11a
262
(K11a
262
)
1
Arc Sequences
8 5 1 2 11 10 3 4 7 6 9
Solving Sequence
5,11 3,6
2 4 10 7 9 1 8
c
5
c
2
c
4
c
10
c
6
c
9
c
11
c
8
c
1
, c
3
, c
7
Representation Ideals
I = I
u
1
I
u
1
= hu
53
u
52
+ ··· + 9u + 1, 3.07507 × 10
69
u
52
+ 3.86826 × 10
69
u
51
+ ··· + 1.66283 × 10
69
b 1.12419 × 10
70
,
1.91019 × 10
70
u
52
+ 2.44245 × 10
70
u
51
+ ··· + 1.66283 × 10
69
a 6.16106 × 10
70
i
There are 1 irreducible components with 53 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
53
u
52
+· · ·+9u +1, 3.08×10
69
u
52
+3.87× 10
69
u
51
+· · ·+1.66 ×10
69
b
1.12× 10
70
, 1.91× 10
70
u
52
+2.44 × 10
70
u
51
+· · · +1.66 × 10
69
a 6.16 × 10
70
i
(i) Arc colorings
a
5
=
0
u
a
11
=
11.4876u
52
14.6885u
51
+ ··· + 216.395u + 37.0517
1.84930u
52
2.32632u
51
+ ··· + 38.0530u + 6.76069
a
3
=
1
0
a
6
=
9.67338u
52
11.9567u
51
+ ··· + 183.640u + 32.0368
2.27137u
52
2.91824u
51
+ ··· + 47.8752u + 8.63455
a
2
=
1
u
2
a
4
=
u
u
3
+ u
a
10
=
16.4508u
52
20.6836u
51
+ ··· + 296.171u + 51.5827
3.58360u
52
5.67911u
51
+ ··· + 92.1711u + 16.0790
a
7
=
19.5319u
52
25.0782u
51
+ ··· + 388.279u + 67.3460
4.85956u
52
7.23004u
51
+ ··· + 124.330u + 22.1567
a
9
=
22.9719u
52
29.8967u
51
+ ··· + 464.490u + 80.9555
7.25469u
52
10.2658u
51
+ ··· + 164.942u + 29.7119
a
1
=
14.6161u
52
16.1157u
51
+ ··· + 220.460u + 42.4563
5.19010u
52
6.15279u
51
+ ··· + 87.9687u + 16.1157
a
8
=
24.3915u
52
32.3082u
51
+ ··· + 512.609u + 89.5027
4.85956u
52
7.23004u
51
+ ··· + 124.330u + 22.1567
a
8
=
24.3915u
52
32.3082u
51
+ ··· + 512.609u + 89.5027
4.85956u
52
7.23004u
51
+ ··· + 124.330u + 22.1567
(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 = 1.60760 0.35805I
a = 0.129745 0.912844I
b = 0.38586 1.49424I
2.00563 1.98586I 8.80886 + 0.48176I
u = 1.60760 + 0.35805I
a = 0.129745 + 0.912844I
b = 0.38586 + 1.49424I
2.00563 + 1.98586I 8.80886 0.48176I
u = 1.47858 0.47070I
a = 0.226912 0.367962I
b = 0.645247 0.275920I
4.45759 + 0.11922I 13.02951 + 0.69964I
u = 1.47858 + 0.47070I
a = 0.226912 + 0.367962I
b = 0.645247 + 0.275920I
4.45759 0.11922I 13.02951 0.69964I
u = 1.41840 0.61660I
a = 0.438667 + 0.179032I
b = 1.62513 + 0.45295I
4.20057 + 3.68117I 11.59505 7.70576I
u = 1.41840 + 0.61660I
a = 0.438667 0.179032I
b = 1.62513 0.45295I
4.20057 3.68117I 11.59505 + 7.70576I
u = 1.40052 0.74759I
a = 0.534626 + 0.814315I
b = 3.31284 + 0.87386I
2.69459 + 5.99005I 7.34268 6.52584I
u = 1.40052 + 0.74759I
a = 0.534626 0.814315I
b = 3.31284 0.87386I
2.69459 5.99005I 7.34268 + 6.52584I
u = 1.12965
a = 0.205610
b = 0.441758
2.24636 1.69409
u = 1.083365 0.105461I
a = 0.24446 1.40153I
b = 3.77495 + 1.79766I
4.76295 + 3.50697I 9.88928 + 9.21254I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.083365 + 0.105461I
