11a
173
(K11a
173
)
1
Arc Sequences
5 1 9 6 2 10 4 11 7 3 8
Solving Sequence
1,5
2 3 6
4,8
7 11 9 10
c
1
c
2
c
5
c
4
c
7
c
11
c
8
c
10
c
3
, c
6
, c
9
Representation Ideals
I =
6
\
i=1
I
u
i
I
u
1
= hb
2
+ 1, u 1, 2b + a 1i
I
u
2
= hb
2
b + 2, u + 1, b + a + 1i
I
u
3
= hu
3
+ u
2
1, b 1, 2a 2u + 1i
I
u
4
= hb
10
b
9
+ 2b
8
4b
7
+ 4b
6
5b
5
+ 3b
4
b
3
+ b
2
+ 1, b
7
b
6
+ b
5
4b
4
+ 2b
3
2b
2
+ b + 2u + 1,
2b
9
b
8
+ b
7
5b
6
+ 4b
5
2b
3
+ b
2
+ 3b + 2ai
I
u
5
= hb
32
5b
31
+ ··· 8b + 1,
20481137056b
31
+ 72795238145b
30
+ ··· + 14963920178a 34443607773,
23037638291b
31
+ 14963920178u + ··· 386076351067b + 44639102550i
I
u
6
= hu
28
2u
27
+ ··· 3u 4,
14767307395u
27
+ 20235323073u
26
+ ··· + 98330713818b + 33355375098,
32428293291u
27
21218621420u
26
+ ··· + 196661427636a + 204360671755i
There are 6 irreducible components with 77 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
= hb
2
+ 1, u 1, 2b + a 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
3
=
0
1
a
6
=
1
0
a
4
=
1
1
a
8
=
2b + 1
b
a
7
=
b
1
a
11
=
b 1
1
a
9
=
b
0
a
10
=
b 1
b
a
10
=
b 1
b
(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 = 1.00000
a = 1.00000 2.00000I
b = 1.00000I
4.93480 12.0000
u = 1.00000
a = 1.00000 + 2.00000I
b = 1.00000I
4.93480 12.0000
3
II. I
u
2
= hb
2
b + 2, u + 1, b + a + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
a
2
=
1
1
a
3
=
0
1
a
6
=
1
0
a
4
=
1
1
a
8
=
b 1
b
a
7
=
b
b + 1
a
11
=
1
b 2
a
9
=
1
2
a
10
=
1
b 1
a
10
=
1
b 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 0.50000 1.32288I
b = 0.50000 1.32288I
8.22467 14.0000
u = 1.00000
a = 0.50000 + 1.32288I
b = 0.50000 + 1.32288I
8.22467 14.0000
5
III. I
u
3
= hu
3
+ u
2
1, b 1, 2a 2u + 1i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
6
=
u
u
2
+ u 1
a
4
=
u
2
+ 1
u
2
a
8
=
u
1
2
1
a
7
=
1
2
u
1
2
u
2
+
1
2
u +
1
2
a
11
=
u +
1
2
1
a
9
=
2u
2
a
10
=
3
2
u
1
2
u
2
1
2
u +
3
2
a
10
=
3
2
u
1
2
u
2
1
2
u +
3
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.877439 0.744862I
a = 1.37744 0.74486I
b = 1.00000
4.66906 2.82812I 1.06503 + 2.38969I
u = 0.877439 + 0.744862I
a = 1.37744 + 0.74486I
b = 1.00000
4.66906 + 2.82812I 1.06503 2.38969I
u = 0.754878
a = 0.254878
b = 1.00000
0.531480 7.38005
7
IV. I
u
4
= hb
10
b
9
+ · · · + b
2
+ 1, b
7
b
6
+ b
5
4b
4
+ 2b
3
2b
2
+ b + 2u +
1, 2b
9
b
8
+ · · · + 3b + 2ai
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1
2
b
7
+
1
2
b
6
+ ···
1
2
b
1
2
a
2
=
1
1
2
b
9
+ b
7
+ ··· b
2
+
3
2
b
a
3
=
1
2
b
9
b
7
+ ···
3
2
b + 1
1
2
b
9
+ b
7
+ ··· b
2
+
3
2
b
a
6
=
1
2
b
7
1
2
b
6
+ ··· +
1
2
b +
1
2
b
7
b
5
+ 2b
4
+ b
2
+ b 1
a
4
=
1
2
b
7
+
1
2
b
6
+ ···
3
2
