11a
344
(K11a
344
)
1
Arc Sequences
9 7 1 8 11 10 2 4 3 5 6
Solving Sequence
6,11
1
5,8
4 9 2 3 7 10
c
11
c
5
c
4
c
8
c
1
c
3
c
7
c
10
c
2
, c
6
, c
9
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
12
+ 7u
11
+ ··· + 229u + 31,
4412543702101u
11
+ 28836571354086u
10
+ ··· + 114285479126408b + 30955066382091,
169369168561787u
11
+ 1108608046173106u
10
+ ··· + 3542849852918648a 7547378000812355i
I
u
2
= hu
76
+ 14u
75
+ ··· + 534558087u + 145440247,
1.38428 × 10
756
u
75
+ 1.91681 × 10
757
u
74
+ ··· + 6.92867 × 10
764
b + 3.09737 × 10
764
,
1.02962 × 10
764
u
75
+ 1.45017 × 10
765
u
74
+ ··· + 5.03854 × 10
772
a + 1.90414 × 10
773
i
There are 2 irreducible components with 88 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
=
hu
12
+7u
11
+· · ·+229u+31, 4.41×10
12
u
11
+2.88×10
13
u
10
+· · ·+1.14×10
14
b+
3.10 × 10
13
, 1.69 × 10
14
u
11
+ 1.11 × 10
15
u
10
+ · · · + 3.54 × 10
15
a 7.55 × 10
15
i
(i) Arc colorings
a
6
=
1
0
a
11
=
0.0478059u
11
0.312914u
10
+ ··· 11.5484u + 2.13031
0.0386098u
11
0.252321u
10
+ ··· 10.4277u 0.270857
a
1
=
0.00919608u
11
0.0605937u
10
+ ··· 1.12071u + 2.40117
0.0386098u
11
0.252321u
10
+ ··· 10.4277u 0.270857
a
5
=
0.104892u
11
+ 0.698010u
10
+ ··· + 29.1352u + 0.586710
0.0466577u
11
+ 0.293505u
10
+ ··· + 11.1405u 0.00722289
a
8
=
0
u
a
4
=
0.104892u
11
+ 0.698010u
10
+ ··· + 29.1352u + 0.586710
0.0402812u
11
+ 0.258655u
10
+ ··· + 16.1862u + 1.11599
a
9
=
0.183710u
11
+ 1.22064u
10
+ ··· + 78.2681u + 10.7667
0.0707886u
11
+ 0.504016u
10
+ ··· + 44.1189u + 6.84301
a
2
=
0.0930906u
11
+ 0.633568u
10
+ ··· + 48.6106u + 8.19539
0.0124555u
11
0.0549720u
10
+ ··· + 15.6465u + 3.41022
a
3
=
0.0615431u
11
+ 0.442606u
10
+ ··· + 39.2690u + 5.13094
0.0546457u
11
+ 0.359420u
10
+ ··· + 26.9037u + 4.30802
a
7
=
0.0599372u
11
0.421466u
10
+ ··· 28.7758u 3.26998
0.0309499u
11
0.180825u
10
+ ··· 8.49381u 0.908836
a
10
=
0.0824440u
11
+ 0.531181u
10
+ ··· + 22.9342u + 2.58036
0.00503971u
11
+ 0.0337247u
10
+ ··· + 4.28606u 0.0527929
a
10
=
0.0824440u
11
+ 0.531181u
10
+ ··· + 22.9342u + 2.58036
0.00503971u
11
+ 0.0337247u
10
+ ··· + 4.28606u 0.0527929
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.78081 2.16280I
a = 0.647314 + 0.222653I
b = 1.181971 0.217891I
0.83736 1.52744I 4.49507 + 0.61060I
u = 1.78081 + 2.16280I
a = 0.647314 0.222653I
b = 1.181971 + 0.217891I
0.83736 + 1.52744I 4.49507 0.61060I
u = 0.84034 1.65188I
a = 0.963860 0.018535I
b = 1.334404 + 0.365970I
1.29267 6.23322I 8.20976 + 5.43660I
u = 0.84034 + 1.65188I
a = 0.963860 + 0.018535I
b = 1.334404 0.365970I
1.29267 + 6.23322I 8.20976 5.43660I
