12a
0153
(K12a
0153
)
A knot diagram
1
Linearized knot diagam
3 5 9 2 10 12 11 1 4 8 7 6
Solving Sequence
3,9
4
5,10
6 2 1 8 11 7 12
c
3
c
9
c
5
c
2
c
1
c
8
c
10
c
7
c
12
c
4
, c
6
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h5.60722 × 10
81
u
57
+ 1.67247 × 10
81
u
56
+ ··· + 2.33772 × 10
82
b + 1.81103 × 10
83
,
7.27818 × 10
82
u
57
+ 4.91560 × 10
82
u
56
+ ··· + 1.87018 × 10
83
a + 1.91879 × 10
84
, u
58
+ u
57
+ ··· + 64u + 32i
I
v
1
= ha, b − 1, v
5
− v
4
+ v
2
+ v −1i
* 2 irreducible components of dim
C
= 0, with total 63 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
=
h5.61×10
81
u
57
+1.67×10
81
u
56
+· · ·+2.34×10
82
b+1.81×10
83
, 7.28×10
82
u
57
+
4.92 × 10
82
u
56
+ · · · + 1.87 × 10
83
a + 1.92 × 10
84
, u
58
+ u
57
+ · · · + 64u + 32i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
5
=
−0.389171u
57
− 0.262841u
56
+ ··· + 4.54781u − 10.2600
−0.239859u
57
− 0.0715429u
56
+ ··· − 7.02146u − 7.74698
a
10
=
u
−u
3
+ u
a
6
=
−0.522817u
57
− 0.268126u
56
+ ··· − 1.68093u − 13.8759
−0.207902u
57
− 0.0373370u
56
+ ··· − 9.31175u − 7.25535
a
2
=
−0.389171u
57
− 0.262841u
56
+ ··· + 4.54781u − 10.2600
0.420518u
57
+ 0.181191u
56
+ ··· + 2.65309u + 11.7895
a
1
=
0.0313472u
57
− 0.0816505u
56
+ ··· + 7.20090u + 1.52957
0.420518u
57
+ 0.181191u
56
+ ··· + 2.65309u + 11.7895
a
8
=
−0.713059u
57
+ 0.0359583u
56
+ ··· − 41.8715u − 42.2736
−0.0618638u
57
+ 0.0517051u
56
+ ··· − 0.420514u + 0.205394
a
11
=
0.427906u
57
+ 0.0462409u
56
+ ··· + 18.0771u + 11.5849
−0.749808u
57
+ 0.0101401u
56
+ ··· − 32.6805u − 32.2330
a
7
=
0.393422u
57
+ 0.397378u
56
+ ··· − 1.00737u + 23.9064
−0.558340u
57
− 0.192853u
56
+ ··· − 13.8407u − 26.9810
a
12
=
0.460418u
57
+ 0.147034u
56
+ ··· + 20.1920u + 18.9774
−0.416036u
57
− 0.145859u
56
+ ··· − 7.89835u − 13.2725
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2.02102u
57
− 0.114366u
56
+ ··· − 107.539u − 65.1509
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
58
+ 26u
57
+ ··· + 36u + 1
c
2
, c
4
u
58
− 6u
57
+ ··· + 12u − 1
c
3
, c
9
u
58
− u
57
+ ··· − 64u + 32
c
5
, c
8
u
58
+ 2u
57
+ ··· − 1314u − 445
c
6
, c
7
, c
10
c
11
, c
12
u
58
+ 2u
57
+ ··· − 2u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
58
+ 18y
57
+ ··· − 1608y + 1
c
2
, c
4
y
58
− 26y
57
+ ··· − 36y + 1
c
3
, c
9
y
58
− 33y
57
+ ··· − 19968y + 1024
c
5
, c
8
y
58
− 38y
57
+ ··· + 2799054y + 198025
c
6
, c
7
, c
10
c
11
, c
12
y
58
+ 74y
57
+ ··· + 6y + 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.988918 + 0.213289I
a = 0.430565 + 0.018643I
b = 1.318190 − 0.100375I
−11.06150 − 4.52126I 2.64115 + 3.57478I
u = −0.988918 − 0.213289I
a = 0.430565 − 0.018643I
b = 1.318190 + 0.100375I
−11.06150 + 4.52126I 2.64115 − 3.57478I
