11n
147
(K11n
147
)
A knot diagram
1
Linearized knot diagam
7 1 6 11 1 10 2 5 4 7 9
Solving Sequence
7,10 4,11
5 6 3 9 1 2 8
c
10
c
4
c
6
c
3
c
9
c
11
c
1
c
8
c
2
, c
5
, c
7
Ideals for irreducible components
2
of X
par
I
u
1
= h1.98756 × 10
46
u
32
+ 1.28266 × 10
46
u
31
+ ··· + 1.35435 × 10
47
b + 2.77751 × 10
46
,
2.97484 × 10
47
u
32
+ 3.19635 × 10
47
u
31
+ ··· + 1.35435 × 10
47
a + 4.86114 × 10
48
, u
33
+ u
32
+ ··· + 14u + 1i
I
u
2
= hu
14
− 3u
12
− u
11
+ u
10
+ 2u
9
+ 7u
8
− 4u
7
− 11u
6
+ 4u
5
+ 6u
4
− 5u
3
− u
2
+ b,
− 73u
14
+ 113u
13
+ ··· + 19a + 238,
u
15
− 4u
13
− u
12
+ 4u
11
+ 3u
10
+ 6u
9
− 6u
8
− 18u
7
+ 8u
6
+ 17u
5
− 9u
4
− 7u
3
+ 5u
2
+ u − 1i
* 2 irreducible components of dim
C
= 0, with total 48 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
= h1.99 × 10
46
u
32
+ 1.28 × 10
46
u
31
+ · · · + 1.35 × 10
47
b + 2.78 × 10
46
, 2.97 ×
10
47
u
32
+3.20×10
47
u
31
+· · ·+1.35×10
47
a+4.86×10
48
, u
33
+u
32
+· · ·+14u+1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
−2.19651u
32
− 2.36006u
31
+ ··· − 288.611u − 35.8928
−0.146754u
32
− 0.0947065u
31
+ ··· − 10.0032u − 0.205081
a
11
=
1
u
2
a
5
=
−2.39829u
32
− 2.50756u
31
+ ··· − 303.100u − 36.2614
−0.153523u
32
− 0.103389u
31
+ ··· − 10.5613u − 0.259363
a
6
=
u
u
a
3
=
−2.25912u
32
− 2.42484u
31
+ ··· − 293.679u − 36.1084
−0.209360u
32
− 0.159488u
31
+ ··· − 15.0713u − 0.420679
a
9
=
1.41506u
32
+ 1.04966u
31
+ ··· + 69.0722u − 12.5718
−0.0802570u
32
− 0.116578u
31
+ ··· − 12.6183u − 1.15166
a
1
=
−1.63104u
32
− 1.63496u
31
+ ··· − 199.736u − 22.5435
−0.0316774u
32
− 0.0129877u
31
+ ··· − 6.21518u − 0.0761096
a
2
=
−1.63104u
32
− 1.63496u
31
+ ··· − 199.736u − 22.5435
−0.00657502u
32
− 0.00502953u
31
+ ··· − 4.52928u − 0.0721915
a
8
=
2.50333u
32
+ 2.57261u
31
+ ··· + 314.930u + 36.4507
0.0683064u
32
+ 0.0388114u
31
+ ··· + 8.35580u + 0.120011
a
8
=
2.50333u
32
+ 2.57261u
31
+ ··· + 314.930u + 36.4507
0.0683064u
32
+ 0.0388114u
31
+ ··· + 8.35580u + 0.120011
(ii) Obstruction class = −1
(iii) Cusp Shapes = 1.80265u
32
+ 1.77164u
31
+ ··· + 131.190u − 2.63139
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
33
− u
32
+ ··· − 377u + 49
c
2
u
33
+ 51u
32
+ ··· − 6243u + 2401
c
3
u
33
+ 4u
32
+ ··· + 1014u + 53
c
4
u
33
− 3u
32
+ ··· + 143u + 167
c
5
u
33
− 31u
31
+ ··· + 31219u + 7513
c
6
, c
10
u
33
+ u
32
+ ··· + 14u + 1
c
8
u
33
+ 3u
32
+ ··· + 43957u + 23657
c
9
u
33
