12a
1114
(K12a
1114
)
A knot diagram
1
Linearized knot diagam
4 7 12 9 10 11 3 1 5 6 2 8
Solving Sequence
5,9
10 6 11 7
1,4
2 8 12 3
c
9
c
5
c
10
c
6
c
4
c
1
c
8
c
12
c
3
c
2
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h49u
21
− 206u
20
+ ··· + 2b − 110, −13u
21
+ 48u
20
+ ··· + 4a + 12, u
22
− 6u
21
+ ··· − 14u + 4i
I
u
2
= h−17691u
8
a
3
+ 8540u
8
a
2
+ ··· + 277099a − 169388, −2u
8
a
3
− 4u
8
a
2
+ ··· − 12a + 70,
u
9
+ u
8
− 6u
7
− 5u
6
+ 11u
5
+ 7u
4
− 6u
3
− 4u
2
− u + 1i
I
u
3
= hu
4
− 3u
2
+ b + 1, u
7
− 6u
5
− u
4
+ 11u
3
+ 3u
2
+ a − 6u − 1,
u
11
− u
10
− 8u
9
+ 7u
8
+ 23u
7
− 16u
6
− 29u
5
+ 13u
4
+ 15u
3
− 2u
2
− u − 1i
* 3 irreducible components of dim
C
= 0, with total 69 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
= h49u
21
− 206u
20
+ · · · + 2b − 110, −13u
21
+ 48u
20
+ · · · + 4a +
12, u
22
− 6u
21
+ · · · − 14u + 4i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
1
=
13
4
u
21
− 12u
20
+ ··· +
51
4
u − 3
−
49
2
u
21
+ 103u
20
+ ··· −
323
2
u + 55
a
4
=
−u
u
a
2
=
265
4
u
21
− 281u
20
+ ··· +
1755
4
u − 149
−
175
2
u
21
+ 372u
20
+ ··· −
1175
2
u + 201
a
8
=
1
2
u
21
−
1
2
u
20
+ ··· −
5
2
u +
3
2
−
17
2
u
21
+ 35u
20
+ ··· −
109
2
u + 18
a
12
=
19u
21
−
163
2
u
20
+ ··· + 127u −
85
2
−
45
2
u
21
+ 97u
20
+ ··· −
313
2
u + 54
a
3
=
49
4
u
21
− 54u
20
+ ··· +
339
4
u − 29
−
23
2
u
21
+ 52u
20
+ ··· −
175
2
u + 31
(ii) Obstruction class = −1
(iii) Cusp Shapes = −42u
21
+ 180u
20
+ 180u
19
− 1614u
18
+ 357u
17
+ 6114u
16
−
4208u
15
− 12099u
14
+ 13221u
13
+ 11109u
12
− 22235u
11
+ 1566u
10
+ 20908u
9
−
13794u
8
− 7898u
7
+ 12460u
6
− 2905u
5
− 4228u
4
+ 2792u
3
+ 18u
2
− 316u + 106
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
22
+ 2u
21
+ ··· − 12u + 1
c
2
, c
7
, c
8
c
12
u
22
+ u
21
+ ··· − 2u + 1
c
3
u
22
+ 21u
21
+ ··· + 2816u + 512
c
4
, c
5
, c
6
c
9
, c
10
u
22
+ 6u
21
+ ··· + 14u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
22
+ 14y
21
+ ··· − 162y + 1
c
2
, c
7
, c
8
c
12
y
22
− 21y
21
+ ··· − 10y + 1
c
3
y
22
− y
21
+ ··· − 7405568y + 262144
c
4
, c
5
, c
6
c
9
, c
10
y
22
− 30y
21
+ ··· − 140y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.043890 + 0.084239I
a = −0.396837 − 0.057037I
b = 0.016671 − 0.768015I
2.64990 − 1.99958I 9.53146 + 3.76378I
u = −1.043890 − 0.084239I
a = −0.396837 + 0.057037I
b = 0.016671 + 0.768015I
2.64990 + 1.99958I 9.53146 − 3.76378I
u = 0.319390 + 0.784311I
a = 0.105537 − 0.519872I
b = −1.332750 + 0.209642I
6.57558 − 3.17716I 14.5871 + 2.3802I
u = 0.319390 − 0.784311I
