11a
129
(K11a
129
)
1
Arc Sequences
6 1 10 11 2 9 3 5 7 4 8
Solving Sequence
1,6
2
3,9
7 10 5 8 11 4
c
1
c
2
c
6
c
9
c
5
c
8
c
11
c
4
c
3
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
3
+ u
2
+ 2u + 1, u
2
+ a + u + 2, u
2
+ 7b + u 4i
I
u
2
= hu
59
+ 2u
58
+ ··· 4u 1, 1.91764 × 10
47
u
58
4.02272 × 10
47
u
57
+ ··· + 2.17831 × 10
47
a + 8.99140 × 10
47
,
7.86460 × 10
47
u
58
8.24857 × 10
47
u
57
+ ··· + 1.52482 × 10
48
b 1.10743 × 10
47
i
There are 2 irreducible components with 62 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
3
+ u
2
+ 2u + 1, u
2
+ a + u + 2, u
2
+ 7b + u 4i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
u
2
u 2
1
7
u
2
1
7
u +
4
7
a
7
=
u
2
u 2
1
7
u
2
+
6
7
u +
4
7
a
10
=
0
u
a
5
=
u
u
2
u 1
a
8
=
4
7
u
2
3
7
u
9
7
0
a
11
=
1
0
a
4
=
u
2
+ 1
u
2
u 1
a
4
=
u
2
+ 1
u
2
u 1
(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 = 0.569840
a = 1.75488
b = 0.699223
2.75839 15.1893
u = 0.215080 1.307141I
a = 0.122561 + 0.744862I
b = 0.364674 + 0.267060I
1.37919 + 2.82812I 6.66044 + 5.49186I
u = 0.215080 + 1.307141I
a = 0.122561 0.744862I
b = 0.364674 0.267060I
1.37919 2.82812I 6.66044 5.49186I
3
II. I
u
2
=
hu
59
+2u
58
+· · ·4u1, 1.92×10
47
u
58
4.02×10
47
u
57
+· · ·+2.18×10
47
a+
8.99 × 10
47
, 7.86× 10
47
u
58
8.25 × 10
47
u
57
+ · · · + 1.52 × 10
48
b 1.11 × 10
47
i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
0.880334u
58
+ 1.84672u
57
+ ··· 1.19036u 4.12769
0.515773u
58
+ 0.540954u
57
+ ··· + 0.869074u + 0.0726268
a
7
=
0.916403u
58
+ 1.87970u
57
+ ··· + 0.895810u 4.08900
0.510090u
58
+ 0.540540u
57
+ ··· + 2.07311u + 0.157472
a
10
=
0.121237u
58
0.128857u
57
+ ··· 4.12161u 0.0703064
0.00350111u
58
0.0347593u
57
+ ··· 1.30073u 0.134750
a
5
=
u
u
3
+ u
a
8
=
0.953991u
58
+ 1.59522u
57
+ ··· 0.962582u 3.72486
0.0272410u
58
+ 0.0233742u
57
+ ··· + 2.16287u + 0.0685969
a
11
=
0.134750u
58
0.273000u
57
+ ··· + 1.08216u 0.761734
0.113618u
58
+ 0.176695u
57
+ ··· 0.555256u 0.121237
a
4
=
0.247325u
58
+ 0.662742u
57
+ ··· 1.63058u + 0.291658
0.168092u
58
0.129263u
57
+ ··· + 1.28096u + 0.247325
a
4
=
0.247325u
58
+ 0.662742u
57
+ ··· 1.63058u + 0.291658
0.168092u
58
0.129263u
57
+ ··· + 1.28096u + 0.247325
(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 = 0.984441 0.529687I
a = 1.004843 0.635720I
b = 1.65051 0.69891I
5.85876 + 0.11889I 12.85983 0.52971I
u = 0.984441 + 0.529687I
a = 1.004843 + 0.635720I
b = 1.65051 + 0.69891I
5.85876 0.11889I 12.85983 + 0.52971I
u = 0.920445 0.536589I
a = 1.02151 1.08830I
