12a
0205
(K12a
0205
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 11 2 4 12 1 5 10 9
Solving Sequence
8,12
9 1
5,10
4 7 3 11 6 2
c
8
c
12
c
9
c
4
c
7
c
3
c
11
c
5
c
2
c
1
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h251u
73
+ 1168u
72
+ ··· + 4b − 189, −50u
73
− 201u
72
+ ··· + 4a + 23, u
74
+ 6u
73
+ ··· − 4u − 1i
I
u
2
= hb
5
− b
4
− 2b
3
+ b
2
+ b + 1, a, u − 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
= h251u
73
+ 1168u
72
+ · · · + 4b − 189, −50u
73
− 201u
72
+ · · · + 4a +
23, u
74
+ 6u
73
+ · · · − 4u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
u
a
9
=
1
u
2
a
1
=
−u
−u
3
+ u
a
5
=
25
2
u
73
+
201
4
u
72
+ ··· −
25
2
u −
23
4
−
251
4
u
73
− 292u
72
+ ··· +
307
2
u +
189
4
a
10
=
−u
2
+ 1
−u
4
+ 2u
2
a
4
=
−
201
4
u
73
−
967
4
u
72
+ ··· + 141u +
83
2
−
251
4
u
73
− 292u
72
+ ··· +
307
2
u +
189
4
a
7
=
0.0625000u
73
+ 0.312500u
72
+ ··· − 4.18750u + 1.93750
0.0625000u
73
+ 0.312500u
72
+ ··· − 1.18750u − 0.0625000
a
3
=
−30.5625u
73
− 147.813u
72
+ ··· + 90.4375u + 26.3125
30.9375u
73
+ 143.938u
72
+ ··· − 72.8125u − 22.1875
a
11
=
u
5
− 2u
3
+ u
u
7
− 3u
5
+ 2u
3
+ u
a
6
=
25
2
u
73
+
269
4
u
72
+ ··· −
71
2
u −
59
4
−
249
4
u
73
−
1131
4
u
72
+ ··· + 141u +
85
2
a
2
=
−15.1875u
73
− 73.6875u
72
+ ··· + 49.3125u + 12.1875
−19.2500u
73
− 93.6250u
72
+ ··· + 54.7500u + 16.8750
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
177
4
u
73
−
1667
8
u
72
+ ··· +
477
4
u +
241
8
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
74
+ 42u
73
+ ··· − 2u + 1
c
2
, c
6
u
74
− 2u
73
+ ··· − 2u − 1
c
3
, c
4
, c
7
u
74
+ 2u
73
+ ··· + 84u − 17
c
5
, c
10
u
74
+ u
73
+ ··· + 96u + 32
c
8
, c
9
, c
12
u
74
− 6u
73
+ ··· + 4u − 1
c
11
u
74
+ 33u
73
+ ··· + 7680u + 1024
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
74
− 18y
73
+ ··· − 70y + 1
c
2
, c
6
y
74
+ 42y
73
+ ··· − 2y + 1
c
3
, c
4
, c
7
y
74
− 78y
73
+ ··· − 14298y + 289
c
5
, c
10
y
74
− 33y
73
+ ··· − 7680y + 1024
c
8
, c
9
, c
12
y
74
− 66y
73
+ ··· − 4y + 1
c
11
y
74
+ 7y
73
+ ··· − 12189696y + 1048576
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.881128 + 0.574262I
a = −0.392145 − 0.461104I
b = 1.51995 + 0.06899I
−10.03960 − 3.52098I 0
u = 0.881128 − 0.574262I
a = −0.392145 + 0.461104I
b = 1.51995 − 0.06899I
−10.03960 + 3.52098I 0
u = 0.988283 + 0.362341I
a = 0.732096 − 0.013015I
b = −0.662384 + 0.595002I
−2.23570 + 2.76072I 0
u = 0.988283 − 0.362341I
a = 0.732096 + 0.013015I