u = 0.741285 0.603477I
a = 0.610967 + 0.942701I
b = 0.215104 0.798845I
3.50536 1.91915I 4.46198 + 0.73730I
u = 0.741285 + 0.603477I
a = 0.610967 0.942701I
b = 0.215104 + 0.798845I
3.50536 + 1.91915I 4.46198 0.73730I
u = 0.388414 0.926516I
a = 0.708746 0.512701I
b = 0.206431 0.331897I
1.27959 + 3.15177I 9.69878 7.80238I
u = 0.388414 + 0.926516I
a = 0.708746 + 0.512701I
b = 0.206431 + 0.331897I
1.27959 3.15177I 9.69878 + 7.80238I
u = 0.236385 0.241436I
a = 3.64494 0.01173I
b = 1.286840 + 0.093791I
4.83854 + 1.75409I 13.7193 4.0775I
u = 0.236385 + 0.241436I
a = 3.64494 + 0.01173I
b = 1.286840 0.093791I
4.83854 1.75409I 13.7193 + 4.0775I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.48724 3.26861I
a = 0.992737 + 0.042270I
b = 1.43060 + 0.17503I
6.80152 + 5.19940I 9.91514 9.30773I
u = 0.48724 + 3.26861I
a = 0.992737 0.042270I
b = 1.43060 0.17503I
6.80152 5.19940I 9.91514 + 9.30773I
4
II. I
u
2
= hu
76
+ 14u
75
+ · · · + 534558087u + 145440247, 1.38 × 10
756
u
75
+
1.92 × 10
757
u
74
+ · · · + 6.93 × 10
764
b + 3.10 × 10
764
, 1.03 × 10
764
u
75
+ 1.45 ×
10
765
u
74
+ · · · + 5.04 × 10
772
a + 1.90 × 10
773
i
(i) Arc colorings
a
6
=
1
0
a
11
=
2.04348 × 10
9
u
75
2.87815 × 10
8
u
74
+ ··· + 6.81727u 3.77915
1.99790 × 10
9
u
75
2.76649 × 10
8
u
74
+ ··· 1.38807u 0.447036
a
1
=
4.55807 × 10
11
u
75
1.11659 × 10
9
u
74
+ ··· + 8.20534u 3.33212
1.99790 × 10
9
u
75
2.76649 × 10
8
u
74
+ ··· 1.38807u 0.447036
a
5
=
5.54334 × 10
9
u
75
7.66477 × 10
8
u
74
+ ··· 6.84711u 1.91543
1.34002 × 10
9
u
75
+ 1.87201 × 10
8
u
74
+ ··· 0.185462u + 0.610633
a
8
=
0
u
a
4
=
5.54334 × 10
9
u
75
7.66477 × 10
8
u
74
+ ··· 6.84711u 1.91543
1.04928 × 10
9
u
75
+ 1.47012 × 10
8
u
74
+ ··· + 0.108047u + 0.471135
a
9
=
1.43858 × 10
9
u
75
+ 2.03918 × 10
8
u
74
+ ··· 5.74003u + 2.30118
1.38996 × 10
9
u
75
+ 1.92608 × 10
8
u
74
+ ··· + 2.59385u + 0.531534
a
2
=
2.33148 × 10
9
u
75
+ 3.11072 × 10
8
u
74
+ ··· + 10.9154u 2.97159
1.85573 × 10
9
u
75
2.52774 × 10
8
u
74
+ ··· 1.64678u 0.533064
a
3
=
2.11477 × 10
8
u
75
2.92699 × 10
7
u
74
+ ··· 7.76058u 11.5985
6.95042 × 10
10
u
75
+ 9.89215 × 10
9
u
74
+ ··· 3.48217u + 1.00693
a
7
=
1.46699 × 10
8
u
75
+ 2.01986 × 10
7
u
74
+ ··· + 18.7966u + 5.91930
2.05162 × 10
9
u
75
2.84554 × 10
8
u
74
+ ··· + 0.687146u 1.55121
a
10
=
4.65811 × 10
9
u
75
6.57289 × 10
8
u
74
+ ··· + 9.04986u 7.06127
1.43923 × 10
9
u
75
1.96669 × 10
8
u
74
+ ··· 1.19055u 0.440475
a
10
=
4.65811 × 10
9
u
75
6.57289 × 10
8
u
74
+ ··· + 9.04986u 7.06127
1.43923 × 10
9
u
75
1.96669 × 10
8
u
74
+ ··· 1.19055u 0.440475