b = 1.75834 0.64446I
13.4212 9.5497I 12.60640 + 3.95803I
u = 0.920445 + 0.536589I
a = 1.02151 + 1.08830I
b = 1.75834 + 0.64446I
13.4212 + 9.5497I 12.60640 3.95803I
u = 0.733377 1.128388I
a = 0.680742 0.713298I
b = 2.18758 0.58843I
4.02435 + 6.11409I 9.29108 4.87960I
u = 0.733377 + 1.128388I
a = 0.680742 + 0.713298I
b = 2.18758 + 0.58843I
4.02435 6.11409I 9.29108 + 4.87960I
u = 0.701304 1.111324I
a = 0.968507 0.757871I
b = 2.70525 0.68048I
11.6590 + 15.5089I 10.31782 8.13959I
u = 0.701304 + 1.111324I
a = 0.968507 + 0.757871I
b = 2.70525 + 0.68048I
11.6590 15.5089I 10.31782 + 8.13959I
u = 0.683737 0.607315I
a = 0.55812 + 1.37162I
b = 0.252187 0.820948I
7.23997 3.63562I 11.83171 + 2.99653I
u = 0.683737 + 0.607315I
a = 0.55812 1.37162I
b = 0.252187 + 0.820948I
7.23997 + 3.63562I 11.83171 2.99653I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.680135 0.786084I
a = 0.73044 + 1.69093I
b = 1.89769 + 0.12489I
11.01857 + 0.16153I 15.3579 0.6458I
u = 0.680135 + 0.786084I
a = 0.73044 1.69093I
b = 1.89769 0.12489I
11.01857 0.16153I 15.3579 + 0.6458I
u = 0.668786 0.902187I
a = 1.49378 + 0.80400I
b = 2.38866 + 0.90347I
10.66654 + 5.04841I 14.3676 5.7051I
u = 0.668786 + 0.902187I
a = 1.49378 0.80400I
b = 2.38866 0.90347I
10.66654 5.04841I 14.3676 + 5.7051I
u = 0.639166 1.007087I
a = 1.127879 0.474560I
b = 0.82739 + 1.19361I
6.06759 + 8.77463I 9.45253 7.92148I
u = 0.639166 + 1.007087I
a = 1.127879 + 0.474560I
b = 0.82739 1.19361I
6.06759 8.77463I 9.45253 + 7.92148I
u = 0.635747
a = 0.649289
b = 0.703411
1.61678 5.27681
u = 0.573063 0.858445I
a = 0.670149 + 0.872588I
b = 3.20509 + 1.62041I
2.15381 + 2.27881I 7.94357 + 3.32360I
u = 0.573063 + 0.858445I
a = 0.670149 0.872588I
b = 3.20509 1.62041I
2.15381 2.27881I 7.94357 3.32360I
u = 0.553519 0.993934I
a = 0.415620 0.151815I
b = 0.408476 0.170231I
0.25044 + 3.21979I 3.90025 0.90131I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.553519 + 0.993934I
a = 0.415620 + 0.151815I
b = 0.408476 + 0.170231I
0.25044 3.21979I 3.90025 + 0.90131I
u = 0.462195 0.671481I
a = 0.119813 + 0.606268I
b = 0.601427 0.188306I
0.818669 + 1.086875I 6.95263 5.92982I
u = 0.462195 + 0.671481I
a = 0.119813 0.606268I
b = 0.601427 + 0.188306I
0.818669 1.086875I 6.95263 + 5.92982I
u = 0.282031 1.157492I
a = 0.302609 0.470483I
b = 0.646754 0.400492I
1.83113 + 3.37489I 0.67684 6.31964I
u = 0.282031 + 1.157492I
a = 0.302609 + 0.470483I
b = 0.646754 + 0.400492I
1.83113 3.37489I 0.67684 + 6.31964I
u = 0.218983
a = 5.02750
b = 0.207976