b = −0.662384 − 0.595002I
−2.23570 − 2.76072I 0
u = 0.900199 + 0.549025I
a = 0.478227 + 0.417353I
b = −1.45382 + 0.10364I
−6.21271 + 1.04580I 0
u = 0.900199 − 0.549025I
a = 0.478227 − 0.417353I
b = −1.45382 − 0.10364I
−6.21271 − 1.04580I 0
u = 0.925360 + 0.561900I
a = −0.535816 − 0.483396I
b = 1.59118 − 0.20476I
−9.79897 + 5.80428I 0
u = 0.925360 − 0.561900I
a = −0.535816 + 0.483396I
b = 1.59118 + 0.20476I
−9.79897 − 5.80428I 0
u = 0.287137 + 0.859379I
a = −1.13110 − 1.36816I
b = 1.62687 + 0.25833I
−7.84795 − 10.78640I 0
u = 0.287137 − 0.859379I
a = −1.13110 + 1.36816I
b = 1.62687 − 0.25833I
−7.84795 + 10.78640I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.314792 + 0.842150I
a = −1.08527 − 1.22153I
b = 1.48731 + 0.00206I
−8.30896 − 1.43299I 0
u = 0.314792 − 0.842150I
a = −1.08527 + 1.22153I
b = 1.48731 − 0.00206I
−8.30896 + 1.43299I 0
u = 0.292088 + 0.841513I
a = 1.05644 + 1.32316I
b = −1.47219 − 0.19833I
−4.34649 − 5.92708I 0
u = 0.292088 − 0.841513I
a = 1.05644 − 1.32316I
b = −1.47219 + 0.19833I
−4.34649 + 5.92708I 0
u = 1.085780 + 0.243540I
a = −0.729453 + 0.365525I
b = 0.124325 − 0.592140I
−0.968890 − 0.789801I 0
u = 1.085780 − 0.243540I
a = −0.729453 − 0.365525I
b = 0.124325 + 0.592140I
−0.968890 + 0.789801I 0
u = 0.201797 + 0.773580I
a = 0.65000 + 1.60035I
b = −0.793170 − 0.734810I
0.15931 − 6.92492I −8.00000 + 9.41570I
u = 0.201797 − 0.773580I
a = 0.65000 − 1.60035I
b = −0.793170 + 0.734810I
0.15931 + 6.92492I −8.00000 − 9.41570I
u = 1.203160 + 0.212321I
a = −0.835102 + 0.755842I
b = −0.352089 − 0.569580I
−1.26241 − 1.26238I 0
u = 1.203160 − 0.212321I
a = −0.835102 − 0.755842I
b = −0.352089 + 0.569580I
−1.26241 + 1.26238I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.636386 + 0.433353I
a = 0.248415 − 0.156107I
b = −0.539496 − 0.235219I
−3.20093 − 2.38936I −17.3308 + 5.2603I
u = 0.636386 − 0.433353I
a = 0.248415 + 0.156107I
b = −0.539496 + 0.235219I
−3.20093 + 2.38936I −17.3308 − 5.2603I
u = 0.174212 + 0.714774I
a = −0.39734 − 1.61036I
b = 0.393692 + 0.706879I
1.68253 − 2.79181I −4.40821 + 4.21273I
u = 0.174212 − 0.714774I
a = −0.39734 + 1.61036I
b = 0.393692 − 0.706879I
1.68253 + 2.79181I −4.40821 − 4.21273I
u = 0.319686 + 0.646062I
a = 0.316719 + 1.035180I
b = −0.300560 + 0.024775I
−2.20621 − 1.45129I −14.5147 + 3.3145I
u = 0.319686 − 0.646062I
a = 0.316719 − 1.035180I
b = −0.300560 − 0.024775I
−2.20621 + 1.45129I −14.5147 − 3.3145I
u = 1.285420 + 0.094016I