b +
1
2
1
2
b
9
+
1
2
b
7
+ ··· + 2b
1
2
a
8
=
b
9
+
1
2
b
8
+ ···
1
2
b
2
3
2
b
b
a
7
=
3
2
b
9
+ b
8
+ ··· b +
3
2
b
9
b
8
+ ··· +
3
2
b
3
2
a
11
=
1
2
b
9
+
3
2
b
8
+ ···
1
2
b
2
+ 2
b
2
a
9
=
1
2
b
7
1
2
b
6
+ ··· +
1
2
b +
1
2
b
3
+ b
a
10
=
1
2
b
9
+ 2b
8
+ ···
1
2
b + 1
b
8
+
1
2
b
7
+ ···
1
2
b +
1
2
a
10
=
1
2
b
9
+ 2b
8
+ ···
1
2
b + 1
b
8
+
1
2
b
7
+ ···
1
2
b +
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
8
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.001865 0.741764I
a = 2.24279 0.22903I
b = 0.67647 1.30286I
1.49357 + 10.61135I 2.76481 7.85454I
u = 1.001865 + 0.741764I
a = 2.24279 + 0.22903I
b = 0.67647 + 1.30286I
1.49357 10.61135I 2.76481 + 7.85454I
u = 0.760506 + 0.815892I
a = 0.658201 0.065826I
b = 0.473774 0.431559I
3.01208 + 1.13825I 0.09602 2.34058I
u = 0.760506 0.815892I
a = 0.658201 + 0.065826I
b = 0.473774 + 0.431559I
3.01208 1.13825I 0.09602 + 2.34058I
u = 0.517281
a = 4.14815 + 3.15299I
b = 0.133790 1.026499I
4.07650 8.66242
u = 0.517281
a = 4.14815 3.15299I
b = 0.133790 + 1.026499I
4.07650 8.66242
u = 0.760506 + 0.815892I
a = 0.686158 + 0.302307I
b = 0.386464 0.809421I
3.01208 + 1.13825I 0.09602 2.34058I
u = 0.760506 0.815892I
a = 0.686158 0.302307I
b = 0.386464 + 0.809421I
3.01208 1.13825I 0.09602 + 2.34058I
u = 1.001865 0.741764I
a = 1.06668 + 1.09068I
b = 1.129988 0.183434I
1.49357 + 10.61135I 2.76481 7.85454I
u = 1.001865 + 0.741764I
a = 1.06668 1.09068I
b = 1.129988 + 0.183434I
1.49357 10.61135I 2.76481 + 7.85454I
9
V.
I
u
5
= hb
32
5b
31
+ · · · 8b + 1, 2.05 × 10
10
b
31
+ 7.28 × 10
10
b
30
+ · · · + 1.50 ×
10
10
a3.44×10
10
, 1.50×10
10
u2.30×10
10
b
31
+· · ·3.86×10
11
b+4.46×10
10
i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
1.53955b
31
7.18864b
30
+ ··· + 25.8005b 2.98312
a
2
=
1
0.909022b
31
4.39341b
30
+ ··· + 9.07362b 0.928257
a
3
=
0.909022b
31
+ 4.39341b
30
+ ··· 9.07362b + 1.92826
0.909022b
31
4.39341b
30
+ ··· + 9.07362b 0.928257
a
6
=
1.53955b
31
+ 7.18864b
30
+ ··· 25.8005b + 2.98312
1.28087b
31
5.57669b
30
+ ··· + 8.26100b 0.801297
a
4
=
0.258678b
31
1.61195b
30
+ ··· + 17.5395b 2.18182
2.42922b
31
10.6152b
30
+ ··· + 21.1426b 2.86468
a
8
=
1.36870b
31
4.86472b
30
+ ··· 13.3541b + 2.30178
b
a
7
=
2.05172b
31
+ 10.9486b
30
+ ··· 21.1458b + 2.48206
1.17245b
31
5.60412b
30
+ ··· + 11.8134b 2.29427
a
11
=
1.97879b
31
10.4094b
30
+ ··· + 13.2514b 0.368701
b
2
a
9
=
0.853298b
31
3.52176b
30
+ ··· + 2.10747b + 0.322988
b
3
+ b
a
10
=
1.22566b
31
4.09973b
30
+ ··· 2.36324b + 0.922730
0.253192b
31
+ 1.14777b
30
+ ··· 8.72270b + 1.06548
a
10
=
1.22566b
31
4.09973b
30
+ ··· 2.36324b + 0.922730
0.253192b
31
+ 1.14777b
