11a
14
(K11a
14
)
1
Arc Sequences
4 1 7 2 9 3 5 11 6 8 10
Solving Sequence
5,9
6
2,10
4 1 3 7 11 8
c
5
c
9
c
4
c
1
c
2
c
6
c
11
c
8
c
3
, c
7
, c
10
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= hb
6
+ 4b
4
+ b
3
+ 4b
2
+ 1, u 1, 2b
5
2b
4
+ 7b
3
5b
2
+ b + 3a 4i
I
u
2
= hu
6
+ u
5
u
4
2u
3
+ u + 1, a, u
4
+ u
3
+ b ui
I
u
3
= hu
12
+ 2u
11
u
10
6u
9
3u
8
+ 6u
7
+ 8u
6
u
5
8u
4
4u
3
+ 3u
2
+ 3u + 1,
u
9
u
8
+ u
7
+ 3u
6
3u
4
2u
3
+ 2u
2
+ b + 2u + 1,
u
10
+ u
9
2u
8
4u
7
+ u
6
+ 5u
5
+ 2u
4
4u
3
3u
2
+ a + u + 2i
I
u
4
= hu
66
+ 6u
65
+ ··· u + 1, 1.00895 × 10
19
u
65
+ 5.41109 × 10
19
u
64
+ ··· + 1.31154 × 10
18
a + 1.76296 × 10
19
,
9.79642 × 10
18
u
65
+ 5.65332 × 10
19
u
64
+ ··· + 6.55768 × 10
17
b + 1.46340 × 10
19
i
There are 4 irreducible components with 90 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
6
+ 4b
4
+ b
3
+ 4b
2
+ 1, u 1, 2b
5
2b
4
+ 7b
3
5b
2
+ b + 3a 4i
(i) Arc colorings
a
5
=
0
1
a
9
=
2
3
b
5
+
2
3
b
4
+ ···
1
3
b +
4
3
b
a
6
=
2
3
b
5
+
1
3
b
4
+ ··· +
4
3
b +
5
3
2
3
b
5
+
1
3
b
4
+ ··· +
4
3
b +
5
3
a
2
=
1
0
a
10
=
1
3
b
5
+
1
3
b
4
+ ···
5
3
b +
2
3
1
3
b
5
1
3
b
4
+ ···
1
3
b
2
3
a
4
=
1
1
a
1
=
0
1
a
3
=
1
1
a
7
=
2
3
b
5
+
1
3
b
4
+ ··· +
4
3
b +
5
3
2
3
b
5
+
1
3
b
4
+ ··· +
4
3
b +
5
3
a
11
=
b
5
+ 3b
3
+ 2b
2
+ b + 1
1
3
b
5
1
3
b
4
+ ···
1
3
b
2
3
a
8
=
2
3
b
5
+
1
3
b
4
+ ··· +
4
3
b +
5
3
0
a
8
=
2
3
b
5
+
1
3
b
4
+ ··· +
4
3
b +
5
3
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4b
5
b
4
12b
3
8b
2
4b 4
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.073950 0.558752I
b = 0.341164 0.940004I
1.64493 + 5.69302I 3.10838 7.09196I
u = 1.00000
a = 1.073950 + 0.558752I
b = 0.341164 + 0.940004I
1.64493 5.69302I 3.10838 + 7.09196I
u = 1.00000
a = 1.002193 0.295542I
b = 0.084211 0.566250I
0.245672 0.924305I 1.11831 + 1.11590I
u = 1.00000
a = 1.002193 + 0.295542I
b = 0.084211 + 0.566250I
0.245672 + 0.924305I 1.11831 1.11590I
u = 1.00000
a = 0.428243 0.664531I
b = 0.25695 1.72779I
3.53554 0.92430I 5.77331 0.83820I
u = 1.00000
a = 0.428243 + 0.664531I
b = 0.25695 + 1.72779I
3.53554 + 0.92430I 5.77331 + 0.83820I
3
II. I
u
2
= hu
6
+ u
5
u
4
2u
3
+ u + 1, a, u
4
+ u
3
+ b ui
(i) Arc colorings
a
5
=
0
u
a
9
=
0
u
4
u
3
+ u
a
6
=
0
u
a
2
=
1
0
a
10
=
0
u
4
u
3
+ u
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
u
2
+ 1
u
4
a
7
=
u
2
1
u
4
a
11
=
u
2
+ 1
u
4
u
3
u
2
+ u
a
8
=
u
2
1
u
2
a
8
=
u
2
1