a = 0.24446 + 1.40153I
b = 3.77495 1.79766I
4.76295 3.50697I 9.88928 9.21254I
u = 1.061345 0.039841I
a = 0.431890 0.454119I
b = 2.98286 + 0.75420I
2.13564 + 1.55948I 19.8548 + 10.4353I
u = 1.061345 + 0.039841I
a = 0.431890 + 0.454119I
b = 2.98286 0.75420I
2.13564 1.55948I 19.8548 10.4353I
u = 0.805306 0.215727I
a = 0.312526 0.483721I
b = 0.356372 1.210508I
0.94420 + 1.17734I 5.61906 3.35640I
u = 0.805306 + 0.215727I
a = 0.312526 + 0.483721I
b = 0.356372 + 1.210508I
0.94420 1.17734I 5.61906 + 3.35640I
u = 0.654944 0.209247I
a = 0.56733 + 2.16568I
b = 2.13752 + 1.89630I
5.71528 2.30391I 3.26115 + 5.58323I
u = 0.654944 + 0.209247I
a = 0.56733 2.16568I
b = 2.13752 1.89630I
5.71528 + 2.30391I 3.26115 5.58323I
u = 0.568250 0.931393I
a = 1.145454 0.765401I
b = 1.73767 1.64465I
5.03695 + 1.09402I 3.76275 4.18839I
u = 0.568250 + 0.931393I
a = 1.145454 + 0.765401I
b = 1.73767 + 1.64465I
5.03695 1.09402I 3.76275 + 4.18839I
u = 0.287768 0.005394I
a = 1.38646 1.19715I
b = 0.519523 0.221947I
0.839103 + 0.963368I 7.10556 5.20772I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.287768 + 0.005394I
a = 1.38646 + 1.19715I
b = 0.519523 + 0.221947I
0.839103 0.963368I 7.10556 + 5.20772I
u = 0.168809 0.980887I
a = 0.209839 0.564144I
b = 0.366885 0.261019I
0.73495 + 2.61446I 6.80748 3.27296I
u = 0.168809 + 0.980887I
a = 0.209839 + 0.564144I
b = 0.366885 + 0.261019I
0.73495 2.61446I 6.80748 + 3.27296I
u = 0.066562 1.132374I
a = 0.564778 0.416385I
b = 1.031359 0.264440I
0.15260 + 6.19554I 4.01481 9.36178I
u = 0.066562 + 1.132374I
a = 0.564778 + 0.416385I
b = 1.031359 + 0.264440I
0.15260 6.19554I 4.01481 + 9.36178I
u = 0.061710 0.224296I
a = 2.94727 + 1.10519I
b = 0.149757 0.481568I
0.14967 + 2.03204I 3.41312 3.39800I
u = 0.061710 + 0.224296I
a = 2.94727 1.10519I
b = 0.149757 + 0.481568I
0.14967 2.03204I 3.41312 + 3.39800I
u = 0.002505 1.226548I
a = 1.280720 0.124168I
b = 2.69445 0.97429I
7.49343 + 8.60231I 0.99797 7.41135I
u = 0.002505 + 1.226548I
a = 1.280720 + 0.124168I
b = 2.69445 + 0.97429I
7.49343 8.60231I 0.99797 + 7.41135I
u = 0.037391 0.377043I
a = 4.10468 + 0.73774I
b = 1.160646 0.367701I
7.21649 + 4.05118I 0.025573 0.974871I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.037391 + 0.377043I
a = 4.10468 0.73774I
b = 1.160646 + 0.367701I
7.21649 4.05118I 0.025573 + 0.974871I
u = 0.211342 0.692763I
a = 1.025877 + 0.184203I
b = 1.076605 0.393531I
2.80915 + 1.17690I 3.10474 1.38405I
u = 0.211342 + 0.692763I
a = 1.025877 0.184203I
b = 1.076605 + 0.393531I
2.80915 1.17690I 3.10474 + 1.38405I
u = 0.434674 0.830989I
a = 1.52244 + 0.76617I
b = 2.65029 0.07121I
10.80677 + 0.74411I 3.05627 1.07981I
u = 0.434674 + 0.830989I
a = 1.52244 0.76617I
