12n
0514
(K12n
0514
)
A knot diagram
1
Linearized knot diagam
3 6 9 7 2 11 4 12 3 6 8 10
Solving Sequence
6,11 3,7
2 1 5 4 8 10 9 12
c
6
c
2
c
1
c
5
c
4
c
7
c
10
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−8.97013 × 10
55
u
29
− 1.58329 × 10
56
u
28
+ ··· + 4.35231 × 10
58
b + 6.55011 × 10
57
,
3.18509 × 10
57
u
29
− 1.03463 × 10
58
u
28
+ ··· + 1.82362 × 10
61
a + 1.17215 × 10
61
,
u
30
+ 2u
29
+ ··· + 100u − 419i
I
u
2
= h−5u
12
+ 21u
10
− 7u
9
− 18u
8
+ 33u
7
− 17u
6
− 26u
5
+ 26u
4
+ 7u
3
− 15u
2
+ 2b + 3u + 5,
11u
12
+ 2u
11
− 48u
10
+ 6u
9
+ 49u
8
− 64u
7
+ 21u
6
+ 72u
5
− 53u
4
− 32u
3
+ 37u
2
+ 2a − u − 14,
u
13
+ u
12
− 4u
11
− 3u
10
+ 4u
9
− 2u
8
− 2u
7
+ 7u
6
+ u
5
− 6u
4
+ 2u
2
− u − 1i
* 2 irreducible components of dim
C
= 0, with total 43 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−8.97 × 10
55
u
29
− 1.58 × 10
56
u
28
+ · · · + 4.35 × 10
58
b + 6.55 ×
10
57
, 3.19 × 10
57
u
29
− 1.03 × 10
58
u
28
+ · · · + 1.82 × 10
61
a + 1.17 ×
10
61
, u
30
+ 2u
29
+ · · · + 100u − 419i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−0.000174658u
29
+ 0.000567352u
28
+ ··· + 1.47843u − 0.642763
0.00206100u
29
+ 0.00363781u
28
+ ··· − 0.596168u − 0.150497
a
7
=
1
−u
2
a
2
=
0.00188635u
29
+ 0.00420517u
28
+ ··· + 0.882267u − 0.793260
0.00206100u
29
+ 0.00363781u
28
+ ··· − 0.596168u − 0.150497
a
1
=
0.00358201u
29
+ 0.00533243u
28
+ ··· − 0.845448u + 0.146579
−0.00430260u
29
− 0.00434093u
28
+ ··· + 2.70318u − 1.08487
a
5
=
0.0000550185u
29
+ 0.00136950u
28
+ ··· + 0.855142u − 0.322525
−0.000908531u
29
+ 0.0000579815u
28
+ ··· + 0.0808855u − 1.03300
a
4
=
0.000107308u
29
+ 0.000594620u
28
+ ··· + 0.877150u + 0.182757
0.0000965840u
29
+ 0.00130720u
28
+ ··· − 0.0289697u − 0.664503
a
8
=
−0.0000748679u
29
+ 0.000914934u
28
+ ··· + 0.654950u + 0.759505
−0.00255893u
29
− 0.00377164u
28
+ ··· + 0.375116u − 0.944810
a
10
=
−u
u
a
9
=
−0.0000732909u
29
− 0.00133981u
28
+ ··· − 1.16207u − 0.158293
0.00125946u
29
+ 0.00337516u
28
+ ··· − 0.328027u + 0.0230528
a
12
=
0.00156530u
29
+ 0.00377669u
28
+ ··· − 0.300258u − 0.872709
−0.00228589u
29
− 0.00278519u
28
+ ··· + 2.15799u − 0.0655795
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.000964221u
29
+ 0.00738326u
28
+ ··· + 11.2158u + 0.582373
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
30
+ 54u
29
+ ··· + 35644u + 961
c
2
, c
5
u
30
+ 2u
29
+ ··· + 274u + 31
c
3
, c
9
u
30
− u
29
+ ··· − 18u − 9
c
4
, c
7
u
30
+ 7u
29
+ ··· − 58u + 7
c
6
, c
10
u
30
+ 2u
29
+ ··· + 100u − 419
c
8
, c
11
u
30
− u
29
+ ··· − u − 1
c
12
u
30
+ 3u
29
+ ··· + 276288u − 31624
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
30
− 166y
29
+ ··· + 2665988060y + 923521
c
2
, c
5
y
30
− 54y
29
+ ··· − 35644y + 961
c
3
, c
9
y
30
+ 47y
29
+ ··· + 972y + 81
c
4
, c
7
y