30
+ ··· 8.72270b + 1.06548
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.724199 + 0.826388I
a = 0.873040 + 1.019050I
b = 0.667529 1.233435I
2.34449 + 4.73566I 1.11364 2.91588I
u = 0.724199 0.826388I
a = 0.873040 1.019050I
b = 0.667529 + 1.233435I
2.34449 4.73566I 1.11364 + 2.91588I
u = 0.977539 0.749941I
a = 0.262243 + 0.231216I
b = 0.494890 0.256259I
2.34449 4.73566I 1.11364 + 2.91588I
u = 0.977539 + 0.749941I
a = 0.262243 0.231216I
b = 0.494890 + 0.256259I
2.34449 + 4.73566I 1.11364 2.91588I
u = 1.017320 + 0.191091I
a = 0.77304 1.40886I
b = 0.436018 1.310654I
4.37117 + 5.29622I 8.10789 6.28296I
u = 1.017320 0.191091I
a = 0.77304 + 1.40886I
b = 0.436018 + 1.310654I
4.37117 5.29622I 8.10789 + 6.28296I
u = 0.059947 0.622852I
a = 0.467003 + 0.890621I
b = 0.378599 1.075258I
0.93480 + 2.67607I 0.38861 3.32415I
u = 0.059947 + 0.622852I
a = 0.467003 0.890621I
b = 0.378599 + 1.075258I
0.93480 2.67607I 0.38861 + 3.32415I
u = 0.866890 0.696274I
a = 1.92331 0.56041I
b = 0.212635 1.014817I
0.93480 2.67607I 0.38861 + 3.32415I
u = 0.866890 + 0.696274I
a = 1.92331 + 0.56041I
b = 0.212635 + 1.014817I
0.93480 + 2.67607I 0.38861 3.32415I
11
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.866890 + 0.696274I
a = 2.69221 1.74930I
b = 0.171716 1.089494I
0.93480 + 2.67607I 0.38861 3.32415I
u = 0.866890 0.696274I
a = 2.69221 + 1.74930I
b = 0.171716 + 1.089494I
0.93480 2.67607I 0.38861 + 3.32415I
u = 0.908738 + 0.252477I
a = 1.69112 0.97289I
b = 0.058000 1.114600I
3.61825 0.25270I 6.38985 + 0.96511I
u = 0.908738 0.252477I
a = 1.69112 + 0.97289I
b = 0.058000 + 1.114600I
3.61825 + 0.25270I 6.38985 0.96511I
u = 0.708362 + 0.611401I
a = 1.56409 + 0.56471I
b = 0.153564 1.382418I
3.61825 + 0.25270I 6.38985 0.96511I
u = 0.708362 0.611401I
a = 1.56409 0.56471I
b = 0.153564 + 1.382418I
3.61825 0.25270I 6.38985 + 0.96511I
u = 0.908738 0.252477I
a = 0.160770 + 1.402057I
b = 0.185966 0.248413I
3.61825 + 0.25270I 6.38985 0.96511I
u = 0.908738 + 0.252477I
a = 0.160770 1.402057I
b = 0.185966 + 0.248413I
3.61825 0.25270I 6.38985 + 0.96511I
u = 0.960503 0.654282I
a = 0.874727 + 0.511465I
b = 0.27490 1.49232I
4.37117 + 5.29622I 8.10789 6.28296I
u = 0.960503 + 0.654282I
a = 0.874727 0.511465I
b = 0.27490 + 1.49232I
4.37117 5.29622I 8.10789 + 6.28296I
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.977539 0.749941I
a = 1.72382 0.29569I
b = 0.336437 0.940681I
2.34449 4.73566I 1.11364 + 2.91588I
u = 0.977539 + 0.749941I
a = 1.72382 + 0.29569I
b = 0.336437 + 0.940681I
2.34449 + 4.73566I 1.11364 2.91588I
u = 0.708362 0.611401I
a = 1.17703 + 1.58536I
b = 0.608496 0.923549I
3.61825 0.25270I 6.38985 + 0.96511I