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes = 3u
4
2u
3
3u
2
2u 1
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.073950 0.558752I
a = 0
b = 0.108378 0.818891I
1.64493 5.69302I 3.10838 + 7.09196I
u = 1.073950 + 0.558752I
a = 0
b = 0.108378 + 0.818891I
1.64493 + 5.69302I 3.10838 7.09196I
u = 0.428243 0.664531I
a = 0
b = 0.659772 0.298454I
0.245672 + 0.924305I 1.11831 1.11590I
u = 0.428243 + 0.664531I
a = 0
b = 0.659772 + 0.298454I
0.245672 0.924305I 1.11831 + 1.11590I
u = 1.002193 0.295542I
a = 0
b = 0.23185 + 1.65564I
3.53554 + 0.92430I 5.77331 + 0.83820I
u = 1.002193 + 0.295542I
a = 0
b = 0.23185 1.65564I
3.53554 0.92430I 5.77331 0.83820I
5
III.
I
u
3
= hu
12
+ 2u
11
+ · · · + 3u + 1, u
9
u
8
+ · · · + b + 1, u
10
+ u
9
+ · · · + a + 2i
(i) Arc colorings
a
5
=
0
u
a
9
=
u
10
u
9
+ 2u
8
+ 4u
7
u
6
5u
5
2u
4
+ 4u
3
+ 3u
2
u 2
u
9
+ u
8
u
7
3u
6
+ 3u
4
+ 2u
3
2u
2
2u 1
a
6
=
u
2
1
u
10
+ u
9
2u
8
3u
7
+ u
6
+ 3u
5
+ u
4
2u
3
u
2
+ u
a
2
=
1
0
a
10
=
u
10
u
9
+ 2u
8
+ 3u
7
u
6
3u
5
u
4
+ 2u
3
+ 2u
2
u 1
u
9
+ u
8
2u
7
3u
6
+ u
5
+ 4u
4
+ 2u
3
2u
2
3u 1
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
u
2
+ 1
u
4
a
7
=
u
11
+ u
10
3u
9
4u
8
+ 3u
7
+ 6u
6
5u
4
3u
3
+ 3u
2
+ 2u 1
u
11
+ 2u
10
2u
9
6u
8
u
7
+ 7u
6
+ 5u
5
3u
4
7u
3
+ 3u + 1
a
11
=
u
11
u
10
+ 3u
9
+ 4u
8
3u
7
7u
6
u
5
+ 6u
4
+ 5u
3
3u
2
3u
u
11
u
10
+ 2u
9
+ 3u
8
u
7
4u
6
2u
5
+ 2u
4
+ 3u
3
a
8
=
u
11
+ u
10
3u
9
4u
8
+ 3u
7
+ 6u
6
5u
4
3u
3
+ 3u
2
+ 2u 1
u
11
+ u
10
2u
9
3u
8
+ u
7
+ 3u
6
+ u
5
2u
4
2u
3
+ u
2
+ u
a
8
=
u
11
+ u
10
3u
9
4u
8
+ 3u
7
+ 6u
6
5u
4
3u
3
+ 3u
2
+ 2u 1
u
11
+ u
10
2u
9
3u
8
+ u
7
+ 3u
6
+ u
5
2u
4
2u
3
+ u
2
+ u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 4u
11
4u
10
+ 4u
9
+ 8u
8
4u
7
8u
6
4u
5
+ 12u
4
+ 4u
3
4u
2
4u + 6
6
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.166620 0.659880I
a = 0.562519 + 0.913040I
b = 0.50156 + 2.87927I
3.6549 16.4066I 0.26530 + 10.19553I
u = 1.166620 + 0.659880I
a = 0.562519 0.913040I
b = 0.50156 2.87927I
3.6549 + 16.4066I 0.26530 10.19553I
u = 1.046968 0.439905I
a = 0.538744 0.724842I
b = 0.592671 1.033488I
2.42744 7.70164I 2.21070 + 10.86632I
u = 1.046968 + 0.439905I
a = 0.538744 + 0.724842I
b = 0.592671 + 1.033488I
2.42744 + 7.70164I 2.21070 10.86632I
u = 0.453738 0.929754I
a = 0.940441 0.956159I
b = 0.81705 1.51269I
8.07063 + 4.68351I 6.05114 1.98346I
u = 0.453738 + 0.929754I
a = 0.940441 + 0.956159I
b = 0.81705 + 1.51269I