u = −1.012520 + 0.149144I
a = 0.62352 + 1.58705I
b = −0.785549 − 0.545845I
1.31063 − 0.82722I 9.15613 − 0.70745I
u = −1.012520 − 0.149144I
a = 0.62352 − 1.58705I
b = −0.785549 + 0.545845I
1.31063 + 0.82722I 9.15613 + 0.70745I
u = 0.670998 + 0.708770I
a = 0.455472 − 0.072472I
b = 1.141310 + 0.340713I
−14.4352 − 1.2271I −2.32982 + 0.23811I
u = 0.670998 − 0.708770I
a = 0.455472 + 0.072472I
b = 1.141310 − 0.340713I
−14.4352 + 1.2271I −2.32982 − 0.23811I
u = 0.120330 + 1.017630I
a = 0.516133 − 0.162101I
b = 0.763532 + 0.553870I
−0.454989 + 0.856173I 4.39334 − 1.34405I
u = 0.120330 − 1.017630I
a = 0.516133 + 0.162101I
b = 0.763532 − 0.553870I
−0.454989 − 0.856173I 4.39334 + 1.34405I
u = −0.023513 + 1.056290I
a = 0.524037 + 0.186326I
b = 0.694092 − 0.602349I
−9.08024 − 2.35274I 2.89470 − 0.08369I
u = −0.023513 − 1.056290I
a = 0.524037 − 0.186326I
b = 0.694092 + 0.602349I
−9.08024 + 2.35274I 2.89470 + 0.08369I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.926509 + 0.140364I
a = 0.436398 − 0.012440I
b = 1.289630 + 0.065266I
−2.19660 + 2.97198I 4.77337 − 5.16018I
u = 0.926509 − 0.140364I
a = 0.436398 + 0.012440I
b = 1.289630 − 0.065266I
−2.19660 − 2.97198I 4.77337 + 5.16018I
u = −0.229073 + 1.043540I
a = 0.495133 + 0.149970I
b = 0.849943 − 0.560327I
1.83802 + 2.24390I 9.07567 − 3.44705I
u = −0.229073 − 1.043540I
a = 0.495133 − 0.149970I
b = 0.849943 + 0.560327I
1.83802 − 2.24390I 9.07567 + 3.44705I
u = −0.898579
a = 0.439075
b = 1.27751
0.376807 11.1020
u = 0.970754 + 0.521236I
a = −0.18922 − 2.00022I
b = −1.046870 + 0.495511I
−13.4454 + 5.9801I 0. − 6.24129I
u = 0.970754 − 0.521236I
a = −0.18922 + 2.00022I
b = −1.046870 − 0.495511I
−13.4454 − 5.9801I 0. + 6.24129I
u = 0.312376 + 1.070610I
a = 0.479995 − 0.143589I
b = 0.912231 + 0.572038I
−0.92817 − 5.38733I 3.26193 + 6.82724I
u = 0.312376 − 1.070610I
a = 0.479995 + 0.143589I
b = 0.912231 − 0.572038I
−0.92817 + 5.38733I 3.26193 − 6.82724I
u = 1.079810 + 0.293215I
a = 0.28949 − 1.67352I
b = −0.899638 + 0.580183I
0.92519 + 3.70734I 7.01990 − 7.67884I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.079810 − 0.293215I
a = 0.28949 + 1.67352I
b = −0.899638 − 0.580183I
0.92519 − 3.70734I 7.01990 + 7.67884I
u = −1.025060 + 0.450289I
a = −0.00985 + 1.87728I
b = −1.002790 − 0.532670I
−3.60799 − 5.37901I 0. + 6.85674I
u = −1.025060 − 0.450289I
a = −0.00985 − 1.87728I
b = −1.002790 + 0.532670I
−3.60799 + 5.37901I 0. − 6.85674I
u = −0.616932 + 0.596574I
a = 0.766075 − 0.434828I
b = −0.012721 + 0.560385I
−11.10310 − 2.21498I 3.03458 + 3.08140I
u = −0.616932 − 0.596574I
a = 0.766075 + 0.434828I
b = −0.012721 − 0.560385I
−11.10310 + 2.21498I 3.03458 − 3.08140I
u = −0.561331 + 0.640996I
a = 0.470504 + 0.066767I