30
+ 23y
29
+ ··· − 1614y + 49
c
6
, c
10
y
30
+ 10y
29
+ ··· + 590846y + 175561
c
8
, c
11
y
30
− 21y
29
+ ··· − 19y + 1
c
12
y
30
+ 121y
29
+ ··· + 1307553376y + 1000077376
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.642590 + 0.700606I
a = 0.106716 − 1.072760I
b = −0.347246 + 1.044670I
0.82927 + 4.60566I 7.38656 − 8.01596I
u = 0.642590 − 0.700606I
a = 0.106716 + 1.072760I
b = −0.347246 − 1.044670I
0.82927 − 4.60566I 7.38656 + 8.01596I
u = −0.814116 + 0.677327I
a = 0.504066 + 1.067370I
b = −0.549219 − 0.145896I
−0.77900 − 2.06540I 3.22171 + 2.38317I
u = −0.814116 − 0.677327I
a = 0.504066 − 1.067370I
b = −0.549219 + 0.145896I
−0.77900 + 2.06540I 3.22171 − 2.38317I
u = 0.560922 + 0.747663I
a = 0.472626 − 0.864157I
b = −0.104866 + 0.109501I
0.327633 − 0.843648I 6.72873 + 1.86017I
u = 0.560922 − 0.747663I
a = 0.472626 + 0.864157I
b = −0.104866 − 0.109501I
0.327633 + 0.843648I 6.72873 − 1.86017I
u = −0.055990 + 1.128490I
a = −0.924318 + 0.178825I
b = 2.41962 − 0.23089I
−10.40080 + 1.46441I −1.99581 − 5.01569I
u = −0.055990 − 1.128490I
a = −0.924318 − 0.178825I
b = 2.41962 + 0.23089I
−10.40080 − 1.46441I −1.99581 + 5.01569I
u = −0.586638 + 0.553835I
a = 0.155793 + 1.119640I
b = −0.651578 − 0.537140I
−1.29989 − 1.54235I 1.52237 + 4.53495I
u = −0.586638 − 0.553835I
a = 0.155793 − 1.119640I
b = −0.651578 + 0.537140I
−1.29989 + 1.54235I 1.52237 − 4.53495I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.307100 + 0.036349I
a = 0.71975 + 1.63357I
b = −0.798397 − 0.708430I
3.26183 − 2.73720I 10.18982 + 2.92398I
u = 1.307100 − 0.036349I
a = 0.71975 − 1.63357I
b = −0.798397 + 0.708430I
3.26183 + 2.73720I 10.18982 − 2.92398I
u = −0.049314 + 1.329620I
a = −0.356304 + 0.123824I
b = 1.85890 − 0.07524I
−11.24640 − 1.91319I 0.75047 + 3.50106I
u = −0.049314 − 1.329620I
a = −0.356304 − 0.123824I
b = 1.85890 + 0.07524I
−11.24640 + 1.91319I 0.75047 − 3.50106I
u = 0.403283 + 1.277970I
a = −0.507314 − 0.949307I
b = 1.40638 + 0.97678I
−3.40270 − 3.64668I 2.86245 + 2.46962I
u = 0.403283 − 1.277970I
a = −0.507314 + 0.949307I
b = 1.40638 − 0.97678I
−3.40270 + 3.64668I 2.86245 − 2.46962I
u = −0.276632 + 1.333170I
a = −0.334409 + 0.791751I
b = 1.39749 − 0.61314I
−7.55076 − 1.32763I −0.010757 + 0.862501I
u = −0.276632 − 1.333170I
a = −0.334409 − 0.791751I
b = 1.39749 + 0.61314I
−7.55076 + 1.32763I −0.010757 − 0.862501I
u = −0.309884 + 0.543530I
a = −0.220039 + 0.852834I
b = −0.933653 − 0.345827I
−1.56864 − 1.53975I 1.10369 + 4.69285I
u = −0.309884 − 0.543530I
a = −0.220039 − 0.852834I
b = −0.933653 + 0.345827I
−1.56864 + 1.53975I 1.10369 − 4.69285I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.242225 + 1.368910I
a = −0.111633 − 0.819227I
b = 1.153510 + 0.418732I
−4.09460 + 6.61711I 2.97271 − 4.66549I
u = 0.242225 − 1.368910I