8.07063 4.68351I 6.05114 + 1.98346I
u = 0.377048 0.377232I
a = 1.203734 + 0.707516I
b = 0.260988 + 0.028807I
1.364800 + 0.359490I 6.91945 0.04590I
u = 0.377048 + 0.377232I
a = 1.203734 0.707516I
b = 0.260988 0.028807I
1.364800 0.359490I 6.91945 + 0.04590I
u = 0.926778 0.513866I
a = 0.734247 + 0.661535I
b = 1.212950 0.071255I
1.88434 + 4.01879I 2.34862 5.57352I
u = 0.926778 + 0.513866I
a = 0.734247 0.661535I
b = 1.212950 + 0.071255I
1.88434 4.01879I 2.34862 + 5.57352I
7
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.117597 0.115595I
a = 0.521315 0.198694I
b = 1.80325 1.18702I
3.84373 + 0.16285I 1.32343 + 10.94047I
u = 1.117597 + 0.115595I
a = 0.521315 + 0.198694I
b = 1.80325 + 1.18702I
3.84373 0.16285I 1.32343 10.94047I
8
IV.
I
u
4
= hu
66
+6u
65
+· · ·u+1, 1.01 ×10
19
u
65
+5.41×10
19
u
64
+· · ·+1.31×10
18
a+
1.76 × 10
19
, 9.80 × 10
18
u
65
+ 5.65 × 10
19
u
64
+ · · · + 6.56 × 10
17
b + 1.46 × 10
19
i
(i) Arc colorings
a
5
=
0
u
a
9
=
7.69287u
65
41.2576u
64
+ ··· + 19.2106u 13.4419
14.9389u
65
86.2092u
64
+ ··· + 50.6067u 22.3158
a
6
=
26.0890u
65
+ 128.388u
64
+ ··· 15.1481u + 19.1788
19.9447u
65
+ 100.602u
64
+ ··· 30.3453u + 17.6460
a
2
=
1
0
a
10
=
0.940878u
65
1.39652u
64
+ ··· + 25.0661u 11.4238
10.6727u
65
64.2938u
64
+ ··· + 48.4532u 19.4674
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
3
=
u
4
u
2
+ 1
u
4
a
7
=
26.7251u
65
+ 130.928u
64
+ ··· 13.2239u + 18.8436
35.7148u
65
+ 185.291u
64
+ ··· 63.8245u + 35.5665
a
11
=
17.4214u
65
+ 87.1646u
64
+ ··· 15.6808u + 18.9867
20.0769u
65
+ 111.236u
64
+ ··· 55.0990u + 25.6164
a
8
=
26.7251u
65
+ 130.928u
64
+ ··· 13.2239u + 18.8436
9.07917u
65
+ 44.9975u
64
+ ··· 7.67709u + 6.14426
a
8
=
26.7251u
65
+ 130.928u
64
+ ··· 13.2239u + 18.8436
9.07917u
65
+ 44.9975u
64
+ ··· 7.67709u + 6.14426
(ii) Obstruction class = 1
(iii) Cusp Shapes =
12086631496832904775
655767731184955984
u
65
7581252097116615619
81970966398119498
u
64
+ ··· +
441245495247013113
655767731184955984
u
4211855983240591645
327883865592477992
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.144109 0.674165I
a = 0.647963 0.823435I
b = 0.57846 2.71155I
5.96795 10.55641I 3.25335 + 6.30423I
u = 1.144109 + 0.674165I
a = 0.647963 + 0 .823435I
b = 0.57846 + 2.71155I
5.96795 + 10.55641I 3.25335 6.30423I
u = 1.122904 0.653215I
a = 0.702847 0.577051I
b = 1.047550 0.554678I
0.94779 9.91324I 0.69067 + 7.72830I
u = 1.122904 + 0.653215I