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.20323 0.75190I
a = 0.759442 0.121766I
b = 1.305037 0.319754I
0.57872 7.31208I 5.91640 + 10.41652I
u = 2.20323 + 0.75190I
a = 0.759442 + 0.121766I
b = 1.305037 + 0.319754I
0.57872 + 7.31208I 5.91640 10.41652I
u = 2.02231 0.70156I
a = 0.461980 0.279686I
b = 1.310423 + 0.247828I
0.27749 3.56587I 6.97391 + 2.39117I
u = 2.02231 + 0.70156I
a = 0.461980 + 0.279686I
b = 1.310423 0.247828I
0.27749 + 3.56587I 6.97391 2.39117I
u = 2.01728 5.23565I
a = 0.874894 + 0.078231I
b = 1.284137 0.219366I
0.12887 2.52959I 8.82438 + 4.08928I
u = 2.01728 + 5.23565I
a = 0.874894 0.078231I
b = 1.284137 + 0.219366I
0.12887 + 2.52959I 8.82438 4.08928I
u = 1.30859 3.18395I
a = 0.952478 + 0.106641I
b = 1.327951 + 0.244567I
4.47754 6.67234I 11.48779 + 6.72054I
u = 1.30859 + 3.18395I
a = 0.952478 0.106641I
b = 1.327951 0.244567I
4.47754 + 6.67234I 11.48779 6.72054I
u = 1.062914 0.011229I
a = 0.507994 0.471503I
b = 0.637024 + 0.316684I
3.01317 + 1.73011I 2.31903 3.39119I
u = 1.062914 + 0.011229I
a = 0.507994 + 0.471503I
b = 0.637024 0.316684I
3.01317 1.73011I 2.31903 + 3.39119I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.994153 0.589075I
a = 0.269890 0.562025I
b = 0.931604 + 0.510293I
0.53464 + 7.36666I 7.21457 4.36224I
u = 0.994153 + 0.589075I
a = 0.269890 + 0.562025I
b = 0.931604 0.510293I
0.53464 7.36666I 7.21457 + 4.36224I
u = 0.85681 3.61586I
a = 0.911715 + 0.045446I
b = 1.41403 0.34833I
2.6277 16.4336I 9.29280 + 9.00941I
u = 0.85681 + 3.61586I
a = 0.911715 0.045446I
b = 1.41403 + 0.34833I
2.6277 + 16.4336I 9.29280 9.00941I
u = 0.854511 0.923875I
a = 0.219686 + 0.885090I
b = 0.402726 0.858164I
3.74004 2.56276I 0.61076 + 11.02950I
u = 0.854511 + 0.923875I
a = 0.219686 0.885090I
b = 0.402726 + 0.858164I
3.74004 + 2.56276I 0.61076 11.02950I
u = 0.725099 1.002225I
a = 0.990480 0.974347I
b = 0.044203 + 0.612297I
4.00054 + 0.42281I 1.53362 + 1.17105I
u = 0.725099 + 1.002225I
a = 0.990480 + 0.974347I
b = 0.044203 0.612297I
4.00054 0.42281I 1.53362 1.17105I
u = 0.66771 2.41967I
a = 1.179377 0.199895I
b = 1.325924 + 0.160373I
5.55889 + 0.47303I 14.2941 + 0.6818I
u = 0.66771 + 2.41967I
a = 1.179377 + 0.199895I
b = 1.325924 0.160373I
5.55889 0.47303I 14.2941 0.6818I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.642690 0.838104I
a = 0.896322 0.618227I
b = 0.968679 0.306013I
3.49997 + 1.86931I 3.81926 1.10656I
u = 0.642690 + 0.838104I
a = 0.896322 + 0.618227I
b = 0.968679 + 0.306013I
3.49997 1.86931I 3.81926 + 1.10656I
u = 0.509211 1.097054I
a = 0.132915 0.157714I
b = 0.099162 0.335506I
1.09766 + 2.44518I 6.25239 + 1.93768I
u = 0.509211 + 1.097054I