a = 0.105537 + 0.519872I
b = −1.332750 − 0.209642I
6.57558 + 3.17716I 14.5871 − 2.3802I
u = 0.495362 + 0.681217I
a = −0.623279 + 1.001900I
b = 1.38604 + 0.33811I
7.16423 + 7.89598I 13.0600 − 7.3152I
u = 0.495362 − 0.681217I
a = −0.623279 − 1.001900I
b = 1.38604 − 0.33811I
7.16423 − 7.89598I 13.0600 + 7.3152I
u = −1.220570 + 0.357902I
a = 1.81374 + 0.84055I
b = −1.48578 + 0.42742I
12.5903 − 11.4735I 15.1438 + 6.9415I
u = −1.220570 − 0.357902I
a = 1.81374 − 0.84055I
b = −1.48578 − 0.42742I
12.5903 + 11.4735I 15.1438 − 6.9415I
u = −1.193250 + 0.493321I
a = −1.23495 − 0.92705I
b = 1.339160 + 0.061996I
11.24460 − 1.24294I 18.1099 + 1.8376I
u = −1.193250 − 0.493321I
a = −1.23495 + 0.92705I
b = 1.339160 − 0.061996I
11.24460 + 1.24294I 18.1099 − 1.8376I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.687446
a = 2.18879
b = −0.499542
−0.430924 21.8170
u = 1.48411
a = −0.786366
b = 0.649714
6.96114 19.0070
u = −0.411824
a = 0.523537
b = −0.318922
0.605966 16.6960
u = −1.58824
a = −1.60194
b = 0.874121
7.51930 14.0920
u = 0.227373 + 0.272091I
a = 0.53987 − 1.57107I
b = 0.082959 − 0.502394I
−1.28640 + 0.84268I −1.69920 − 4.23368I
u = 0.227373 − 0.272091I
a = 0.53987 + 1.57107I
b = 0.082959 + 0.502394I
−1.28640 − 0.84268I −1.69920 + 4.23368I
u = 1.74549 + 0.01514I
a = 0.268462 + 0.256545I
b = −0.047072 − 0.943997I
12.75810 + 2.36846I 10.71272 − 2.85205I
u = 1.74549 − 0.01514I
a = 0.268462 − 0.256545I
b = −0.047072 + 0.943997I
12.75810 − 2.36846I 10.71272 + 2.85205I
u = 1.78669 + 0.09389I
a = −2.11796 + 0.46248I
b = 1.56385 + 0.48092I
−16.0394 + 13.4812I 15.5774 − 5.8403I
u = 1.78669 − 0.09389I
a = −2.11796 − 0.46248I
b = 1.56385 − 0.48092I
−16.0394 − 13.4812I 15.5774 + 5.8403I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.79765 + 0.12560I
a = 1.73341 − 0.61996I
b = −1.375760 − 0.072217I
−17.4882 + 3.9741I 17.1708 − 2.2051I
u = 1.79765 − 0.12560I
a = 1.73341 + 0.61996I
b = −1.375760 + 0.072217I
−17.4882 − 3.9741I 17.1708 + 2.2051I
7
II. I
u
2
= h−1.77 × 10
4
a
3
u
8
+ 8540a
2
u
8
+ · · · + 2.77 × 10
5
a − 1.69 ×
10
5
, −2u
8
a
3
− 4u
8
a
2
+ · · · − 12a + 70, u
9
+ u
8
+ · · · − u + 1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
1
=
a
0.0802571a
3
u
8
− 0.0387426a
2
u
8
+ ··· − 1.25709a + 0.768447
a
4
=
−u
u
a
2
=
−0.709439a
3
u
8
+ 0.329072a
2
u
8
+ ··· + 2.30427a − 1.91298
0.789696a
3
u
8
− 0.367815a
2
u
8
+ ··· − 2.56136a + 2.68143
a
8
=
−0.307278a
3
u
8
+ 0.496604a
2
u
8
+ ··· − 0.507896a − 2.73403
0.428369a
3
u
8
+ 0.0229598a
2
u
8
+ ··· + 0.390062a + 3.89304