a = 0.702847 + 0.577051I
b = 1.047550 + 0.554678I
0.94779 + 9.91324I 0.69067 7.72830I
u = 1.117621 0.541451I
a = 0.586789 + 0.082840I
b = 0.740285 + 0.230414I
1.19449 4.90633I 1.49511 0.07047I
u = 1.117621 + 0.541451I
a = 0.586789 0.082840I
b = 0.740285 0.230414I
1.19449 + 4.90633I 1.49511 + 0.07047I
u = 1.100319 0.643486I
a = 0.566740 + 0.582790I
b = 1.13556 + 2 .66256I
0.15117 7.27375I 0.28092 + 6.51443I
u = 1.100319 + 0.643486I
a = 0.566740 0.582790I
b = 1.13556 2.66256I
0.15117 + 7.27375I 0.28092 6.51443I
u = 1.067512 0.658022I
a = 0.471025 + 0 .692896I
b = 0.804021 + 0 .774050I
1.98821 5.14475I 1.15894 + 2.87802I
u = 1.067512 + 0.658022I
a = 0.471025 0.692896I
b = 0.804021 0.774050I
1.98821 + 5.14475I 1.15894 2.87802I
10
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.053813 0.724277I
a = 0.952309 0.524725I
b = 0.54792 1.86374I
7.69426 5.94756I 4.85895 + 5.19354I
u = 1.053813 + 0.724277I
a = 0.952309 + 0 .524725I
b = 0.54792 + 1.86374I
7.69426 + 5.94756I 4.85895 5.19354I
u = 1.002327 0.741441I
a = 1.060194 + 0.381824I
b = 0.41322 + 1 .47059I
6.67035 3.81626
u = 1.002327 + 0.741441I
a = 1.060194 0.381824I
b = 0.41322 1.47059I
6.67035 3.81626
u = 0.957231 0.541430I
a = 0.100517 + 0.805361I
b = 0.020763 + 1 .139898I
0.32108 4.39805I 1.68085 + 6.72354I
u = 0.957231 + 0.541430I
a = 0.100517 0.805361I
b = 0.020763 1.139898I
0.32108 + 4.39805I 1.68085 6.72354I
u = 0.914238 0.471505I
a = 0.948969 + 0 .215051I
b = 0.646094 + 0.637510I
2.80746 3.11554I 2.13601 + 3.78726I
u = 0.914238 + 0.471505I
a = 0.948969 0.215051I
b = 0.646094 0.637510I
2.80746 + 3.11554I 2.13601 3.78726I
u = 0.862360 0.437489I
a = 0.196633 1.058797I
b = 0.21466 1.51870I
2.55962 0.56819I 1.77829 + 3.22974I
u = 0.862360 + 0.437489I
a = 0.196633 + 1 .058797I
b = 0.21466 + 1 .51870I
2.55962 + 0.56819I 1.77829 3.22974I
11
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.853729 0.285494I
a = 1.329830 + 0 .295840I
b = 0.275461 + 0 .718535I
1.19449 + 4.90633I 1.49511 + 0.07047I
u = 0.853729 + 0.285494I
a = 1.329830 0.295840I
b = 0.275461 0.718535I
1.19449 4.90633I 1.49511 0.07047I
u = 0.726072 0.397331I
a = 1.187682 0.038310I
b = 0.056637 0.290521I
1.240675 + 0.272253I 4.90559 + 1.40386I
u = 0.726072 + 0.397331I
a = 1.187682 + 0.038310I
b = 0.056637 + 0.290521I
1.240675 0.272253I 4.90559 1.40386I
u = 0.665888 0.873727I
a = 0.381736 + 1.237003I
b = 0.70928 + 1 .91516I
7.69426 5.94756I 4.85895 + 5.19354I