+ u
32
+ ··· − 194u + 69
c
11
u
33
+ 2u
32
+ ··· + 12u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
33
− 51y
32
+ ··· − 6243y −2401
c
2
y
33
− 127y
32
+ ··· − 823598607y −5764801
c
3
y
33
− 62y
32
+ ··· + 1267120y −2809
c
4
y
33
+ 13y
32
+ ··· + 203815y −27889
c
5
y
33
− 62y
32
+ ··· − 187379697y −56445169
c
6
, c
10
y
33
− 31y
32
+ ··· − 58y −1
c
8
y
33
− 35y
32
+ ··· + 2107894731y −559653649
c
9
y
33
+ 13y
32
+ ··· − 3488y −4761
c
11
y
33
+ 4y
32
+ ··· + 94y −1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.127190 + 0.291980I
a = 0.90634 + 1.24177I
b = −0.280294 + 0.848945I
−4.91531 − 2.57543I −14.7490 + 3.5042I
u = 1.127190 − 0.291980I
a = 0.90634 − 1.24177I
b = −0.280294 − 0.848945I
−4.91531 + 2.57543I −14.7490 − 3.5042I
u = −0.258449 + 1.156160I
a = 0.118269 + 0.247166I
b = 0.381205 − 0.236102I
2.26695 + 2.07000I 4.04253 + 2.66758I
u = −0.258449 − 1.156160I
a = 0.118269 − 0.247166I
b = 0.381205 + 0.236102I
2.26695 − 2.07000I 4.04253 − 2.66758I
u = −1.214840 + 0.304735I
a = −0.676508 + 1.000140I
b = −0.363295 + 1.180830I
−2.65106 + 0.57067I −7.43301 + 1.59468I
u = −1.214840 − 0.304735I
a = −0.676508 − 1.000140I
b = −0.363295 − 1.180830I
−2.65106 − 0.57067I −7.43301 − 1.59468I
u = −1.203030 + 0.458288I
a = −0.26246 + 1.71772I
b = 1.23330 + 1.31569I
−4.39762 + 3.59048I −13.6557 − 4.4501I
u = −1.203030 − 0.458288I
a = −0.26246 − 1.71772I
b = 1.23330 − 1.31569I
−4.39762 − 3.59048I −13.6557 + 4.4501I
u = 1.235800 + 0.362699I
a = −0.03086 + 1.63923I
b = −0.508343 + 0.929615I
−1.99613 − 4.92165I −6.31797 + 5.98553I
u = 1.235800 − 0.362699I
a = −0.03086 − 1.63923I
b = −0.508343 − 0.929615I
−1.99613 + 4.92165I −6.31797 − 5.98553I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.569481
a = −0.688600
b = −0.604199
−1.00066 −10.2820
u = −0.173547 + 0.479626I
a = −0.525769 − 0.734371I
b = −0.526827 + 0.796028I
−1.45039 + 0.21379I −8.69019 − 1.03252I
u = −0.173547 − 0.479626I
a = −0.525769 + 0.734371I
b = −0.526827 − 0.796028I
−1.45039 − 0.21379I −8.69019 + 1.03252I
u = 0.129625 + 0.488487I
a = −0.477469 + 0.473795I
b = 0.889420 + 0.379105I
1.34993 + 1.55576I 0.80167 − 1.35691I
u = 0.129625 − 0.488487I
a = −0.477469 − 0.473795I
b = 0.889420 − 0.379105I
1.34993 − 1.55576I 0.80167 + 1.35691I
u = −1.52232 + 0.04381I
a = −0.703268 − 0.941307I
b = 0.711491 − 0.715800I
−14.5102 − 1.0864I −12.76434 + 6.06201I
u = −1.52232 − 0.04381I
a = −0.703268 + 0.941307I