a = 0.132915 + 0.157714I
b = 0.099162 + 0.335506I
1.09766 2.44518I 6.25239 1.93768I
u = 0.481614 1.043300I
a = 0.979250 0.553626I
b = 0.248826 + 0.843265I
2.65342 12.13501I 5.18296 + 8.02614I
u = 0.481614 + 1.043300I
a = 0.979250 + 0.553626I
b = 0.248826 0.843265I
2.65342 + 12.13501I 5.18296 8.02614I
u = 0.417510 0.135864I
a = 0.748912 0.683008I
b = 0.075482 0.672046I
1.83137 + 1.88031I 3.15463 4.07325I
u = 0.417510 + 0.135864I
a = 0.748912 + 0.683008I
b = 0.075482 + 0.672046I
1.83137 1.88031I 3.15463 + 4.07325I
u = 0.352321 0.972093I
a = 1.157701 + 0.262629I
b = 1.308302 + 0.270202I
2.49885 + 5.30835I 8.91119 5.70079I
u = 0.352321 + 0.972093I
a = 1.157701 0.262629I
b = 1.308302 0.270202I
2.49885 5.30835I 8.91119 + 5.70079I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.328408 0.476460I
a = 1.06307 1.06164I
b = 1.334668 + 0.401679I
1.28728 + 4.79520I 8.26299 2.51783I
u = 0.328408 + 0.476460I
a = 1.06307 + 1.06164I
b = 1.334668 0.401679I
1.28728 4.79520I 8.26299 + 2.51783I
u = 0.200692 0.121850I
a = 4.98012 0.85333I
b = 0.062116 + 0.761993I
3.69493 3.40892I 2.10008 + 7.62336I
u = 0.200692 + 0.121850I
a = 4.98012 + 0.85333I
b = 0.062116 0.761993I
3.69493 + 3.40892I 2.10008 7.62336I
u = 0.172907 0.388957I
a = 0.99152 1.75984I
b = 1.389277 0.027409I
3.13133 2.04238I 7.55561 + 4.38736I
u = 0.172907 + 0.388957I
a = 0.99152 + 1.75984I
b = 1.389277 + 0.027409I
3.13133 + 2.04238I 7.55561 4.38736I
u = 0.01582 3.27736I
a = 0.849131 0.159223I
b = 1.45271 + 0.36773I
2.09696 7.08063I 10.9741 + 9.9581I
u = 0.01582 + 3.27736I
a = 0.849131 + 0.159223I
b = 1.45271 0.36773I
2.09696 + 7.08063I 10.9741 9.9581I
u = 0.01335 3.53117I
a = 0.895935 + 0.051222I
b = 1.53494 + 0.03855I
8.13102 + 6.65132I 12.5564 7.5708I
u = 0.01335 + 3.53117I
a = 0.895935 0.051222I
b = 1.53494 0.03855I
8.13102 6.65132I 12.5564 + 7.5708I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.089403 0.771981I
a = 1.122944 0.113637I
b = 0.369901 0.560002I
1.20192 + 1.77591I 8.18323 1.57822I
u = 0.089403 + 0.771981I
a = 1.122944 + 0.113637I
b = 0.369901 + 0.560002I
1.20192 1.77591I 8.18323 + 1.57822I
u = 0.156017 0.924940I
a = 0.622632 0.128006I
b = 0.368179 0.508001I
1.29394 + 1.64438I 9.75127 4.13442I
u = 0.156017 + 0.924940I
a = 0.622632 + 0.128006I
b = 0.368179 + 0.508001I
1.29394 1.64438I 9.75127 + 4.13442I
u = 0.167192 0.826007I
a = 1.27139 0.68692I
b = 0.075467 0.609557I
0.03422 3.55485I 4.57668 + 5.47640I
u = 0.167192 + 0.826007I
a = 1.27139 + 0.68692I
b = 0.075467 + 0.609557I
0.03422 + 3.55485I 4.57668 5.47640I
u = 0.192003 0.943910I
a = 0.1143964 + 0.0331876I