u = 0.665888 + 0.873727I
a = 0.381736 1.237003I
b = 0.70928 1.91516I
7.69426 + 5.94756I 4.85895 5.19354I
u = 0.603634 0.892529I
a = 0.536574 1.172815I
b = 0.74912 1.88252I
9.06216 6.76549
u = 0.603634 + 0.892529I
a = 0.536574 + 1 .172815I
b = 0.74912 + 1.88252I
9.06216 6.76549
u = 0.544139 0.827076I
a = 0.929148 0.522983I
b = 0.321385 + 0.007011I
3.57176 0.40211I 3.54240 + 2.20234I
u = 0.544139 + 0.827076I
a = 0.929148 + 0.522983I
b = 0.321385 0.007011I
3.57176 + 0.40211I 3.54240 2.20234I
12
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.480350 0.829100I
a = 0.655886 + 0.784470I
b = 1.15304 + 1 .79278I
1.71328 + 1.77212I 3.77576 1.74268I
u = 0.480350 + 0.829100I
a = 0.655886 0.784470I
b = 1.15304 1.79278I
1.71328 1.77212I 3.77576 + 1.74268I
u = 0.455132 0.872435I
a = 0.824733 + 0 .813896I
b = 0.346745 + 0 .175683I
2.96228 + 4.26802I 2.35970 3.59869I
u = 0.455132 + 0.872435I
a = 0.824733 0.813896I
b = 0.346745 0.175683I
2.96228 4.26802I 2.35970 + 3.59869I
u = 0.407462 0.942447I
a = 1.076964 + 0.889919I
b = 0.77617 + 1 .33740I
5.96795 + 10.55641I 3.25335 6.30423I
u = 0.407462 + 0.942447I
a = 1.076964 0.889919I
b = 0.77617 1.33740I
5.96795 10.55641I 3.25335 + 6.30423I
u = 0.209151 0.653417I
a = 0.231138 + 1.204018I
b = 0.157146 + 0.302634I
1.240675 + 0.272253I 4.90559 + 1.40386I
u = 0.209151 + 0.653417I
a = 0.231138 1.204018I
b = 0.157146 0.302634I
1.240675 0.272253I 4.90559 1.40386I
u = 0.085935 0.142884I
a = 3.86205 + 0.02618I
b = 0.567403 0.551123I
1.74022 + 0.71657I 3.97070 0.74474I
u = 0.085935 + 0 .142884I
a = 3.86205 0.02618I
b = 0.567403 + 0 .551123I
1.74022 0.71657I 3.97070 + 0.74474I
13
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.114209 0.585210I
a = 0.29597 1.82323I
b = 0.541228 0.418586I
0.32108 + 4.39805I 1.68085 6.72354I
u = 0.114209 + 0 .585210I
a = 0.29597 + 1 .82323I
b = 0.541228 + 0 .418586I
0.32108 4.39805I 1.68085 + 6.72354I
u = 0.636940 0.614253I
a = 1.41838 0.53552I
b = 0.84113 1.64193I
1.98821 5.14475I 1.15894 + 2.87802I
u = 0.636940 + 0 .614253I
a = 1.41838 + 0.53552I
b = 0.84113 + 1 .64193I
1.98821 + 5.14475I 1.15894 2.87802I
u = 0.732260 0.589717I
a = 1.212818 + 0 .617907I
b = 1.02528 + 1.90877I
3.57176 + 0.40211I 3.54240 2.20234I
u = 0.732260 + 0 .589717I
a = 1.212818 0.617907I
b = 1.02528 1.90877I
3.57176 0.40211I 3.54240 + 2.20234I
u = 0.770621 0.443457I
a = 0.355931 0.947784I
b = 1.104908 0.188466I
1.31058 1.00874
