 + 3.11626I
b = −0.72887 + 4.08987I
9.22742 − 1.71660I 0
u = −0.02316 + 1.70966I
a = −0.43712 − 1.36309I
b = −1.14797 − 1.80302I
10.01640 + 1.89978I 0
u = −0.02316 − 1.70966I
a = −0.43712 + 1.36309I
b = −1.14797 + 1.80302I
10.01640 − 1.89978I 0
u = 0.03865 + 1.71177I
a = 1.64069 + 0.08478I
b = 2.76769 + 0.00130I
11.79830 − 5.46026I 0
u = 0.03865 − 1.71177I
a = 1.64069 − 0.08478I
b = 2.76769 − 0.00130I
11.79830 + 5.46026I 0
u = −0.09249 + 1.72353I
a = −1.00407 − 1.43069I
b = −0.84968 − 2.10785I
16.7807 + 3.8111I 0
u = −0.09249 − 1.72353I
a = −1.00407 + 1.43069I
b = −0.84968 + 2.10785I
16.7807 − 3.8111I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.01534 + 1.72861I
a = −3.06068 + 1.08280I
b = −2.72644 + 1.01992I
13.59990 − 0.32504I 0
u = 0.01534 − 1.72861I
a = −3.06068 − 1.08280I
b = −2.72644 − 1.01992I
13.59990 + 0.32504I 0
u = 0.10151 + 1.73858I
a = 0.30042 − 2.09901I
b = −0.09887 − 2.80202I
11.7585 − 8.8832I 0
u = 0.10151 − 1.73858I
a = 0.30042 + 2.09901I
b = −0.09887 + 2.80202I
11.7585 + 8.8832I 0
u = −0.06180 + 1.74280I
a = 0.02606 + 2.99792I
b = −0.42662 + 4.03827I
18.3544 + 7.4189I 0
u = −0.06180 − 1.74280I
a = 0.02606 − 2.99792I
b = −0.42662 − 4.03827I
18.3544 − 7.4189I 0
u = −0.09644 + 1.74449I
a = −0.35373 − 2.76349I
b = 0.12777 − 3.62070I
15.3794 + 14.6067I 0
u = −0.09644 − 1.74449I
a = −0.35373 + 2.76349I
b = 0.12777 + 3.62070I
15.3794 − 14.6067I 0
u = 0.04860 + 1.74694I
a = −0.05763 + 2.17932I
b = 0.31904 + 2.84558I
14.6212 − 3.2967I 0
u = 0.04860 − 1.74694I
a = −0.05763 − 2.17932I
b = 0.31904 − 2.84558I
14.6212 + 3.2967I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.05441 + 1.76916I
a = 0.76218 + 1.84328I
b = 0.78075 + 2.48268I
17.4935 − 1.1900I 0
u = −0.05441 − 1.76916I
a = 0.76218 − 1.84328I
b = 0.78075 − 2.48268I
17.4935 + 1.1900I 0
11
II.