b = 0.150149 0.934780I
3.32458 + 0.03587I 1.51662 0.27967I
u = 0.192003 + 0.943910I
a = 0.1143964 0.0331876I
b = 0.150149 + 0.934780I
3.32458 0.03587I 1.51662 + 0.27967I
u = 0.218191
a = 1.26606
b = 0.375740
0.725667 13.9612
u = 0.222067 0.752508I
a = 0.293505 1.100755I
b = 1.264017 0.200993I
3.68056 + 0.68832I 9.17940 0.50372I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.222067 + 0.752508I
a = 0.293505 + 1.100755I
b = 1.264017 + 0.200993I
3.68056 0.68832I 9.17940 + 0.50372I
u = 0.281042 0.261863I
a = 2.07631 2.51644I
b = 1.009885 + 0.581338I
0.66505 5.23954I 3.62914 + 7.76404I
u = 0.281042 + 0.261863I
a = 2.07631 + 2.51644I
b = 1.009885 0.581338I
0.66505 + 5.23954I 3.62914 7.76404I
u = 0.36191 1.51092I
a = 0.449823 + 0.117824I
b = 1.203071 + 0.312929I
0.209490 0.491453I 7.67661 3.15939I
u = 0.36191 + 1.51092I
a = 0.449823 0.117824I
b = 1.203071 0.312929I
0.209490 + 0.491453I 7.67661 + 3.15939I
u = 0.452707 1.011520I
a = 1.044819 + 0.574001I
b = 1.38264 + 0.31570I
0.83133 9.81598I 6.84669 + 7.76989I
u = 0.452707 + 1.011520I
a = 1.044819 0.574001I
b = 1.38264 0.31570I
0.83133 + 9.81598I 6.84669 7.76989I
u = 0.48117 2.93037I
a = 1.039495 0.086989I
b = 1.40631 + 0.21816I
6.84634 + 4.36487I 14.8568 3.0206I
u = 0.48117 + 2.93037I
a = 1.039495 + 0.086989I
b = 1.40631 0.21816I
6.84634 4.36487I 14.8568 + 3.0206I
u = 0.525156 1.158406I
a = 0.799603 0.660757I
b = 0.211230 + 0.692166I
1.61113 + 5.99074I 7.07123 7.64863I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.525156 + 1.158406I
a = 0.799603 + 0.660757I
b = 0.211230 0.692166I
1.61113 5.99074I 7.07123 + 7.64863I
u = 0.539549 0.273320I
a = 0.270010 + 1.233085I
b = 0.201569 + 0.767240I
5.85346 + 5.89693I 1.84592 6.16015I
u = 0.539549 + 0.273320I
a = 0.270010 1.233085I
b = 0.201569 0.767240I
5.85346 5.89693I 1.84592 + 6.16015I
u = 0.567068 0.209580I
a = 0.166667 0.594032I
b = 1.234808 0.206791I
1.62348 + 1.28005I 6.93474 0.13383I
u = 0.567068 + 0.209580I
a = 0.166667 + 0.594032I
b = 1.234808 + 0.206791I
1.62348 1.28005I 6.93474 + 0.13383I
u = 0.57048 4.13793I
a = 0.897731 + 0.050483I
b = 1.42980 0.07326I
9.55152 1.46003I 15.2290 + 0.9919I
u = 0.57048 + 4.13793I
a = 0.897731 0.050483I
b = 1.42980 + 0.07326I
9.55152 + 1.46003I 15.2290 0.9919I
u = 0.645057 0.431474I
a = 0.82159 1.20031I
b = 0.564347 + 0.281716I
3.26194 2.66752I 12.49560 + 1.19911I
u = 0.645057 + 0.431474I
a = 0.82159 + 1.20031I
b = 0.564347 0.281716I
3.26194 + 2.66752I 12.49560 1.19911I
u = 0.64991 3.14998I
a = 0.992358 + 0.013233I
b = 1.43258 + 0.21432I
6.96863 + 4.63471I 13.22357 + 2.74920I
12