u = 0.770621 + 0 .443457I
a = 0.355931 + 0 .947784I
b = 1.104908 + 0 .188466I
1.31058 1.00874
u = 0.904759 0.446690I
a = 0.620936 0.525482I
b = 1.88918 2.64938I
2.95867 + 1.76219I 0.52242 4.84972I
u = 0.904759 + 0 .446690I
a = 0.620936 + 0.525482I
b = 1.88918 + 2 .64938I
2.95867 1.76219I 0.52242 + 4.84972I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.929321 0.583508I
a = 0.770582 + 0 .912339I
b = 1.12317 + 2.65317I
2.96228 + 4.26802I 2.35970 3.59869I
u = 0.929321 + 0 .583508I
a = 0.770582 0.912339I
b = 1.12317 2.65317I
2.96228 4.26802I 2.35970 + 3.59869I
u = 0.961832 0.210042I
a = 0.118406 0.400375I
b = 0.609032 0.703460I
1.74022 + 0.71657I 3.97070 0.74474I
u = 0.961832 + 0 .210042I
a = 0.118406 + 0.400375I
b = 0.609032 + 0 .703460I
1.74022 0.71657I 3.97070 + 0.74474I
u = 0.982708 0.588767I
a = 0.647580 1.020800I
b = 1.05218 2.82658I
0.94779 + 9.91324I 0.69067 7.72830I
u = 0.982708 + 0 .588767I
a = 0.647580 + 1.020800I
b = 1.05218 + 2 .82658I
0.94779 9.91324I 0.69067 + 7.72830I
u = 1.115560 0.407709I
a = 0.773744 0.052312I
b = 0.939464 0.752730I
2.55962 0.56819I 1.77829 + 3.22974I
u = 1.115560 + 0 .407709I
a = 0.773744 + 0.052312I
b = 0.939464 + 0.752730I
2.55962 + 0.56819I 1.77829 3.22974I
u = 1.195920 0.308871I
a = 0.663500 + 0 .443628I
b = 0.676490 + 1 .235201I
2.80746 + 3.11554I 2.13601 3.78726I
u = 1.195920 + 0 .308871I
a = 0.663500 0.443628I
b = 0.676490 1.235201I
2.80746 3.11554I 2.13601 + 3.78726I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.228300 0.089688I
a = 0.200441 + 0 .744488I
b = 0.12838 + 1 .75306I
2.95867 1.76219I 0.52242 + 4.84972I
u = 1.228300 + 0 .089688I
a = 0.200441 0.744488I
b = 0.12838 1.75306I
2.95867 + 1.76219I 0.52242 4.84972I
u = 1.307613 0.078191I
a = 0.941100 + 0.203468I
b = 0.099422 + 0 .620777I
1.71328 1.77212I 3.77576 + 1.74268I
u = 1.307613 + 0 .078191I
a = 0.941100 0.203468I
b = 0.099422 0.620777I
1.71328 + 1.77212I 3.77576 1.74268I
u = 1.322012 0.130704I
a = 0.954553 0.349455I
b = 0.074240 1.007027I
0.15117 7.27375I 0.28092 + 6.51443I
u = 1.322012 + 0 .130704I
a = 0.954553 + 0 .349455I
b = 0.074240 + 1 .007027I
0.15117 + 7.27375I 0.28092 6.51443I
16
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
6
(u
6
+ u
5
+ ··· + u + 1)(u
12
+ 2u
11
+ ··· + 3u + 1)
(u
66
+ 6u
65
+ ··· u + 1)
c
2
(u + 1)
6
(u
6
+ 3u
5
+ ··· + u + 1)(u
12
+ 6u
11
+ ··· + 3 u + 1)
(u
66
+ 30u
65
+ ··· 25u + 1)
c
3
, c
5
u
6
(u
6
u
5
u
4
+ 2u
3
u + 1)
(u