a = 0.456290 − 1.265580I
b = 0.430143 − 0.102358I
−4.61992 + 0.36511I 0
u = 1.285420 − 0.094016I
a = 0.456290 + 1.265580I
b = 0.430143 + 0.102358I
−4.61992 − 0.36511I 0
u = −1.287860 + 0.072895I
a = 0.147765 + 0.194840I
b = −1.36565 − 0.38952I
−8.72493 − 4.01377I 0
u = −1.287860 − 0.072895I
a = 0.147765 − 0.194840I
b = −1.36565 + 0.38952I
−8.72493 + 4.01377I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.273630 + 0.234512I
a = 1.06836 − 0.97934I
b = 0.772121 + 0.649670I
−2.86722 − 5.13648I 0
u = 1.273630 − 0.234512I
a = 1.06836 + 0.97934I
b = 0.772121 − 0.649670I
−2.86722 + 5.13648I 0
u = −1.310770 + 0.210855I
a = −0.365749 − 0.628451I
b = 0.464829 + 0.924450I
−3.02836 + 0.78893I 0
u = −1.310770 − 0.210855I
a = −0.365749 + 0.628451I
b = 0.464829 − 0.924450I
−3.02836 − 0.78893I 0
u = −1.327870 + 0.109441I
a = −0.078373 − 0.356478I
b = 1.041460 + 0.386661I
−5.77899 + 0.48003I 0
u = −1.327870 − 0.109441I
a = −0.078373 + 0.356478I
b = 1.041460 − 0.386661I
−5.77899 − 0.48003I 0
u = 0.090587 + 0.645600I
a = −0.05614 − 1.76780I
b = −0.143845 + 0.767387I
2.07073 − 1.86749I −2.85319 + 4.16997I
u = 0.090587 − 0.645600I
a = −0.05614 + 1.76780I
b = −0.143845 − 0.767387I
2.07073 + 1.86749I −2.85319 − 4.16997I
u = −1.331220 + 0.247307I
a = 0.423310 + 0.804300I
b = −0.061462 − 0.941261I
−2.41235 + 5.09301I 0
u = −1.331220 − 0.247307I
a = 0.423310 − 0.804300I
b = −0.061462 + 0.941261I
−2.41235 − 5.09301I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.372500 + 0.208067I
a = 1.18530 − 1.51605I
b = 1.47714 + 0.15260I
−7.28647 − 3.73730I 0
u = 1.372500 − 0.208067I
a = 1.18530 + 1.51605I
b = 1.47714 − 0.15260I
−7.28647 + 3.73730I 0
u = 1.384380 + 0.195037I
a = −1.14266 + 1.61351I
b = −1.51278 + 0.02690I
−11.19560 + 0.80901I 0
u = 1.384380 − 0.195037I
a = −1.14266 − 1.61351I
b = −1.51278 − 0.02690I
−11.19560 − 0.80901I 0
u = −1.368220 + 0.287711I
a = 0.456831 + 1.079290I
b = 0.530276 − 0.801232I
−3.20875 + 6.42514I 0
u = −1.368220 − 0.287711I
a = 0.456831 − 1.079290I
b = 0.530276 + 0.801232I
−3.20875 − 6.42514I 0
u = 0.001762 + 0.601615I
a = −0.18960 + 1.93159I
b = 0.582995 − 0.743414I
1.09588 + 2.08440I −5.27577 − 3.44831I
u = 0.001762 − 0.601615I
a = −0.18960 − 1.93159I
b = 0.582995 + 0.743414I
1.09588 − 2.08440I −5.27577 + 3.44831I
u = 1.381070 + 0.220674I
a = −1.27621 + 1.52980I
b = −1.61885 − 0.22827I
−10.84100 − 8.56310I 0
u = 1.381070 − 0.220674I
a = −1.27621 − 1.52980I
b = −1.61885 + 0.22827I