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.64991 + 3.14998I
a = 0.992358 0.013233I
b = 1.43258 0.21432I
6.96863 4.63471I 13.22357 2.74920I
u = 0.79344 4.20755I
a = 0.904111 + 0.077494I
b = 1.379299 0.285950I
6.65323 + 9.56425I 11.60991 7.84069I
u = 0.79344 + 4.20755I
a = 0.904111 0.077494I
b = 1.379299 + 0.285950I
6.65323 9.56425I 11.60991 + 7.84069I
u = 1.19588
a = 0.848554
b = 1.33405
5.87122 16.9540
u = 1.41923 0.79905I
a = 0.841178 + 0.672685I
b = 1.184461 0.087532I
3.89513 + 3.10544I 9.40045 5.74894I
u = 1.41923 + 0.79905I
a = 0.841178 0.672685I
b = 1.184461 + 0.087532I
3.89513 3.10544I 9.40045 + 5.74894I
13
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
12
+ 2u
9
+ 2u
8
u
7
u
5
+ u
4
+ u
3
u
2
u + 1)
(u
76
+ 5u
75
+ ··· + u 2)
c
2
(u
12
+ 6u
10
+ u
9
+ 14u
8
+ 4u
7
+ 17u
6
+ 6u
5
+ 12u
4
+ 3u
3
+ 5u
2
+ u + 1)
(u
76
+ u
75
+ ··· + 23u 101)
c
3
(u
12
2u
10
u
9
+ 2u
8
+ 2u
7
+ 3u
6
+ 4u
5
+ 2u
4
+ u
3
+ 3u
2
+ 3u + 1)
(u
76
+ 11u
75
+ ··· 9u + 11)
c
4
(u
12
u
11
+ 5u
10
3u
9
+ 12u
8
6u
7
+ 17u
6
4u
5
+ 14u
4
u
3
+ 6u
2
+ 1)
(u
76
+ 2u
75
+ ··· 198u 29)
c
5
(u
12
6u
10
+ 13u
8
+ u
7
10u
6
4u
5
2u
4
+ 5u
3
+ 4u
2
2u + 1)
(u
76
+ u
75
+ ··· 12u 7)
c
6
(u
12
+ 2u
10
3u
9
+ 4u
8
+ 4u
7
+ 12u
6
+ 7u
5
+ 3u
4
+ 4u
3
+ 4u
2
2u + 1)
(u
76
+ 3u
75
+ ··· 3283u + 4312)
c
7
(u
12
+ 6u
10
u
9
+ 14u
8
4u
7
+ 17u
6
6u
5
+ 12u
4
3u
3
+ 5u
2
u + 1)
(u
76
+ u
75
+ ··· + 23u 101)
c
8
(u
12
+ u
11
+ 5u
10
+ 3u
9
+ 12u
8
+ 6u
7
+ 17u
6
+ 4u
5
+ 14u
4
+ u
3
+ 6u
2
+ 1)
(u
76
+ 2u
75
+ ··· 198u 29)
c
9
(u
12
+ u
11
u
10
u
9
+ u
8
+ u
7
+ u
5
+ 2u
4
2u
3
+ 1)
(u
76
+ 7u
74
+ ··· + 7948u 1013)
c
10
(u
12
6u
10
+ 13u
8
u
7
10u
6
+ 4u
5
2u
4
5u
3
+ 4u
2
+ 2u + 1)
(u
76
+ u
75
+ ··· 12u 7)
c
11
(u
12
6u
10
+ 13u
8
u
7
10u
6
+ 4u
5
2u
4
5u
3
+ 4u
2
+ 2u + 1)
(u
76
+ u
75
+ ··· 12u 7)
14
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
12
+ 4y
10
4y
9
+ 10y
8
+ y
7
+ y
5
+ 5y
4
5y
3
+ 5y
2
3y + 1)
(y
76
3y
75
+ ··· + 63y + 4)
c
2
, c
7
(y
12
+ 12y
11
+ ··· + 9y + 1)(y
76
+ 53y
75
+ ··· + 200865y + 10201)
c
3
(y
12
4y
11
+ 8y
10
3y
9
+ 14y
7
7y
6
+ 6y
5
+ 6y
4
7y
3
+ 7y
2
3y + 1)
(y
76
11y
75
+ ··· 2567y + 121)
c
4
, c
8
(y
12
+ 9y
11
+ ··· + 12y + 1)(y
76
+ 46y
75
+ ··· 29344y + 841)
c
5
(y
12
12y
11
+ ··· + 4y + 1)(y
76
67y
75
+ ··· + 500y + 49)
c
6
(y
12
+ 4y
11
+ ··· + 4y + 1)
(y
76
+ 25y
75
+ ··· 18824281y + 18593344)
c
9
(y
12
3y
11
+ 5y
10
5y
9
+ 5y
8
+ y
7
+ y
5
+ 10y
4
4y
3
+ 4y
2
+ 1)
(y
76
+ 14y
75
+ ··· + 25053492y + 1026169)
c
10
(y
12
12y
11
+ ··· + 4y + 1)(y
76
67y
75
+ ··· + 500y + 49)
c
11
(y
12
12y
11
+ ··· + 4y + 1)(y
76
67y
75
+ ··· + 500y + 49)
15