a
12
=
0.229521a
3
u
8
− 0.705855a
2
u
8
+ ··· + 0.724728a + 3.72904
−0.441407a
3
u
8
+ 2.28443a
2
u
8
+ ··· − 3.25779a − 5.21324
a
3
=
−0.946141a
3
u
8
− 0.800857a
2
u
8
+ ··· + 1.80509a − 3.49748
1.15803a
3
u
8
− 0.777715a
2
u
8
+ ··· + 0.727971a + 3.98169
(ii) Obstruction class = −1
(iii) Cusp Shapes = −
31188
20039
u
8
a
3
−
18668
20039
u
8
a
2
+ ··· +
7244
20039
a +
311386
20039
8
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
36
− 11u
35
+ ··· − 22476u + 2977
c
2
, c
7
, c
8
c
12
u
36
− u
35
+ ··· − 12u + 1
c
3
(u
2
− u + 1)
18
c
4
, c
5
, c
6
c
9
, c
10
(u
9
− u
8
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− u − 1)
4
9
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
36
+ 19y
35
+ ··· + 113199956y + 8862529
c
2
, c
7
, c
8
c
12
y
36
− 33y
35
+ ··· + 13206y
2
+ 1
c
3
(y
2
+ y + 1)
18
c
4
, c
5
, c
6
c
9
, c
10
(y
9
− 13y
8
+ 68y
7
− 183y
6
+ 269y
5
− 211y
4
+ 80y
3
− 18y
2
+ 9y −1)
4
10
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.115700 + 0.218357I
a = −0.583676 − 0.658151I
b = −0.0692851 + 0.0614982I
6.69287 + 1.83365I 14.03791 − 0.54536I
u = 1.115700 + 0.218357I
a = −0.648434 − 0.438924I
b = 0.381836 + 1.212390I
6.69287 + 5.89342I 14.0379 − 7.4736I
u = 1.115700 + 0.218357I
a = −1.48443 + 0.60451I
b = 1.294760 + 0.266822I
6.69287 + 1.83365I 14.03791 − 0.54536I
u = 1.115700 + 0.218357I
a = 1.72894 − 1.32529I
b = −1.278910 − 0.315259I
6.69287 + 5.89342I 14.0379 − 7.4736I
u = 1.115700 − 0.218357I
a = −0.583676 + 0.658151I
b = −0.0692851 − 0.0614982I
6.69287 − 1.83365I 14.03791 + 0.54536I
u = 1.115700 − 0.218357I
a = −0.648434 + 0.438924I
b = 0.381836 − 1.212390I
6.69287 − 5.89342I 14.0379 + 7.4736I
u = 1.115700 − 0.218357I
a = −1.48443 − 0.60451I
b = 1.294760 − 0.266822I
6.69287 − 1.83365I 14.03791 + 0.54536I
u = 1.115700 − 0.218357I
a = 1.72894 + 1.32529I
b = −1.278910 + 0.315259I
6.69287 − 5.89342I 14.0379 + 7.4736I
u = −1.15527
a = −2.01543 + 0.07577I
b = 1.63501 + 0.66222I
10.43600 + 2.02988I 18.5753 − 3.4641I
u = −1.15527
a = −2.01543 − 0.07577I
b = 1.63501 − 0.66222I
10.43600 − 2.02988I 18.5753 + 3.4641I
11
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.15527
a = 2.74857 + 1.19407I
b = −1.263110 − 0.018083I
10.43600 + 2.02988I 18.5753 − 3.4641I
u = −1.15527
a = 2.74857 − 1.19407I
b = −1.263110 + 0.018083I
10.43600 − 2.02988I 18.5753 + 3.4641I
u = −0.344156 + 0.466288I
a = −0.231060 + 0.764559I
b = −1.169060 − 0.018719I
2.08691 + 0.47566I 8.94040 + 0.84117I
u = −0.344156 + 0.466288I
a = 1.310650 − 0.167710I