u = 0.708362 + 0.611401I
a = 1.17703 1.58536I
b = 0.608496 + 0.923549I
3.61825 + 0.25270I 6.38985 0.96511I
u = 0.059947 0.622852I
a = 1.186916 0.555131I
b = 0.645301 0.131928I
0.93480 + 2.67607I 0.38861 3.32415I
u = 0.059947 + 0.622852I
a = 1.186916 + 0.555131I
b = 0.645301 + 0.131928I
0.93480 2.67607I 0.38861 + 3.32415I
u = 0.960503 + 0.654282I
a = 2.47726 0.17457I
b = 0.723528 1.103513I
4.37117 5.29622I 8.10789 + 6.28296I
u = 0.960503 0.654282I
a = 2.47726 + 0.17457I
b = 0.723528 + 1.103513I
4.37117 + 5.29622I 8.10789 6.28296I
u = 1.017320 0.191091I
a = 0.080344 0.145257I
b = 0.930500 0.053773I
4.37117 5.29622I 8.10789 + 6.28296I
u = 1.017320 + 0.191091I
a = 0.080344 + 0.145257I
b = 0.930500 + 0.053773I
4.37117 + 5.29622I 8.10789 6.28296I
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 0.724199 + 0.826388I
a = 1.62577 0.21392I
b = 1.060700 0.232760I
2.34449 + 4.73566I 1.11364 2.91588I
u = 0.724199 0.826388I
a = 1.62577 + 0.21392I
b = 1.060700 + 0.232760I
2.34449 4.73566I 1.11364 + 2.91588I
13
VI. I
u
6
=
hu
28
2u
27
+· · ·3u4, 1.48×10
10
u
27
+2.02×10
10
u
26
+· · ·+9.83×10
10
b+
3.34 × 10
10
, 3.24 × 10
10
u
27
2.12 × 10
10
u
26
+ · · · + 1.97 × 10
11
a + 2.04 × 10
11
i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
6
=
u
u
3
+ u
a
4
=
u
3
u
5
u
3
+ u
a
8
=
0.164894u
27
+ 0.107894u
26
+ ··· 2.21519u 1.03915
0.150180u
27
0.205788u
26
+ ··· + 0.595130u 0.339216
a
7
=
0.160609u
27
+ 0.110297u
26
+ ··· 2.13491u 1.03465
0.227707u
27
0.221295u
26
+ ··· + 0.789310u 0.0177292
a
11
=
0.206489u
27
0.182794u
26
+ ··· + 1.38239u + 1.44504
0.198851u
27
+ 0.240301u
26
+ ··· + 0.0000310478u + 0.278301
a
9
=
0.312509u
27
+ 0.216909u
26
+ ··· 2.81796u 1.93782
0.373802u
27
0.449982u
26
+ ··· + 0.400981u 0.382402
a
10
=
0.137090u
27
0.0589378u
26
+ ··· + 1.47329u + 1.50912
0.199975u
27
+ 0.238265u
26
+ ··· 0.339747u + 0.201391
a
10
=
0.137090u
27
0.0589378u
26
+ ··· + 1.47329u + 1.50912
0.199975u
27
+ 0.238265u
26
+ ··· 0.339747u + 0.201391
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.156720 0.209637I
a = 0.79174 1.21845I
b = 0.465804 1.280601I
8.43358 10.19255I 10.18832 + 7.63922I
u = 1.156720 + 0.209637I
a = 0.79174 + 1.21845I
b = 0.465804 + 1.280601I
8.43358 + 10.19255I 10.18832 7.63922I
u = 1.074081 0.691225I
a = 1.41798 + 0.69280I
b = 0.422318 + 1.038381I
0.23866 8.48658I 4.72348 + 9.14479I
u = 1.074081 + 0.691225I
a = 1.41798 0.69280I
b = 0.422318 1.038381I
0.23866 + 8.48658I 4.72348 9.14479I
u = 0.903785 0.845201I
a = 1.078649 + 0.117582I
b = 0.379054 0.705257I
3.28350 4.57627I 2.13594 + 7.47854I
u = 0.903785 + 0.845201I
a = 1.078649 0.117582I