b = 1.083430 − 0.295649I
−5.09839 + 1.07706I −3.30982 − 0.29304I
u = −0.561331 − 0.640996I
a = 0.470504 − 0.066767I
b = 1.083430 + 0.295649I
−5.09839 − 1.07706I −3.30982 + 0.29304I
u = −0.365820 + 1.106240I
a = 0.469197 + 0.142290I
b = 0.951796 − 0.591908I
−9.86525 + 7.09450I 0. − 5.09520I
u = −0.365820 − 1.106240I
a = 0.469197 − 0.142290I
b = 0.951796 + 0.591908I
−9.86525 − 7.09450I 0. + 5.09520I
u = 0.821553 + 0.120863I
a = 1.20206 − 1.80781I
b = −0.744954 + 0.383569I
−2.46309 − 1.43775I 4.26235 + 0.30434I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.821553 − 0.120863I
a = 1.20206 + 1.80781I
b = −0.744954 − 0.383569I
−2.46309 + 1.43775I 4.26235 − 0.30434I
u = −0.727877 + 0.161089I
a = 1.58949 + 2.25794I
b = −0.791536 − 0.296132I
−11.94240 + 2.62554I 4.16578 + 2.14464I
u = −0.727877 − 0.161089I
a = 1.58949 − 2.25794I
b = −0.791536 + 0.296132I
−11.94240 − 2.62554I 4.16578 − 2.14464I
u = 0.518918 + 0.402182I
a = 0.931285 + 0.375334I
b = −0.076260 − 0.372294I
−2.01038 + 1.63657I 4.07721 − 4.69025I
u = 0.518918 − 0.402182I
a = 0.931285 − 0.375334I
b = −0.076260 + 0.372294I
−2.01038 − 1.63657I 4.07721 + 4.69025I
u = −1.336420 + 0.272826I
a = 0.447495 − 0.910443I
b = −0.565183 + 0.884648I
4.83453 + 1.13962I 0
u = −1.336420 − 0.272826I
a = 0.447495 + 0.910443I
b = −0.565183 − 0.884648I
4.83453 − 1.13962I 0
u = 1.329630 + 0.349002I
a = 0.459401 + 0.858056I
b = −0.515046 − 0.905782I
7.02632 + 2.30073I 0
u = 1.329630 − 0.349002I
a = 0.459401 − 0.858056I
b = −0.515046 + 0.905782I
7.02632 − 2.30073I 0
u = −1.316660 + 0.413705I
a = 0.469503 − 0.816218I
b = −0.470472 + 0.920569I
4.18115 − 5.70575I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.316660 − 0.413705I
a = 0.469503 + 0.816218I
b = −0.470472 − 0.920569I
4.18115 + 5.70575I 0
u = 1.377690 + 0.196979I
a = 0.403381 + 0.956988I
b = −0.625994 − 0.887297I
−3.49813 − 2.89761I 0
u = 1.377690 − 0.196979I
a = 0.403381 − 0.956988I
b = −0.625994 + 0.887297I
−3.49813 + 2.89761I 0
u = 1.317010 + 0.468560I
a = 0.468183 + 0.782796I
b = −0.437256 − 0.940900I
−4.76531 + 7.61575I 0
u = 1.317010 − 0.468560I
a = 0.468183 − 0.782796I
b = −0.437256 + 0.940900I
−4.76531 − 7.61575I 0
u = 1.296970 + 0.533749I
a = −0.15451 − 1.41849I
b = −1.075890 + 0.696711I
3.27838 + 4.69767I 0
u = 1.296970 − 0.533749I
a = −0.15451 + 1.41849I
b = −1.075890 − 0.696711I
3.27838 − 4.69767I 0
u = −1.336730 + 0.459923I
a = −0.067104 + 1.368720I
b = −1.035730 − 0.728859I
−4.74657 − 3.04886I 0
u = −1.336730 − 0.459923I
a = −0.067104 − 1.368720I
b = −1.035730 + 0.728859I
−4.74657 + 3.04886I 0
u = −1.29402 + 0.59257I
a = −0.22697 + 1.41455I
b = −1.110590 − 0.689193I
5.21330 − 8.16966I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.29402 − 0.59257I