12
3u
10
+ 5u
8
2u
7
2u
6
+ 5u
5
4u
3
+ u
2
+ 3u + 1)
(u
66
+ 2u
65
+ ··· + 64 u + 64)
c
4
(u + 1)
6
(u
6
u
5
+ ··· u + 1)(u
12
+ 2u
11
+ ··· + 3u + 1)
(u
66
+ 6u
65
+ ··· u + 1)
c
6
u
6
(u
6
+ u
5
u
4
2u
3
+ u + 1)
(u
12
3u
10
+ 5u
8
2u
7
2u
6
+ 5u
5
4u
3
+ u
2
+ 3u + 1)
(u
66
+ 2u
65
+ ··· + 64 u + 64)
c
7
(1 u + 2u
2
4u
3
+ 5u
4
3u
5
+ u
6
)
2
(u
12
+ 7u
11
+ ··· + 36u + 8)
(49 + 84u + 108u
2
262u
3
877u
4
+ 1208u
5
+ 1544u
6
2970u
7
+ 255u
8
+ 3112u
9
3310u
10
130u
11
+ 3472u
12
2364u
13
937u
14
+ 1691u
15
499u
16
21u
17
+ 100u
18
340u
19
+ 377u
20
132u
21
200u
22
+ 355u
23
86u
24
215u
25
+ 142u
26
+ 53u
27
72u
28
+ 4u
29
+ 18u
30
5u
31
2u
32
+ u
33
)
2
c
8
(u 1)
6
(u
6
+ u
5
+ ··· + u + 1)(u
12
+ 2u
11
+ ··· + 3u + 1)
(u
66
+ 6u
65
+ ··· u + 1)
c
9
u
6
(u
6
+ u
5
u
4
2u
3
+ u + 1)
(u
12
3u
10
+ 5u
8
2u
7
2u
6
+ 5u
5
4u
3
+ u
2
+ 3u + 1)
(u
66
+ 2u
65
+ ··· + 64 u + 64)
c
10
(u + 1)
6
(u
6
u
5
+ ··· u + 1)(u
12
+ 2u
11
+ ··· + 3u + 1)
(u
66
+ 6u
65
+ ··· u + 1)
c
11
(u + 1)
6
(u
6
+ 3u
5
+ ··· + u + 1)(u
12
+ 6u
11
+ ··· + 3 u + 1)
(u
66
+ 30u
65
+ ··· 25u + 1)
17
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y 1)
6
(y
6
3y
5
+ ··· y + 1)(y
12
6y
11
+ ··· 3y + 1)
(y
66
30y
65
+ ··· + 25 y + 1)
c
2
(y 1)
6
(y
6
+ y
5
+ ··· + 3y + 1)(y
12
+ 2y
11
+ ··· + 25y + 1)
(y
66
+ 18y
65
+ ··· + 1453 y + 1)
c
3
, c
5
, c
6
y
6
(y
6
3y
5
+ ··· y + 1)(y
12
6y
11
+ ··· 7y + 1)
(y
66
36y
65
+ ··· 36864y + 4096)
c
7
(1 + 3y + 6y
2
+ 5y
4
+ y
5
+ y
6
)
2
(y
12
5y
11
+ ··· 112y + 64)
(2401 3528y + 3.03 × 10
4
y
2
+ 3.10 × 10
5
y
3
2.26 × 10
6
y
4
+ 6.52 × 10
6
y
5
1.04 × 10
7
y
6
+ 8.76 × 10
6
y
7
7.79 × 10
5
y
8
6.72 × 10
6
y
9
+ 6.51 × 10
6
y
10
+ 4.81 × 10
5
y
11
7.03 × 10
6
y
12
+ 8.14 × 10
6
y
13
4.84 × 10
6
y
14
+ 1.07 × 10
6
y
15
+ 6.54 × 10
5
y
16
4.50 × 10
5
y
17
2.55 × 10
5
y
18
+ 4.80 × 10
5
y
19
2.43 × 10
5
y
20
1.05 × 10
4
y
21
+ 5.94 × 10
4
y
22
+ 1.21 × 10
4
y
23
6.77 × 10
4
y
24
+ 6.86 × 10
4
y
25
4.32 × 10
4
y
26
+ 2.00 × 10
4
y
27
7356y
28
+ 2216y
29
546y
30
+ 105y
31
14y
32
+ y
33
)
2
c
8
(y 1)
6
(y
6
3y
5
+ ··· y + 1)(y
12
6y
11
+ ··· 3y + 1)
(y
66
30y
65
+ ··· + 25 y + 1)
c
9
y
6
(y
6
3y
5
+ ··· y + 1)(y
12
6y
11
+ ··· 7y + 1)
(y
66
36y
65
+ ··· 36864y + 4096)
c
10
(y 1)
6
(y
6
3y
5
+ ··· y + 1)(y
12
6y
11
+ ··· 3y + 1)
(y
66
30y
65
+ ··· + 25 y + 1)
c
11
(y 1)
6
(y
6
+ y
5
+ ··· + 3y + 1)(y
12
+ 2y
11
+ ··· + 25y + 1)
(y
66
+ 18y
65
+ ··· + 1453 y + 1)
18