b = 0.082806 + 0.524016I
2.08691 + 0.47566I 8.94040 + 0.84117I
u = −0.344156 + 0.466288I
a = 0.032067 + 0.569438I
b = −0.222763 + 0.891266I
2.08691 − 3.58411I 8.94040 + 7.76937I
u = −0.344156 + 0.466288I
a = −0.05497 − 1.80281I
b = 1.203490 − 0.203190I
2.08691 − 3.58411I 8.94040 + 7.76937I
u = −0.344156 − 0.466288I
a = −0.231060 − 0.764559I
b = −1.169060 + 0.018719I
2.08691 − 0.47566I 8.94040 − 0.84117I
u = −0.344156 − 0.466288I
a = 1.310650 + 0.167710I
b = 0.082806 − 0.524016I
2.08691 − 0.47566I 8.94040 − 0.84117I
u = −0.344156 − 0.466288I
a = 0.032067 − 0.569438I
b = −0.222763 − 0.891266I
2.08691 + 3.58411I 8.94040 − 7.76937I
u = −0.344156 − 0.466288I
a = −0.05497 + 1.80281I
b = 1.203490 + 0.203190I
2.08691 + 3.58411I 8.94040 − 7.76937I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.362481
a = 1.11687 + 1.72823I
b = −1.38930 + 0.48183I
5.49604 − 2.02988I 19.6128 + 3.4641I
u = 0.362481
a = 1.11687 − 1.72823I
b = −1.38930 − 0.48183I
5.49604 + 2.02988I 19.6128 − 3.4641I
u = 0.362481
a = −3.85979 + 3.02264I
b = 1.225600 − 0.198299I
5.49604 − 2.02988I 19.6128 + 3.4641I
u = 0.362481
a = −3.85979 − 3.02264I
b = 1.225600 + 0.198299I
5.49604 + 2.02988I 19.6128 − 3.4641I
u = −1.76115 + 0.05266I
a = 0.634605 − 0.837704I
b = −0.43558 + 1.42750I
17.1037 − 7.0247I 14.8663 + 6.3722I
u = −1.76115 + 0.05266I
a = 0.263385 − 0.472901I
b = 0.086713 − 0.200842I
17.1037 − 2.9650I 14.8663 − 0.5560I
u = −1.76115 + 0.05266I
a = 1.82935 + 0.17038I
b = −1.43895 + 0.44937I
17.1037 − 2.9650I 14.8663 − 0.5560I
u = −1.76115 + 0.05266I
a = −1.94297 − 0.82339I
b = 1.326930 − 0.380702I
17.1037 − 7.0247I 14.8663 + 6.3722I
u = −1.76115 − 0.05266I
a = 0.634605 + 0.837704I
b = −0.43558 − 1.42750I
17.1037 + 7.0247I 14.8663 − 6.3722I
u = −1.76115 − 0.05266I
a = 0.263385 + 0.472901I
b = 0.086713 + 0.200842I
17.1037 + 2.9650I 14.8663 + 0.5560I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.76115 − 0.05266I
a = 1.82935 − 0.17038I
b = −1.43895 − 0.44937I
17.1037 + 2.9650I 14.8663 + 0.5560I
u = −1.76115 − 0.05266I
a = −1.94297 + 0.82339I
b = 1.326930 + 0.380702I
17.1037 + 7.0247I 14.8663 − 6.3722I
u = 1.77199
a = 2.19492 + 0.22581I
b = −1.78129 − 0.74916I
−18.3509 + 2.0299I 18.1228 − 3.4641I
u = 1.77199
a = 2.19492 − 0.22581I
b = −1.78129 + 0.74916I
−18.3509 − 2.0299I 18.1228 + 3.4641I
u = 1.77199
a = −2.53859 + 0.82107I
b = 1.311100 + 0.065235I
−18.3509 − 2.0299I 18.1228 + 3.4641I
u = 1.77199
a = −2.53859 − 0.82107I
b = 1.311100 − 0.065235I
−18.3509 + 2.0299I 18.1228 − 3.4641I
14
III.