a = −0.22697 − 1.41455I
b = −1.110590 + 0.689193I
5.21330 + 8.16966I 0
u = 1.28224 + 0.63700I
a = −0.28338 − 1.41775I
b = −1.135570 + 0.678245I
2.15742 + 11.57290I 0
u = 1.28224 − 0.63700I
a = −0.28338 + 1.41775I
b = −1.135570 − 0.678245I
2.15742 − 11.57290I 0
u = −1.27688 + 0.67254I
a = −0.32722 + 1.41208I
b = −1.155740 − 0.672085I
−6.9557 − 13.5111I 0
u = −1.27688 − 0.67254I
a = −0.32722 − 1.41208I
b = −1.155740 + 0.672085I
−6.9557 + 13.5111I 0
u = 0.233547 + 0.502739I
a = 0.516311 − 0.040838I
b = 0.924775 + 0.152243I
−1.61764 − 0.55942I −2.71688 + 2.11275I
u = 0.233547 − 0.502739I
a = 0.516311 + 0.040838I
b = 0.924775 − 0.152243I
−1.61764 + 0.55942I −2.71688 − 2.11275I
u = −0.394574
a = 1.19015
b = −0.159767
0.637461 15.7740
10
II. I
v
1
= ha, b − 1, v
5
− v
4
+ v
2
+ v − 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
v
0
a
4
=
1
0
a
5
=
0
1
a
10
=
v
0
a
6
=
v
2
1
a
2
=
1
−1
a
1
=
0
−1
a
8
=
v
v
a
11
=
−v
3
+ v
−v
3
a
7
=
v
4
− v
3
− v
2
+ 1
v
4
− v
2
+ 1
a
12
=
v
4
v
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3v
4
− 4v
2
+ 3v + 4
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
5
c
3
, c
9
u
5
c
4
(u + 1)
5
c
5
, c
8
u
5
+ u
4
− u
2
+ u + 1
c
6
, c
7
u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1
c
10
, c
11
, c
12
u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
5
c
3
, c
9
y
5
c
5
, c
8
y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1
c
6
, c
7
, c
10
c
11
, c
12
y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.758138 + 0.584034I
a = 0
b = 1.00000
−3.46474 − 2.21397I −1.39794 + 4.05273I
v = −0.758138 − 0.584034I
a = 0
b = 1.00000
−3.46474 + 2.21397I −1.39794 − 4.05273I
v = 0.935538 + 0.903908I
a = 0
b = 1.00000
−12.60320 + 3.33174I −1.99723 − 3.46299I
v = 0.935538 − 0.903908I
a = 0
b = 1.00000
−12.60320 − 3.33174I −1.99723 + 3.46299I
v = 0.645200
a = 0
b = 1.00000
−0.762751 4.79030
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
5
)(u
58
+ 26u
57
+ ··· + 36u + 1)
c
2
((u − 1)
5
)(u
58
− 6u
57
+ ··· + 12u − 1)
c
3
, c
9
u
5
(u
58
− u
57
+ ··· − 64u + 32)
c
4
((u + 1)
5
)(u
58
− 6u
57
+ ··· + 12u − 1)
c
5
, c
8
(u
5
+ u
4
− u
2
+ u + 1)(u
58
+ 2u
57
+ ··· − 1314u − 445)
c
6
, c
7
(u
5
+ u
4
+ 4u
3
+ 3u
2
+ 3u + 1)(u
58
+ 2u
57
+ ··· − 2u − 1)
c
10
, c
11
, c
12
(u
5
− u
4
+ 4u
3
− 3u
2
+ 3u − 1)(u
58
+ 2u
57
+ ··· − 2u − 1)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
5
)(y
58
+ 18y
57
+ ··· − 1608y + 1)
c
2
, c
4
((y − 1)
5
)(y
58
− 26y
57
+ ··· − 36y + 1)
c
3
, c
9
y
5
(y
58
− 33y
57
+ ··· − 19968y + 1024)
c
5
, c
8
(y
5
− y
4
+ 4y
3
− 3y
2
+ 3y − 1)
· (y
58
− 38y
57
+ ··· + 2799054y + 198025)
c
6
, c
7
, c
10
c
11
, c
12
(y
5
+ 7y
4
+ 16y
3
+ 13y
2
+ 3y − 1)(y
58
+ 74y
57
+ ··· + 6y + 1)
16