b = 0.711491 + 0.715800I
−14.5102 + 1.0864I −12.76434 − 6.06201I
u = −0.078681 + 0.424703I
a = −0.651126 + 0.856956I
b = −0.868396 − 0.574824I
0.04954 + 4.46270I −2.71293 − 8.43854I
u = −0.078681 − 0.424703I
a = −0.651126 − 0.856956I
b = −0.868396 + 0.574824I
0.04954 − 4.46270I −2.71293 + 8.43854I
u = 1.59376 + 0.04874I
a = −0.476576 − 0.859038I
b = −1.93979 − 1.30100I
−15.3428 − 2.1802I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.59376 − 0.04874I
a = −0.476576 + 0.859038I
b = −1.93979 + 1.30100I
−15.3428 + 2.1802I 0
u = 1.62635 + 0.11374I
a = 0.254364 − 1.108810I
b = 0.80851 − 1.54572I
−6.41445 − 6.00796I 0
u = 1.62635 − 0.11374I
a = 0.254364 + 1.108810I
b = 0.80851 + 1.54572I
−6.41445 + 6.00796I 0
u = −1.65170 + 0.20395I
a = 0.329105 − 0.879132I
b = −0.047223 − 1.078280I
−5.75926 − 1.26707I 0
u = −1.65170 − 0.20395I
a = 0.329105 + 0.879132I
b = −0.047223 + 1.078280I
−5.75926 + 1.26707I 0
u = 0.17496 + 1.66747I
a = −0.0254572 − 0.0404340I
b = 0.312479 − 1.241810I
−11.57590 − 4.55852I 0
u = 0.17496 − 1.66747I
a = −0.0254572 + 0.0404340I
b = 0.312479 + 1.241810I
−11.57590 + 4.55852I 0
u = −1.65356 + 0.67060I
a = 0.202508 − 1.183540I
b = −1.06866 − 1.49216I
−17.3332 + 12.6517I 0
u = −1.65356 − 0.67060I
a = 0.202508 + 1.183540I
b = −1.06866 + 1.49216I
−17.3332 − 12.6517I 0
u = −0.0667735 + 0.0884449I
a = −16.3648 − 15.7170I
b = 0.429817 − 0.686138I
−9.04777 + 1.61427I −11.19487 + 6.80933I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.0667735 − 0.0884449I
a = −16.3648 + 15.7170I
b = 0.429817 + 0.686138I
−9.04777 − 1.61427I −11.19487 − 6.80933I
u = 1.71996 + 0.81176I
a = −0.271982 − 0.744516I
b = 0.638698 − 1.235990I
−16.3377 − 4.4651I 0
u = 1.71996 − 0.81176I
a = −0.271982 + 0.744516I
b = 0.638698 + 1.235990I
−16.3377 + 4.4651I 0
8
II. I
u
2
= hu
14
− 3u
12
+ · · · − u
2
+ b, −73u
14
+ 113u
13
+ · · · + 19a +
238, u
15
− 4u
13
+ · · · + u − 1i
(i) Arc colorings
a
7
=
0
u
a
10
=
1
0
a
4
=
3.84211u
14
− 5.94737u
13
+ ··· + 24.1053u − 12.5263
−u
14
+ 3u
12
+ ··· + 5u
3
+ u
2
a
11
=
1
u
2
a
5
=
0.526316u
14
− 3.84211u
13
+ ··· + 14.3158u − 6.57895
−3.36842u
14
+ 0.789474u
13
+ ··· − 5.42105u + 2.10526
a
6
=
u
u
a
3
=
0.526316u
14
− 3.84211u
13
+ ··· + 13.3158u − 6.57895
−4.31579u
14
+ 2.10526u
13
+ ··· − 10.7895u + 5.94737
a
9
=
−9.31579u
14
+ 4.10526u
13
+ ··· − 29.7895u + 8.94737
−3u
13
+ 10u
11
+ ··· + 4u − 4
a
1
=
−0.526316u
14
+ 3.84211u
13