−10.84100 + 8.56310I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.406650 + 0.108118I
a = −0.224298 + 0.479931I
b = −0.889838 + 0.012840I
−9.56584 + 3.88184I 0
u = −1.406650 − 0.108118I
a = −0.224298 − 0.479931I
b = −0.889838 − 0.012840I
−9.56584 − 3.88184I 0
u = −1.38177 + 0.31309I
a = −0.519776 − 1.227890I
b = −0.894583 + 0.801624I
−4.86125 + 10.84660I 0
u = −1.38177 − 0.31309I
a = −0.519776 + 1.227890I
b = −0.894583 − 0.801624I
−4.86125 − 10.84660I 0
u = −0.217146 + 0.536055I
a = 0.60175 − 2.16828I
b = −1.52812 + 0.24824I
−5.74382 + 5.73352I −9.31960 − 3.96496I
u = −0.217146 − 0.536055I
a = 0.60175 + 2.16828I
b = −1.52812 − 0.24824I
−5.74382 − 5.73352I −9.31960 + 3.96496I
u = −1.40915 + 0.25179I
a = −0.157565 − 1.105170I
b = −0.323961 + 0.190846I
−7.68685 + 4.72210I 0
u = −1.40915 − 0.25179I
a = −0.157565 + 1.105170I
b = −0.323961 − 0.190846I
−7.68685 − 4.72210I 0
u = −0.195506 + 0.494386I
a = −0.60346 + 2.10373I
b = 1.332360 − 0.127865I
−2.28691 + 1.08117I −6.04411 − 0.68667I
u = −0.195506 − 0.494386I
a = −0.60346 − 2.10373I
b = 1.332360 + 0.127865I
−2.28691 − 1.08117I −6.04411 + 0.68667I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.43492 + 0.33574I
a = −0.42182 − 1.57242I
b = −1.52280 + 0.24815I
−9.8574 + 10.1740I 0
u = −1.43492 − 0.33574I
a = −0.42182 + 1.57242I
b = −1.52280 − 0.24815I
−9.8574 − 10.1740I 0
u = −0.244545 + 0.465151I
a = 0.66363 − 2.09922I
b = −1.43543 − 0.11457I
−6.00989 − 3.31774I −9.52284 + 2.54149I
u = −0.244545 − 0.465151I
a = 0.66363 + 2.09922I
b = −1.43543 + 0.11457I
−6.00989 + 3.31774I −9.52284 − 2.54149I
u = −1.43676 + 0.34496I
a = 0.46165 + 1.62078I
b = 1.67048 − 0.27980I
−13.3475 + 15.1287I 0
u = −1.43676 − 0.34496I
a = 0.46165 − 1.62078I
b = 1.67048 + 0.27980I
−13.3475 − 15.1287I 0
u = −1.44511 + 0.33011I
a = 0.34935 + 1.59979I
b = 1.49951 − 0.06456I
−13.9374 + 5.6612I 0
u = −1.44511 − 0.33011I
a = 0.34935 − 1.59979I
b = 1.49951 + 0.06456I
−13.9374 − 5.6612I 0
u = −1.52087
a = −0.926353
b = −1.58708
−14.6359 0
u = −1.52946 + 0.01186I
a = 0.979765 − 0.076295I
b = 1.64505 − 0.09028I
−18.4592 + 4.8158I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.52946 − 0.01186I
a = 0.979765 + 0.076295I
b = 1.64505 + 0.09028I
−18.4592 − 4.8158I 0
u = 0.438993
a = −0.875494
b = 0.359702
−0.831134 −11.9340
u = −0.131466 + 0.110386I
a = −0.73310 + 2.64270I
b = 0.295035 + 0.455623I
−0.50060 − 1.35724I −5.01014 + 4.53923I
u = −0.131466 − 0.110386I