b = 0.379054 + 0.705257I
3.28350 + 4.57627I 2.13594 7.47854I
u = 0.878060 0.825409I
a = 0.366900 0.450231I
b = 0.338313 + 0.571686I
3.34352 1.62496I 2.45048 1.41829I
u = 0.878060 + 0.825409I
a = 0.366900 + 0.450231I
b = 0.338313 0.571686I
3.34352 + 1.62496I 2.45048 + 1.41829I
u = 0.838400
a = 0.287249
b = 1.20069
0.271501 23.7364
u = 0.566116 0.813544I
a = 0.534639 + 0.137883I
b = 0.471357 0.915613I
1.74883 + 2.81556I 1.14300 4.42775I
15
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.566116 + 0.813544I
a = 0.534639 0.137883I
b = 0.471357 + 0.915613I
1.74883 2.81556I 1.14300 + 4.42775I
u = 0.357231 0.322552I
a = 0.478268 + 0.914294I
b = 0.587531 + 0.365743I
1.12674 1.01957I 4.42993 + 4.67672I
u = 0.357231 + 0.322552I
a = 0.478268 0.914294I
b = 0.587531 0.365743I
1.12674 + 1.01957I 4.42993 4.67672I
u = 0.167815 0.852338I
a = 0.800362 0.593310I
b = 0.442426 + 1.154502I
3.88792 + 6.82425I 4.62158 6.71855I
u = 0.167815 + 0.852338I
a = 0.800362 + 0.593310I
b = 0.442426 1.154502I
3.88792 6.82425I 4.62158 + 6.71855I
u = 0.679059 0.893968I
a = 0.932511 + 0.786849I
b = 0.600465 1.265066I
0.89815 10.64775I 3.82752 + 5.52190I
u = 0.679059 + 0.893968I
a = 0.932511 0.786849I
b = 0.600465 + 1.265066I
0.89815 + 10.64775I 3.82752 5.52190I
u = 0.682847
a = 0.725706
b = 0.129567
0.926639 11.5883
u = 0.805429 0.748611I
a = 1.99187 0.34421I
b = 1.193818 0.462931I
4.99503 + 1.79073I 1.05075 + 2.61493I
u = 0.805429 + 0.748611I
a = 1.99187 + 0.34421I
b = 1.193818 + 0.462931I
4.99503 1.79073I 1.05075 2.61493I
16
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.928400 0.721425I
a = 1.19972 1.35918I
b = 1.278548 + 0.388894I
4.61539 + 3.79849I 3.70384 8.50950I
u = 0.928400 + 0.721425I
a = 1.19972 + 1.35918I
b = 1.278548 0.388894I
4.61539 3.79849I 3.70384 + 8.50950I
u = 1.050059 0.753206I
a = 2.17570 + 0.35594I
b = 0.60850 + 1.30717I
2.0462 + 16.7456I 5.37386 9.80445I
u = 1.050059 + 0.753206I
a = 2.17570 0.35594I
b = 0.60850 1.30717I
2.0462 16.7456I 5.37386 + 9.80445I
u = 1.168360 0.434244I
a = 0.627774 0.344147I
b = 0.309881 1.145953I
7.10420 2.17526I 9.93897 + 4.23335I
u = 1.168360 + 0.434244I
a = 0.627774 + 0.344147I
b = 0.309881 + 1.145953I
7.10420 + 2.17526I 9.93897 4.23335I
u = 1.214648 0.097151I
a = 0.222900 + 0.987308I
b = 0.155309 + 0.849372I
4.05629 0.93128I 2.23485 + 6.88947I
u = 1.214648 + 0.097151I
a = 0.222900 0.987308I
b = 0.155309 0.849372I
4.05629 + 0.93128I 2.23485 6.88947I
17
VII. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
4
(u
3
+ u
2
1)(u
5
+ u
4
+ 2u + 1)
2
(1 + 2u + 2u
2
4u
4
5u
5
+ 3u
6
+ 9u
7
10u
9
3u
10
+ 7u
11
+ 4u
12
3u
13
2u
14
+ u
15
+ u
16
)
2
(u
28
+ 2u
27