I
u
3
= hu
4
−3u
2
+b+1, u
7
−6u
5
−u
4
+11u
3
+3u
2
+a−6u−1, u
11
−u
10
+· · ·−u−1i
(i) Arc colorings
a
5
=
0
u
a
9
=
1
0
a
10
=
1
−u
2
a
6
=
u
−u
3
+ u
a
11
=
−u
2
+ 1
u
4
− 2u
2
a
7
=
−u
3
+ 2u
u
5
− 3u
3
+ u
a
1
=
−u
7
+ 6u
5
+ u
4
− 11u
3
− 3u
2
+ 6u + 1
−u
4
+ 3u
2
− 1
a
4
=
−u
u
a
2
=
u
9
− 7u
7
+ 17u
5
+ u
4
− 17u
3
− 3u
2
+ 6u + 1
−u
9
+ 6u
7
− 11u
5
− u
4
+ 6u
3
+ 3u
2
− 1
a
8
=
u
10
− u
9
− 8u
8
+ 7u
7
+ 22u
6
− 16u
5
− 24u
4
+ 14u
3
+ 8u
2
− 5u + 1
u
8
− 6u
6
+ 11u
4
− 6u
2
+ 1
a
12
=
−u
9
+ 7u
7
− 16u
5
+ 13u
3
− u
2
− 2u + 2
u
9
− 7u
7
+ 16u
5
+ u
4
− 13u
3
− 3u
2
+ 2u + 1
a
3
=
u
9
− 8u
7
+ 22u
5
+ u
4
− 24u
3
− 3u
2
+ 8u + 1
−u
4
+ 3u
2
+ u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −4u
10
+ 2u
9
+ 31u
8
− 14u
7
− 82u
6
+ 27u
5
+ 84u
4
− 6u
3
− 23u
2
− 10u + 5
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
11
u
11
+ 2u
10
+ 3u
9
+ 4u
8
+ u
7
− 2u
6
− 5u
5
− 5u
4
− 2u
3
+ u
2
+ 2u + 1
c
2
, c
8
u
11
+ u
10
+ ··· − 4u − 1
c
3
u
11
− 2u
10
+ u
9
+ 2u
8
− 5u
7
+ 5u
6
− 2u
5
− u
4
+ 4u
3
− 3u
2
+ 2u − 1
c
4
, c
5
, c
6
u
11
+ u
10
+ ··· − u + 1
c
7
, c
12
u
11
− u
10
+ ··· − 4u + 1
c
9
, c
10
u
11
− u
10
+ ··· − u − 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
11
y
11
+ 2y
10
− 5y
9
− 12y
8
+ 3y
7
+ 14y
6
+ y
5
− 5y
4
− 2y
3
+ y
2
+ 2y −1
c
2
, c
7
, c
8
c
12
y
11
− 13y
10
+ ··· + 38y −1
c
3
y
11
− 2y
10
− y
9
+ 2y
8
+ 5y
7
− y
6
− 14y
5
− 3y
4
+ 12y
3
+ 5y
2
− 2y −1
c
4
, c
5
, c
6
c
9
, c
10
y
11
− 17y
10
+ ··· − 3y −1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.003860 + 0.215654I
a = −0.834543 − 0.532608I
b = 1.147190 − 0.466546I
7.60023 − 3.64229I 16.7867 + 4.7032I
u = −1.003860 − 0.215654I
a = −0.834543 + 0.532608I
b = 1.147190 + 0.466546I
7.60023 + 3.64229I 16.7867 − 4.7032I
u = 1.288880 + 0.118905I
a = −1.87499 + 0.32616I
b = 1.322320 − 0.090164I
9.54739 − 0.09465I 15.9387 + 0.1893I
u = 1.288880 − 0.118905I
a = −1.87499 − 0.32616I
b = 1.322320 + 0.090164I
9.54739 + 0.09465I 15.9387 − 0.1893I
u = 0.550251
a = 1.93961
b = −0.183345
−0.771716 −1.63370
u = −1.53837
a = −0.987197