a = −0.73310 − 2.64270I
b = 0.295035 − 0.455623I
−0.50060 + 1.35724I −5.01014 − 4.53923I
12
II. I
u
2
= hb
5
− b
4
− 2b
3
+ b
2
+ b + 1, a, u − 1i
(i) Arc colorings
a
8
=
1
0
a
12
=
0
1
a
9
=
1
1
a
1
=
−1
0
a
5
=
0
b
a
10
=
0
1
a
4
=
b
b
a
7
=
−b
2
+ 1
−b
2
a
3
=
−b
3
+ 2b
−b
3
+ b
a
11
=
0
1
a
6
=
0
b
a
2
=
−b
3
+ 2b
−b
4
− b
3
+ b
2
+ 2b + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = b
4
+ 2b
3
− 5b − 14
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
5
− 3u
4
+ 4u
3
− u
2
− u + 1
c
2
u
5
− u
4
+ 2u
3
− u
2
+ u − 1
c
3
, c
4
u
5
+ u
4
− 2u
3
− u
2
+ u − 1
c
5
, c
10
, c
11
u
5
c
6
u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1
c
7
u
5
− u
4
− 2u
3
+ u
2
+ u + 1
c
8
, c
9
(u − 1)
5
c
12
(u + 1)
5
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1
c
2
, c
6
y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1
c
3
, c
4
, c
7
y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1
c
5
, c
10
, c
11
y
5
c
8
, c
9
, c
12
(y −1)
5
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0
b = −1.21774
−4.04602 −9.32390
u = 1.00000
a = 0
b = −0.309916 + 0.549911I
−1.97403 + 1.53058I −12.02124 − 2.62456I
u = 1.00000
a = 0
b = −0.309916 − 0.549911I
−1.97403 − 1.53058I −12.02124 + 2.62456I
u = 1.00000
a = 0
b = 1.41878 + 0.21917I
−7.51750 − 4.40083I −12.31681 + 3.97407I
u = 1.00000
a = 0
b = 1.41878 − 0.21917I
−7.51750 + 4.40083I −12.31681 − 3.97407I
16
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
5
− 3u
4
+ 4u
3
− u
2
− u + 1)(u
74
+ 42u
73
+ ··· − 2u + 1)
c
2
(u
5
− u
4
+ 2u
3
− u
2
+ u − 1)(u
74
− 2u
73
+ ··· − 2u − 1)
c
3
, c
4
(u
5
+ u
4
− 2u
3
− u
2
+ u − 1)(u
74
+ 2u
73
+ ··· + 84u − 17)
c
5
, c
10
u
5
(u
74
+ u
73
+ ··· + 96u + 32)
c
6
(u
5
+ u
4
+ 2u
3
+ u
2
+ u + 1)(u
74
− 2u
73
+ ··· − 2u − 1)
c
7
(u
5
− u
4
− 2u
3
+ u
2
+ u + 1)(u
74
+ 2u
73
+ ··· + 84u − 17)
c
8
, c
9
((u − 1)
5
)(u
74
− 6u
73
+ ··· + 4u − 1)
c
11
u
5
(u
74
+ 33u
73
+ ··· + 7680u + 1024)
c
12
((u + 1)
5
)(u
74
− 6u
73
+ ··· + 4u − 1)
17
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
5
− y
4
+ 8y
3
− 3y
2
+ 3y −1)(y
74
− 18y
73
+ ··· − 70y + 1)
c
2
, c
6
(y
5
+ 3y
4
+ 4y
3
+ y
2
− y −1)(y
74
+ 42y
73
+ ··· − 2y + 1)
c
3
, c
4
, c
7
(y
5
− 5y
4
+ 8y
3
− 3y
2
− y −1)(y
74
− 78y
73
+ ··· − 14298y + 289)
c
5
, c
10
y
5
(y
74
− 33y
73
+ ··· − 7680y + 1024)
c
8
, c
9
, c
12
((y −1)
5
)(y
74
− 66y
73
+ ··· − 4y + 1)
c
11
y
5
(y
74
+ 7y
73
+ ··· − 1.21897 × 10
7
y + 1048576)
18