+ ··· + 3u 4)
c
2
(u + 1)
4
(u
3
+ u
2
+ 2u + 1)(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
(1 4u
2
10u
3
8u
4
+ 15u
5
+ 67u
6
+ 133u
7
+ 190u
8
+ 212u
9
+ 193u
10
+ 145u
11
+ 90u
12
+ 45u
13
+ 18u
14
+ 5u
15
+ u
16
)
2
(u
28
+ 10u
27
+ ··· + 97u + 16)
c
3
u
3
(u + 1)
2
(u
2
+ 1)(u
5
u
4
+ 2u 1)
2
(1 2u + 2u
2
4u
4
+ 5u
5
+ 3u
6
9u
7
+ 10u
9
3u
10
7u
11
+ 4u
12
+ 3u
13
2u
14
u
15
+ u
16
)
2
(u
28
+ 3u
27
+ ··· + 736u + 128)
c
4
(u 1)
2
(u + 1)
2
(u
3
u
2
+ 2u 1)(u
5
+ u
4
+ 4u
3
+ 2u
2
+ 4u + 1)
2
(1 4u
2
10u
3
8u
4
+ 15u
5
+ 67u
6
+ 133u
7
+ 190u
8
+ 212u
9
+ 193u
10
+ 145u
11
+ 90u
12
+ 45u
13
+ 18u
14
+ 5u
15
+ u
16
)
2
(u
28
+ 10u
27
+ ··· + 97u + 16)
c
5
(u 1)
2
(u + 1)
2
(u
3
u
2
+ 1)(u
5
+ u
4
+ 2u + 1)
2
(1 + 2u + 2u
2
4u
4
5u
5
+ 3u
6
+ 9u
7
10u
9
3u
10
+ 7u
11
+ 4u
12
3u
13
2u
14
+ u
15
+ u
16
)
2
(u
28
+ 2u
27
+ ··· + 3u 4)
c
6
, c
8
(u + 1)
3
(u
2
+ 1)(u
2
+ u + 2)
(u
10
+ u
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 5u
5
+ 3u
4
+ u
3
+ u
2
+ 1)
(u
28
3u
27
+ ··· 5u 1)(u
32
+ 5u
31
+ ··· + 8u + 1)
c
7
(u 1)
2
(u
2
2u + 2)(8u
3
+ 4u
2
+ 4u + 1)
(u
10
+ 4u
9
+ 8u
8
+ 6u
7
+ 6u
6
+ 7u
5
+ 25u
4
+ 43u
3
+ 56u
2
+ 36u + 8)
(8u
28
12u
27
+ ··· + 4u + 2)(u
32
+ u
31
+ ··· 402u + 73)
c
9
, c
11
(u 1)
3
(u
2
+ 1)(u
2
+ u + 2)
(u
10
+ u
9
+ 2u
8
+ 4u
7
+ 4u
6
+ 5u
5
+ 3u
4
+ u
3
+ u
2
+ 1)
(u
28
3u
27
+ ··· 5u 1)(u
32
+ 5u
31
+ ··· + 8u + 1)
c
10
(u 1)
2
(u
2
+ 2u + 2)(8u
3
4u
2
+ 4u 1)
(u
10
+ 4u
9
+ 8u
8
+ 6u
7
+ 6u
6
+ 7u
5
+ 25u
4
+ 43u
3
+ 56u
2
+ 36u + 8)
(8u
28
12u
27
+ ··· + 4u + 2)(u
32
+ u
31
+ ··· 402u + 73)
18
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y 1)
4
(y
3
y
2
+ 2y 1)(y
5
y
4
+ 4y
3
2y
2
+ 4y 1)
2
(1 4y
2
+ 10y
3
8y
4
15y
5
+ 67y
6
133y
7
+ 190y
8
212y
9
+ 193y
10
145y
11
+ 90y
12
45y
13
+ 18y
14
5y
15
+ y
16
)
2
(y
28
10y
27
+ ··· 97y + 16)
c
2
, c
4
(y 1)
4
(y
3
+ 3y
2
+ 2y 1)(y
5
+ 7y
4
+ 20y
3
+ 26y
2
+ 12y 1)
2
(1 8y + 98y
3
+ 208y
4
+ 229y
5
+ 335y
6
+ 539y
7
+ 538y
8
+ 340y
9
+ 245y
10
+ 279y
11
+ 258y
12
+ 151y
13
+ 54y
14
+ 11y
15
+ y
16
)
2
(y
28
+ 18y
27
+ ··· + 8543y + 256)
c
3
y
3
(y 1)
2
(y + 1)
2
(y
5
y
4
+ 4y
3
2y
2
+ 4y 1)
2
(1 4y
2
+ 10y
3
8y
4
15y
5
+ 67y
6
133y
7
+ 190y
8
212y
9
+ 193y
10
145y
11
+ 90y
12
45y
13
+ 18y
14
5y
15
+ y
16
)
2
(y
28
5y
27
+ ··· 238592y + 16384)
c
6
, c
8
, c
9
c
11
(y 1)
3
(y + 1)
2
(y
2
+ 3y + 4)
(y
10
+ 3y
9
+ 4y
8
4y
7
12y
6
3y
5
+ 11y
4
+ 13y
3
+ 7y
2
+ 2y + 1)
(y
28
+ 11y
27
+ ··· 51y + 1)(y
32
+ 21y
31
+ ··· + 6y + 1)
c
7
, c
10
(y 1)
2
(y
2
+ 4)(64y
3
+ 48y
2
+ 8y 1)(y
10
+ 28y
8
+ ··· 400y + 64)
(64y
28
+ 176y
27
+ ··· + 40y + 4)(y
32
15y
31
+ ··· 89626y + 5329)
19