b = 0.499049
6.40308 3.17420
u = −0.146441 + 0.318421I
a = −0.12310 + 2.31687I
b = −1.237540 − 0.294692I
4.72595 + 1.79241I 7.60505 + 0.27412I
u = −0.146441 − 0.318421I
a = −0.12310 − 2.31687I
b = −1.237540 + 0.294692I
4.72595 − 1.79241I 7.60505 − 0.27412I
u = 1.74679 + 0.05665I
a = 1.167540 − 0.166105I
b = −1.107360 − 0.612780I
17.5808 + 4.7820I 16.4667 − 3.6309I
u = 1.74679 − 0.05665I
a = 1.167540 + 0.166105I
b = −1.107360 + 0.612780I
17.5808 − 4.7820I 16.4667 + 3.6309I
18
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.78263
a = 2.37775
b = −1.56492
−18.7427 16.8650
19
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
11
(u
11
+ 2u
10
+ 3u
9
+ 4u
8
+ u
7
− 2u
6
− 5u
5
− 5u
4
− 2u
3
+ u
2
+ 2u + 1)
· (u
22
+ 2u
21
+ ··· − 12u + 1)(u
36
− 11u
35
+ ··· − 22476u + 2977)
c
2
, c
8
(u
11
+ u
10
+ ··· − 4u − 1)(u
22
+ u
21
+ ··· − 2u + 1)
· (u
36
− u
35
+ ··· − 12u + 1)
c
3
(u
2
− u + 1)
18
· (u
11
− 2u
10
+ u
9
+ 2u
8
− 5u
7
+ 5u
6
− 2u
5
− u
4
+ 4u
3
− 3u
2
+ 2u − 1)
· (u
22
+ 21u
21
+ ··· + 2816u + 512)
c
4
, c
5
, c
6
(u
9
− u
8
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− u − 1)
4
· (u
11
+ u
10
+ ··· − u + 1)(u
22
+ 6u
21
+ ··· + 14u + 4)
c
7
, c
12
(u
11
− u
10
+ ··· − 4u + 1)(u
22
+ u
21
+ ··· − 2u + 1)
· (u
36
− u
35
+ ··· − 12u + 1)
c
9
, c
10
(u
9
− u
8
− 6u
7
+ 5u
6
+ 11u
5
− 7u
4
− 6u
3
+ 4u
2
− u − 1)
4
· (u
11
− u
10
+ ··· − u − 1)(u
22
+ 6u
21
+ ··· + 14u + 4)
20
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
11
(y
11
+ 2y
10
− 5y
9
− 12y
8
+ 3y
7
+ 14y
6
+ y
5
− 5y
4
− 2y
3
+ y
2
+ 2y −1)
· (y
22
+ 14y
21
+ ··· − 162y + 1)
· (y
36
+ 19y
35
+ ··· + 113199956y + 8862529)
c
2
, c
7
, c
8
c
12
(y
11
− 13y
10
+ ··· + 38y −1)(y
22
− 21y
21
+ ··· − 10y + 1)
· (y
36
− 33y
35
+ ··· + 13206y
2
+ 1)
c
3
(y
2
+ y + 1)
18
· (y
11
− 2y
10
− y
9
+ 2y
8
+ 5y
7
− y
6
− 14y
5
− 3y
4
+ 12y
3
+ 5y
2
− 2y −1)
· (y
22
− y
21
+ ··· − 7405568y + 262144)
c
4
, c
5
, c
6
c
9
, c
10
(y
9
− 13y
8
+ 68y
7
− 183y
6
+ 269y
5
− 211y
4
+ 80y
3
− 18y
2
+ 9y −1)
4
· (y
11
− 17y
10
+ ··· − 3y −1)(y
22
− 30y
21
+ ··· − 140y + 16)
21