+ ··· − 9.31579u + 7.57895
−5.47368u
14
+ 8.15789u
13
+ ··· − 28.6842u + 17.4211
a
2
=
−0.526316u
14
+ 3.84211u
13
+ ··· − 9.31579u + 7.57895
−6.42105u
14
+ 9.47368u
13
+ ··· − 33.0526u + 21.2632
a
8
=
3.94737u
14
− 4.31579u
13
+ ··· + 14.3684u − 10.8421
6.57895u
14
− 10.5263u
13
+ ··· + 36.9474u − 21.7368
a
8
=
3.94737u
14
− 4.31579u
13
+ ··· + 14.3684u − 10.8421
6.57895u
14
− 10.5263u
13
+ ··· + 36.9474u − 21.7368
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
124
19
u
14
+
301
19
u
13
+
478
19
u
12
−
941
19
u
11
−
746
19
u
10
+
339
19
u
9
−
2
19
u
8
+
2898
19
u
7
+
696
19
u
6
−
5366
19
u
5
−
218
19
u
4
+
4007
19
u
3
−
1063
19
u
2
−
1032
19
u +
296
19
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
15
− 8u
13
+ ··· − 4u − 1
c
2
u
15
+ 16u
14
+ ··· + 18u + 1
c
3
u
15
− 11u
14
+ ··· + 73u − 19
c
4
u
15
− 2u
13
+ ··· − 2u − 1
c
5
u
15
− u
14
+ ··· − 4u − 1
c
6
u
15
− 4u
13
+ ··· + u + 1
c
7
u
15
− 8u
13
+ ··· − 4u + 1
c
8
u
15
− 2u
13
+ ··· + 2u + 1
c
9
u
15
+ 2u
12
+ 3u
10
+ 4u
8
+ 6u
7
− 6u
6
+ 10u
5
+ 5u
4
− 2u
3
+ 6u
2
− u + 1
c
10
u
15
− 4u
13
+ ··· + u − 1
c
11
u
15
− 3u
14
+ ··· + 3u + 1
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
15
− 16y
14
+ ··· + 18y −1
c
2
y
15
− 24y
14
+ ··· + 2y −1
c
3
y
15
− 19y
14
+ ··· + 1529y −361
c
4
y
15
− 4y
14
+ ··· − 12y −1
c
5
y
15
− 7y
14
+ ··· − 8y −1
c
6
, c
10
y
15
− 8y
14
+ ··· + 11y −1
c
8
y
15
− 4y
14
+ ··· − 4y −1
c
9
y
15
− 4y
12
+ ··· − 11y −1
c
11
y
15
− y
14
+ ··· + 7y −1
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.016610 + 0.431054I
a = −0.855984 + 1.067750I
b = 0.281730 + 1.208910I
−3.57736 + 1.80398I −10.22776 − 1.35849I
u = −1.016610 − 0.431054I
a = −0.855984 − 1.067750I
b = 0.281730 − 1.208910I
−3.57736 − 1.80398I −10.22776 + 1.35849I
u = 1.145500 + 0.390052I
a = −0.03040 + 1.79678I
b = −0.645353 + 1.166310I
−2.97120 − 6.42822I −8.47318 + 7.69759I
u = 1.145500 − 0.390052I
a = −0.03040 − 1.79678I
b = −0.645353 − 1.166310I
−2.97120 + 6.42822I −8.47318 − 7.69759I
u = 0.694258 + 0.135962I
a = −0.274946 + 0.699949I
b = 1.072130 + 0.630700I
−0.80659 + 4.08294I −10.81787 − 3.73998I
u = 0.694258 − 0.135962I
a = −0.274946 − 0.699949I
b = 1.072130 − 0.630700I
−0.80659 − 4.08294I −10.81787 + 3.73998I
u = −0.681806 + 0.019577I
a = −0.553972 − 0.968044I
b = −1.268190 + 0.099774I
0.12222 − 1.54750I −8.44941 + 2.09198I
u = −0.681806 − 0.019577I
a = −0.553972 + 0.968044I