2.11871 0.678539
u = 0.133043 0.520766I
a = 0.708635 + 0.999139I
b = 0.191283 0.635509I
0.674447 + 1.055544I 6.88917 6.16079I
u = 0.133043 + 0.520766I
a = 0.708635 0.999139I
b = 0.191283 + 0.635509I
0.674447 1.055544I 6.88917 + 6.16079I
u = 0.089273 1.378351I
a = 0.140713 0.801528I
b = 0.274085 0.302994I
1.23742 + 3.26694I 11.3663 10.6974I
u = 0.089273 + 1.378351I
a = 0.140713 + 0.801528I
b = 0.274085 + 0.302994I
1.23742 3.26694I 11.3663 + 10.6974I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.032617 0.990758I
a = 0.888441 0.029789I
b = 0.905148 0.901763I
2.38922 3.00723I 3.42401 + 2.53679I
u = 0.032617 + 0.990758I
a = 0.888441 + 0.029789I
b = 0.905148 + 0.901763I
2.38922 + 3.00723I 3.42401 2.53679I
u = 0.058861 1.275218I
a = 0.333588 1.017961I
b = 0.476010 + 0.072636I
6.48770 7.42956I 8.09632 + 5.49471I
u = 0.058861 + 1.275218I
a = 0.333588 + 1.017961I
b = 0.476010 0.072636I
6.48770 + 7.42956I 8.09632 5.49471I
u = 0.137524 1.027835I
a = 0.626107 0.222992I
b = 0.781828 0.617316I
3.28171 + 0.39501I 2.00061 1.54672I
u = 0.137524 + 1.027835I
a = 0.626107 + 0.222992I
b = 0.781828 + 0.617316I
3.28171 0.39501I 2.00061 + 1.54672I
u = 0.390405 0.817622I
a = 0.611929 + 0.822418I
b = 2.16734 1.76190I
6.34398 2.28663I 11.09109 4.75818I
u = 0.390405 + 0.817622I
a = 0.611929 0.822418I
b = 2.16734 + 1.76190I
6.34398 + 2.28663I 11.09109 + 4.75818I
u = 0.398582
a = 3.47163
b = 0.324585
8.30655 10.7681
u = 0.426307 0.460098I
a = 1.359150 + 0.181107I
b = 0.644001 0.367019I
6.50215 2.38989I 11.27204 + 2.30285I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.426307 + 0.460098I
a = 1.359150 0.181107I
b = 0.644001 + 0.367019I
6.50215 + 2.38989I 11.27204 2.30285I
u = 0.552687 0.945630I
a = 0.090574 + 0.320422I
b = 0.34144 1.82231I
5.48223 1.81992I 9.39092 + 3.32570I
u = 0.552687 + 0.945630I
a = 0.090574 0.320422I
b = 0.34144 + 1.82231I
5.48223 + 1.81992I 9.39092 3.32570I
u = 0.604324 0.573388I
a = 0.395116 + 0.973940I
b = 0.065984 0.490421I
0.92823 + 1.58622I 7.27802 5.02607I
u = 0.604324 + 0.573388I
a = 0.395116 0.973940I
b = 0.065984 + 0.490421I
0.92823 1.58622I 7.27802 + 5.02607I
u = 0.608030 1.009496I
a = 0.807649 0.370771I
b = 0.622216 + 0.676749I
0.33205 6.44214I 4.62600 + 9.28024I
u = 0.608030 + 1.009496I
a = 0.807649 + 0.370771I
b = 0.622216 0.676749I
0.33205 + 6.44214I 4.62600 9.28024I
u = 0.628580 0.787255I
a = 0.60556 + 1.31607I
b = 1.54203 + 0.70665I
4.05953 0.76565I 13.67462 0.08522I
u = 0.628580 + 0.787255I
a = 0.60556 1.31607I