b = 2.65029 + 0.07121I
10.80677 0.74411I 3.05627 + 1.07981I
u = 1.027982 0.455273I
a = 0.61884 1.32570I
b = 1.58302 1.70146I
8.94151 5.46940I 0.01723 + 6.48286I
u = 1.027982 + 0.455273I
a = 0.61884 + 1.32570I
b = 1.58302 + 1.70146I
8.94151 + 5.46940I 0.01723 6.48286I
u = 1.130743 0.236854I
a = 0.451929 1.304782I
b = 1.84400 0.62589I
4.20208 6.58081I 4.95504 + 8.51654I
u = 1.130743 + 0.236854I
a = 0.451929 + 1.304782I
b = 1.84400 + 0.62589I
4.20208 + 6.58081I 4.95504 8.51654I
u = 1.134872 0.110271I
a = 0.625446 0.533391I
b = 1.032295 0.482009I
3.29153 3.40743I 13.0359 + 10.0924I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.134872 + 0.110271I
a = 0.625446 + 0.533391I
b = 1.032295 + 0.482009I
3.29153 + 3.40743I 13.0359 10.0924I
u = 1.157103 0.030135I
a = 0.650417 0.206298I
b = 0.604097 + 0.059371I
4.51390 1.24711I 18.3925 + 3.9738I
u = 1.157103 + 0.030135I
a = 0.650417 + 0.206298I
b = 0.604097 0.059371I
4.51390 + 1.24711I 18.3925 3.9738I
u = 1.160090 0.255953I
a = 0.379044 0.839855I
b = 0.635372 0.692551I
0.20296 4.75561I 5.44165 + 8.22126I
u = 1.160090 + 0.255953I
a = 0.379044 + 0.839855I
b = 0.635372 + 0.692551I
0.20296 + 4.75561I 5.44165 8.22126I
u = 1.303556 0.338629I
a = 0.144361 0.947693I
b = 0.270241 0.639621I
0.47934 4.72102I 5.64731 + 4.20752I
u = 1.303556 + 0.338629I
a = 0.144361 + 0.947693I
b = 0.270241 + 0.639621I
0.47934 + 4.72102I 5.64731 4.20752I
u = 1.36138 0.45603I
a = 0.375155 0.346466I
b = 0.593029 + 0.138240I
5.42859 7.69645I 8.91950 + 3.87764I
u = 1.36138 + 0.45603I
a = 0.375155 + 0.346466I
b = 0.593029 0.138240I
5.42859 + 7.69645I 8.91950 3.87764I
u = 1.37904 0.51660I
a = 0.532434 + 0.275105I
b = 1.73301 + 0.65668I
4.38092 11.94557I 6.49757 + 9.10409I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.37904 + 0.51660I
a = 0.532434 0.275105I
b = 1.73301 0.65668I
4.38092 + 11.94557I 6.49757 9.10409I
u = 1.38731 0.56687I
a = 0.512042 + 0.933320I
b = 3.17251 + 0.88693I
3.1210 14.8139I 3.40221 + 7.99396I
u = 1.38731 + 0.56687I
a = 0.512042 0.933320I
b = 3.17251 0.88693I
3.1210 + 14.8139I 3.40221 7.99396I
8
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
53
+ 3u
52
+ ··· u 1)
c
2
, c
4
(u
53
+ u
52
+ ··· + 9u 1)
c
3
(u
53
+ 9u
52
+ ··· + u + 1)
c
5
, c
6
, c
9
c
10
(u
53
+ u
52
+ ··· + 3u 1)
c
7
(u
53
+ u
52
+ ··· 721u 271)
c
8
(u
53
+ u
52
+ ··· + 37u + 89)
c
11
(u
53
+ 11u
52
+ ··· + 1317u + 163)
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
53
9y
52
+ ··· + 3y 1)
c
2
, c
4
(y
53
37y
52
+ ··· 9y 1)
c
3
(y
53
+ 3y
52
+ ··· 9y 1)
c
5
, c
6
, c
9
c
10
(y
53
+ 59y
52
+ ··· + 3y 1)
c
7
(y
53
+ 35y
52
+ ··· + 1272679y 73441)
c
8
(y
53
+ 59y
52
+ ··· 255841y 7921)
c
11
(y
53
+ 19y
52
+ ··· + 1976055y 26569)
10