b = −1.268190 − 0.099774I
0.12222 + 1.54750I −8.44941 − 2.09198I
u = 0.510989 + 0.449107I
a = 3.49622 − 0.96709I
b = 0.250601 + 0.599760I
−9.05250 − 2.11036I −11.5344 + 8.6463I
u = 0.510989 − 0.449107I
a = 3.49622 + 0.96709I
b = 0.250601 − 0.599760I
−9.05250 + 2.11036I −11.5344 − 8.6463I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.149147 + 1.334590I
a = 0.156974 − 0.043596I
b = 0.015421 + 0.481518I
1.95997 + 2.29980I −12.9306 − 8.8872I
u = −0.149147 − 1.334590I
a = 0.156974 + 0.043596I
b = 0.015421 − 0.481518I
1.95997 − 2.29980I −12.9306 + 8.8872I
u = −1.292720 + 0.392522I
a = −0.131181 + 1.312820I
b = 0.822319 + 0.854855I
−3.07019 + 3.17344I −7.31876 − 2.82917I
u = −1.292720 − 0.392522I
a = −0.131181 − 1.312820I
b = 0.822319 − 0.854855I
−3.07019 − 3.17344I −7.31876 + 2.82917I
u = 1.57907
a = 0.386597
b = −1.05733
−14.5567 −11.4960
13
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
15
− 8u
13
+ ··· − 4u − 1)(u
33
− u
32
+ ··· − 377u + 49)
c
2
(u
15
+ 16u
14
+ ··· + 18u + 1)(u
33
+ 51u
32
+ ··· − 6243u + 2401)
c
3
(u
15
− 11u
14
+ ··· + 73u − 19)(u
33
+ 4u
32
+ ··· + 1014u + 53)
c
4
(u
15
− 2u
13
+ ··· − 2u − 1)(u
33
− 3u
32
+ ··· + 143u + 167)
c
5
(u
15
− u
14
+ ··· − 4u − 1)(u
33
− 31u
31
+ ··· + 31219u + 7513)
c
6
(u
15
− 4u
13
+ ··· + u + 1)(u
33
+ u
32
+ ··· + 14u + 1)
c
7
(u
15
− 8u
13
+ ··· − 4u + 1)(u
33
− u
32
+ ··· − 377u + 49)
c
8
(u
15
− 2u
13
+ ··· + 2u + 1)(u
33
+ 3u
32
+ ··· + 43957u + 23657)
c
9
(u
15
+ 2u
12
+ 3u
10
+ 4u
8
+ 6u
7
− 6u
6
+ 10u
5
+ 5u
4
− 2u
3
+ 6u
2
− u + 1)
· (u
33
+ u
32
+ ··· − 194u + 69)
c
10
(u
15
− 4u
13
+ ··· + u − 1)(u
33
+ u
32
+ ··· + 14u + 1)
c
11
(u
15
− 3u
14
+ ··· + 3u + 1)(u
33
+ 2u
32
+ ··· + 12u + 1)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
15
− 16y
14
+ ··· + 18y −1)(y
33
− 51y
32
+ ··· − 6243y −2401)
c
2
(y
15
− 24y
14
+ ··· + 2y −1)
· (y
33
− 127y
32
+ ··· − 823598607y −5764801)
c
3
(y
15
− 19y
14
+ ··· + 1529y −361)
· (y
33
− 62y
32
+ ··· + 1267120y −2809)
c
4
(y
15
− 4y
14
+ ··· − 12y −1)(y
33
+ 13y
32
+ ··· + 203815y −27889)
c
5
(y
15
− 7y
14
+ ··· − 8y −1)
· (y
33
− 62y
32
+ ··· − 187379697y −56445169)
c
6
, c
10
(y
15
− 8y
14
+ ··· + 11y −1)(y
33
− 31y
32
+ ··· − 58y −1)
c
8
(y
15
− 4y
14
+ ··· − 4y −1)
· (y
33
− 35y
32
+ ··· + 2107894731y −559653649)
c
9
(y
15
− 4y
12
+ ··· − 11y −1)(y
33
+ 13y
32
+ ··· − 3488y −4761)
c
11
(y
15
− y
14
+ ··· + 7y −1)(y
33
+ 4y
32
+ ··· + 94y −1)
15