b = 1.54203 0.70665I
4.05953 + 0.76565I 13.67462 + 0.08522I
u = 0.630391 0.897646I
a = 1.100086 + 0.718650I
b = 2.35260 + 0.70043I
3.71804 4.17211I 12.3249 + 7.4178I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.630391 + 0.897646I
a = 1.100086 0.718650I
b = 2.35260 0.70043I
3.71804 + 4.17211I 12.3249 7.4178I
u = 0.709501 1.162292I
a = 0.518508 0.861817I
b = 1.98938 0.21989I
10.90239 1.52833I 13.38061 + 1.32991I
u = 0.709501 + 1.162292I
a = 0.518508 + 0.861817I
b = 1.98938 + 0.21989I
10.90239 + 1.52833I 13.38061 1.32991I
u = 0.714424 1.111054I
a = 0.846597 0.704968I
b = 2.46864 0.69900I
4.44674 11.62550I 8.00562 + 8.71394I
u = 0.714424 + 1.111054I
a = 0.846597 + 0.704968I
b = 2.46864 + 0.69900I
4.44674 + 11.62550I 8.00562 8.71394I
u = 0.941643 0.550391I
a = 0.947634 0.890259I
b = 1.69875 0.66677I
6.17346 + 5.56581I 10.67180 4.54709I
u = 0.941643 + 0.550391I
a = 0.947634 + 0.890259I
b = 1.69875 + 0.66677I
6.17346 5.56581I 10.67180 + 4.54709I
u = 0.962528 0.479411I
a = 1.253286 0.475732I
b = 1.58637 0.78610I
12.98449 4.58039I 14.2893 + 3.5875I
u = 0.962528 + 0.479411I
a = 1.253286 + 0.475732I
b = 1.58637 + 0.78610I
12.98449 + 4.58039I 14.2893 3.5875I
10
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
3
+ u
2
+ 2u + 1)(u
59
+ 2u
58
+ ··· 4u 1)
c
2
(u
3
+ 3u
2
+ 2u 1)(u
59
+ 24u
58
+ ··· + 10u 1)
c
3
, c
4
(u
3
+ u
2
1)(u
59
+ 2u
58
+ ··· + 5u
2
1)
c
5
(u
3
u
2
+ 2u 1)(u
59
+ 2u
58
+ ··· 4u 1)
c
6
(u + 1)
3
(u
59
+ 4u
58
+ ··· 257u + 49)
c
7
(7u
3
+ u
2
+ u 1)(7u
59
+ 22u
58
+ ··· 126239u 81841)
c
8
(7u
3
u
2
4u 1)(7u
59
+ 6u
58
+ ··· + 6234u 1903)
c
9
(u 1)
3
(u
59
+ 4u
58
+ ··· 257u + 49)
c
10
(u
3
u
2
+ 1)(u
59
+ 2u
58
+ ··· + 5u
2
1)
c
11
u
3
(u
59
+ 5u
58
+ ··· 868u + 392)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
3
+ 3y
2
+ 2y 1)(y
59
+ 24y
58
+ ··· + 10y 1)
c
2
(y
3
5y
2
+ 10y 1)(y
59
+ 24y
58
+ ··· + 462y 1)
c
3
(y
3
y
2
+ 2y 1)(y
59
60y
58
+ ··· + 10y 1)
c
4
1.000000000000000
(1y
3
y
2
+ 2.000000000000000y 1.000000000000000)
(1.00y
59
60.0y
58
+ ··· + 10.0y 1.00)
c
6
(y 1)
3
(y
59
50y
58
+ ··· + 74183y 2401)
c
7
(49y
3
+ 13y
2
+ 3y 1)
(49y
59
+ 3394y
58
+ ··· 90830373521y 6697949281)
c
8
(49y
3
57y
2
+ 14y 1)
(49y
59
64y
58
+ ··· + 229562386y 3621409)
c
9
1.0000000000000(1y 1.00000000000000)
3
(1.00y
59
50.0y
58
+ ··· + 7.42 × 10
4
y 2.40 × 10
3
)
c
10
1.0000000000000000
(1y
3
y
2
+ 2.000000000000000y 1.0000000000000000)
(1.00y
59
60.0y
58
+ ··· + 10.0y 1.00)
c
11
1y
3
(1.00y
59
+ 21.0y
58
+ ··· 2.15 × 10
6
y 1.54 × 10
5
)
12