I
u
2
= h−5u
3
+2u
2
+8b−9u+3, −5u
3
+2u
2
+8a−9u+3, u
4
−u
3
+3u
2
−2u+1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
7
=
1
−u
2
a
1
=
−u
u
3
+ u
a
3
=
5
8
u
3
−
1
4
u
2
+
9
8
u −
3
8
5
8
u
3
−
1
4
u
2
+
9
8
u −
3
8
a
6
=
u
2
+ 1
−u
3
+ u
2
− 2u + 1
a
2
=
7
8
u
3
−
3
4
u
2
+
11
8
u −
9
8
5
4
u
3
−
1
2
u
2
+
9
4
u −
3
4
a
11
=
u
u
a
9
=
u
2
+ 1
u
2
a
4
=
7
8
u
3
−
3
4
u
2
+
19
8
u −
9
8
1
4
u
3
−
1
2
u
2
+
5
4
u −
3
4
a
10
=
u
u
a
5
=
u
−u
3
− u
(ii) Obstruction class = 1
(iii) Cusp Shapes =
279
64
u
3
−
51
32
u
2
+
731
64
u −
609
64
12
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u − 1)
4
c
2
8(8u
4
− 15u
3
+ 12u
2
− 5u + 1)
c
3
8(8u
4
− 3u
3
+ 6u
2
− u + 1)
c
4
(u + 1)
4
c
5
u
4
− u
3
+ u
2
+ 1
c
6
, c
7
, c
8
u
4
− u
3
+ 3u
2
− 2u + 1
c
9
u
4
+ u
3
+ u
2
+ 1
c
10
u
4
c
11
, c
12
u
4
+ u
3
+ 3u
2
+ 2u + 1
13
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
(y −1)
4
c
2
64(64y
4
− 33y
3
+ 10y
2
− y + 1)
c
3
64(64y
4
+ 87y
3
+ 46y
2
+ 11y + 1)
c
5
, c
9
y
4
+ y
3
+ 3y
2
+ 2y + 1
c
6
, c
7
, c
8
c
11
, c
12
y
4
+ 5y
3
+ 7y
2
+ 2y + 1
c
10
y
4
14
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.395123 + 0.506844I
a = −0.057058 + 0.537058I
b = −0.057058 + 0.537058I
−1.85594 − 1.41510I −5.90053 + 5.61802I
u = 0.395123 − 0.506844I
a = −0.057058 − 0.537058I
b = −0.057058 − 0.537058I
−1.85594 + 1.41510I −5.90053 − 5.61802I
u = 0.10488 + 1.55249I
a = −0.130442 − 0.641504I
b = −0.130442 − 0.641504I
5.14581 − 3.16396I −7.79478 + 1.12451I
u = 0.10488 − 1.55249I
a = −0.130442 + 0.641504I
b = −0.130442 + 0.641504I
5.14581 + 3.16396I −7.79478 − 1.12451I
15
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
4
)(u
62
− 5u
61
+ ··· − 321u + 64)
c
2
64(8u
4
− 15u
3
+ ··· − 5u + 1)(8u
62
− 57u
61
+ ··· − 5508u + 7609)
c
3
64(8u
4
− 3u
3
+ ··· − u + 1)(8u
62
− 21u
61
+ ··· + 2370u + 179)
c
4
((u + 1)
4
)(u
62
− 5u
61
+ ··· − 321u + 64)
c
5
(u
4
− u
3
+ u
2
+ 1)(u
62
+ 2u
61
+ ··· + 3u + 1)
c
6
, c
7
, c
8
(u
4
− u
3
+ 3u
2
− 2u + 1)(u
62
− 2u
61
+ ··· − 3u + 1)
c
9
(u
4
+ u
3
+ u
2
+ 1)(u
62
+ 2u
61
+ ··· + 3u + 1)
c
10
u
4
(u
62
+ 3u
61
+ ··· + 2496u + 1024)
c
11
, c
12
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
62
− 2u
61
+ ··· − 3u + 1)
16
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
4
((y −1)
4
)(y
62
− 31y
61
+ ··· + 34687y + 4096)
c
2
4096(64y
4
− 33y
3
+ 10y
2
− y + 1)
· (64y
62
+ 223y
61
+ ··· + 795786284y + 57896881)
c
3
4096(64y
4
+ 87y
3
+ 46y
2
+ 11y + 1)
· (64y
62
− 2857y
61
+ ··· − 2988464y + 32041)
c
5
, c
9
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
62
− 34y
61
+ ··· − 5y + 1)
c
6
, c
7
, c
8
c
11
, c
12
(y
4
+ 5y
3
+ 7y
2
+ 2y + 1)(y
62
+ 82y
61
+ ··· − 5y + 1)
c
10
y
4
(y
62
− 27y
61
+ ··· − 9949184y + 1048576)
17