a = −0.111633 + 0.819227I
b = 1.153510 − 0.418732I
−4.09460 − 6.61711I 2.97271 + 4.66549I
u = 0.531314
a = 0.442861
b = 0.183744
0.719441 14.3760
u = −1.55692
a = −0.621196
b = 0.986893
7.16181 20.2020
u = −1.34575 + 1.55021I
a = 1.43706 + 0.93333I
b = −2.22516 − 0.41486I
−15.4447 − 11.8067I 3.77024 + 5.11220I
u = −1.34575 − 1.55021I
a = 1.43706 − 0.93333I
b = −2.22516 + 0.41486I
−15.4447 + 11.8067I 3.77024 − 5.11220I
u = 1.48358 + 1.48152I
a = 1.42930 − 1.02156I
b = −2.15106 + 0.44424I
−19.4159 + 5.5271I 1.12565 − 2.12056I
u = 1.48358 − 1.48152I
a = 1.42930 + 1.02156I
b = −2.15106 − 0.44424I
−19.4159 − 5.5271I 1.12565 + 2.12056I
u = −1.68857 + 1.42229I
a = 1.44579 + 1.14500I
b = −2.06005 − 0.54414I
−14.5803 + 0.6531I 6.00000 + 0.I
u = −1.68857 − 1.42229I
a = 1.44579 − 1.14500I
b = −2.06005 + 0.54414I
−14.5803 − 0.6531I 6.00000 + 0.I
7
II. I
u
2
=
h−5u
12
+21u
10
+· · ·+2b+5, 11u
12
+2u
11
+· · ·+2a−14, u
13
+u
12
+· · ·−u−1i
(i) Arc colorings
a
6
=
1
0
a
11
=
0
u
a
3
=
−
11
2
u
12
− u
11
+ ··· +
1
2
u + 7
5
2
u
12
−
21
2
u
10
+ ··· −
3
2
u −
5
2
a
7
=
1
−u
2
a
2
=
−3u
12
− u
11
+ ··· − u +
9
2
5
2
u
12
−
21
2
u
10
+ ··· −
3
2
u −
5
2
a
1
=
−
3
2
u
12
− 2u
11
+ ··· −
3
2
u + 5
3
2
u
12
+
1
2
u
11
+ ··· − 2u −
3
2
a
5
=
2u
12
+ u
11
+ ··· − u −
3
2
5
2
u
12
+
1
2
u
11
+ ··· +
17
2
u
2
−
7
2
a
4
=
−u
12
+ 5u
10
− u
9
− 7u
8
+ 6u
7
− 9u
5
+ 6u
4
+ 7u
3
− 6u
2
− 2u + 3
3u
12
+ u
11
+ ··· + u −
11
2
a
8
=
−
11
2
u
12
− u
11
+ ··· +
3
2
u +
9
2
3u
12
−
1
2
u
11
+ ··· + 6u
2
−
5
2
u
a
10
=
−u
u
a
9
=
−
1
2
u
12
+
3
2
u
11
+ ··· + 4u − 2
−u
12
−
1
2
u
11
+ ··· +
1
2
u + 2
a
12
=
−4u
12
− 2u
11
+ ··· − 14u
2
+
13
2
4u
12
+
1
2
u
11
+ ··· −
7
2
u − 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 3u
12
−4u
11
−
21
2
u
10
+
39
2
u
9
−
7
2
u
8
−
51
2
u
7
+ 42u
6
−15u
5
−
41
2
u
4
+
41
2
u
3
−3u
2
−12u +
21
2
8
(iv) u-Polynomials at the component
9
Crossings u-Polynomials at each crossing
c
1
u
13
− 13u
12
+ ··· + 7u − 1
c
2
u
13
+ 3u
12
+ ··· − 3u − 1
c
3
u
13
+ 8u
11
+ ··· + 3u + 1
c
4
u
13
+ 2u
11
+ ··· + 3u + 1
c
5
u
13
− 3u
12
+ ··· − 3u + 1
c
6
u
13
+ u
12
+ ··· − u − 1
c
7
u
13
+ 2u
11
+ ··· + 3u − 1
c
8
u
13
− 6u
11
+ ··· − 2u − 3
c
9
u
13
+ 8u
11
+ ··· + 3u − 1
c
10
u
13
− u
12
+ ··· − u + 1
c
11
u
13
− 6u
11
+ ··· − 2u + 3
c
12
u
13
− 2u
12
+ ··· − 13u + 1
10
11
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
13
− 37y
12
+ ··· + 11y −1
c
2
, c
5
y
13
− 13y
12
+ ··· + 7y −1
c
3
, c
9
y
13
+ 16y
12
+ ··· − 5y −1
c
4
, c
7
y
13
+ 4y
12
+ ··· + y −1
c
6
, c
10
y
13
− 9y
12
+ ··· + 5y −1
c
8
, c
11
y
13
− 12y
12
+ ··· + 46y −9
c
12
y
13
+ 30y
12
+ ··· + 25y −1
12
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.954573 + 0.260088I
a = −0.92363 − 1.20575I
b = 0.582097 − 0.018888I
−3.98060 + 1.00568I 1.162112 − 0.615451I
u = 0.954573 − 0.260088I
a = −0.92363 + 1.20575I
b = 0.582097 + 0.018888I
−3.98060 − 1.00568I 1.162112 + 0.615451I
u = 0.266976 + 1.054200I
a = −0.532456 + 0.412592I
b = 2.10432 − 0.01987I
−9.61091 − 1.01135I 7.06702 − 0.15470I
u = 0.266976 − 1.054200I
a = −0.532456 − 0.412592I
b = 2.10432 + 0.01987I
−9.61091 + 1.01135I 7.06702 + 0.15470I
u = −0.752928 + 0.297393I
a = 1.030040 + 0.709707I
b = −0.921610 − 0.177058I
−0.796848 − 0.470467I 2.94539 − 1.34493I
u = −0.752928 − 0.297393I
a = 1.030040 − 0.709707I
b = −0.921610 + 0.177058I
−0.796848 + 0.470467I 2.94539 + 1.34493I
u = −0.684151 + 0.344382I
a = −1.27505 + 0.67741I
b = 0.314319 + 0.549467I
−1.36517 − 5.98644I 4.94299 + 5.64527I
u = −0.684151 − 0.344382I
a = −1.27505 − 0.67741I
b = 0.314319 − 0.549467I
−1.36517 + 5.98644I 4.94299 − 5.64527I
u = 0.460968 + 0.533555I
a = 0.56985 − 1.90658I
b = −0.813036 + 0.713273I
0.43653 + 3.26322I 5.30243 − 3.80898I
u = 0.460968 − 0.533555I
a = 0.56985 + 1.90658I
b = −0.813036 − 0.713273I
0.43653 − 3.26322I 5.30243 + 3.80898I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.60034 + 0.28645I
a = −0.84754 + 1.61343I
b = 0.858896 − 0.743211I
2.06490 + 2.83942I 2.96766 − 2.65257I
u = −1.60034 − 0.28645I
a = −0.84754 − 1.61343I
b = 0.858896 + 0.743211I
2.06490 − 2.83942I 2.96766 + 2.65257I
u = 1.70981
a = 0.957563
b = −1.24998
6.76499 −0.775210
14
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
13
− 13u
12
+ ··· + 7u − 1)(u
30
+ 54u
29
+ ··· + 35644u + 961)
c
2
(u
13
+ 3u
12
+ ··· − 3u − 1)(u
30
+ 2u
29
+ ··· + 274u + 31)
c
3
(u
13
+ 8u
11
+ ··· + 3u + 1)(u
30
− u
29
+ ··· − 18u − 9)
c
4
(u
13
+ 2u
11
+ ··· + 3u + 1)(u
30
+ 7u
29
+ ··· − 58u + 7)
c
5
(u
13
− 3u
12
+ ··· − 3u + 1)(u
30
+ 2u
29
+ ··· + 274u + 31)
c
6
(u
13
+ u
12
+ ··· − u − 1)(u
30
+ 2u
29
+ ··· + 100u − 419)
c
7
(u
13
+ 2u
11
+ ··· + 3u − 1)(u
30
+ 7u
29
+ ··· − 58u + 7)
c
8
(u
13
− 6u
11
+ ··· − 2u − 3)(u
30
− u
29
+ ··· − u − 1)
c
9
(u
13
+ 8u
11
+ ··· + 3u − 1)(u
30
− u
29
+ ··· − 18u − 9)
c
10
(u
13
− u
12
+ ··· − u + 1)(u
30
+ 2u
29
+ ··· + 100u − 419)
c
11
(u
13
− 6u
11
+ ··· − 2u + 3)(u
30
− u
29
+ ··· − u − 1)
c
12
(u
13
− 2u
12
+ ··· − 13u + 1)(u
30
+ 3u
29
+ ··· + 276288u − 31624)
15
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
13
− 37y
12
+ ··· + 11y −1)
· (y
30
− 166y
29
+ ··· + 2665988060y + 923521)
c
2
, c
5
(y
13
− 13y
12
+ ··· + 7y −1)(y
30
− 54y
29
+ ··· − 35644y + 961)
c
3
, c
9
(y
13
+ 16y
12
+ ··· − 5y −1)(y
30
+ 47y
29
+ ··· + 972y + 81)
c
4
, c
7
(y
13
+ 4y
12
+ ··· + y −1)(y
30
+ 23y
29
+ ··· − 1614y + 49)
c
6
, c
10
(y
13
− 9y
12
+ ··· + 5y −1)(y
30
+ 10y
29
+ ··· + 590846y + 175561)
c
8
, c
11
(y
13
− 12y
12
+ ··· + 46y −9)(y
30
− 21y
29
+ ··· − 19y + 1)
c
12
(y
13
+ 30y
12
+ ··· + 25y −1)
· (y
30
+ 121y
29
+ ··· + 1307553376y + 1000077376)
16
