11a
299
(K11a
299
)
1
Arc Sequences
4 8 1 9 2 11 10 5 3 7 6
Solving Sequence
1,3
4
2,6
5 11 7 10 8 9
c
3
c
1
c
5
c
11
c
6
c
10
c
7
c
9
c
2
, c
4
, c
8
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hb
3
+ b
2
+ 2b + 1, u 1, b
2
+ 2b + 5a + 4i
I
u
2
= hu
51
+ 4u
50
+ ··· 49u 25, 1.73640 × 10
65
u
50
+ 5.49678 × 10
65
u
49
+ ··· + 1.64457 × 10
65
b 5.18267 × 10
66
,
2.66280 × 10
66
u
50
7.12472 × 10
66
u
49
+ ··· + 8.22283 × 10
66
a 3.83237 × 10
66
i
There are 2 irreducible components with 54 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
3
+ b
2
+ 2b + 1, u 1, b
2
+ 2b + 5a + 4i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
1
a
4
=
1
1
a
2
=
0
1
a
6
=
1
5
b
2
2
5
b
4
5
b
a
5
=
1
5
b
2
2
5
b
4
5
1
5
b
2
+
7
5
b +
4
5
a
11
=
1
5
b
2
+
2
5
b +
4
5
b
2
a
7
=
2
5
b
2
4
5
b
3
5
b
2
b 1
a
10
=
3
5
b
2
+
1
5
b +
2
5
b
2
b 1
a
8
=
0
b
2
2b 2
a
9
=
3
5
b
2
+
1
5
b +
2
5
8
5
b
2
6
5
b
7
5
a
9
=
3
5
b
2
+
1
5
b +
2
5
8
5
b
2
6
5
b
7
5
(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 = 0.637007
b = 0.569840
2.75839 14.9031
u = 1.00000
a = 0.381496 + 0.410401I
b = 0.215080 1.307141I
1.37919 2.82812I 14.9284 + 3.3378I
u = 1.00000
a = 0.381496 0.410401I
b = 0.215080 + 1.307141I
1.37919 + 2.82812I 14.9284 3.3378I
3
II. I
u
2
=
hu
51
+4u
50
+· · ·49u25, 1.74×10
65
u
50
+5.50×10
65
u
49
+· · ·+1.64×10
65
b
5.18× 10
66
, 2.66×10
66
u
50
7.12 ×10
66
u
49
+· · · +8.22 ×10
66
a 3.83× 10
66
i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
2
=
u
2
+ 1
u
2
a
6
=
0.323830u
50
+ 0.866457u
49
+ ··· 9.10394u + 0.466064
1.05584u
50
3.34239u
49
+ ··· + 23.6711u + 31.5139
a
5
=
0.189742u
50
+ 0.584034u
49
+ ··· 5.52625u + 1.24281
1.79580u
50
5.77878u
49
+ ··· + 39.9107u + 50.9480
a
11
=
0.445659u
50
+ 1.37893u
49
+ ··· 17.6080u 14.3558
0.122342u
50
+ 0.664939u
49
+ ··· 3.14254u 8.39179
a
7
=
0.762366u
50
+ 2.21591u
49
+ ··· 28.5399u 26.4849
0.710038u
50
+ 2.35049u
49
+ ··· 17.6295u 24.1743
a
10
=
0.0779482u
50
+ 0.351189u
49
+ ··· + 8.86230u + 4.60922
0.926742u
50
2.85371u
49
+ ··· + 15.8059u + 23.8797
a
8
=
0.488327u
50
+ 1.46749u
49
+ ··· 17.7433u 15.1867
2.26776u
50
+ 7.28910u
49
+ ··· 50.9593u 68.9021
a
9
=
0.0779482u
50
+ 0.351189u
49
+ ··· + 8.86230u + 4.60922
1.00165u
50
3.14194u
49
+ ··· + 11.9267u + 22.8948
a
9
=
0.0779482u
50
+ 0.351189u
49
+ ··· + 8.86230u + 4.60922
1.00165u
50
3.14194u
49
+ ··· + 11.9267u + 22.8948
(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 = 1.30371 0.73473I
a = 1.36012 + 1.44880I
b = 0.16225 1.65033I
11.0558 14.3418I 5.64679 + 7.44685I
u = 1.30371 + 0.73473I
a = 1.36012 1.44880I
b = 0.16225 + 1.65033I
11.0558 + 14.3418I 5.64679 7.44685I
u = 1.242445 0.646879I
a = 0.822718 + 0.850455I
b = 0.552527 0.820307I
2.62483 11.59537I 7.79067 + 8.85645I
u = 1.242445 + 0.646879I
a = 0.822718 0.850455I
b = 0.552527 + 0.820307I
2.62483 + 11.59537I 7.79067 8.85645I
u = 1.192413 0.594620I
a = 1.35362 1.24885I
b = 0.17216 + 1.64138I
7.44997 8.60283I 8.37609 + 5.25476I
u = 1.192413 + 0.594620I
a = 1.35362 + 1.24885I
b = 0.17216 1.64138I
7.44997 + 8.60283I 8.37609 5.25476I
u = 1.146744 0.549997I
a = 0.396576 + 0.218624I
b = 0.744224 + 0.089987I
0.42114 7.27131I 10.81656 + 5.67006I
u = 1.146744 + 0.549997I
a = 0.396576 0.218624I
b = 0.744224 0.089987I
0.42114 + 7.27131I 10.81656 5.67006I
u = 1.090942 0.461623I
a = 0.878372 0.695545I
b = 0.589306 + 0.788540I
0.80955 5.70999I 10.32903 + 7.24097I
u = 1.090942 + 0.461623I
a = 0.878372 + 0.695545I
b = 0.589306 0.788540I
0.80955 + 5.70999I 10.32903 7.24097I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.946910 0.304002I
a = 0.558232 0.204153I
b = 0.773905 0.191317I
2.64708 1.15805I 10.73331 + 5.02870I
u = 0.946910 + 0.304002I
a = 0.558232 + 0.204153I
b = 0.773905 + 0.191317I
2.64708 + 1.15805I 10.73331 5.02870I
u = 0.946433 0.502421I
a = 0.142015 0.509292I
b = 0.433100 + 0.988087I
3.75291 3.24873I 5.67642 + 3.82013I
u = 0.946433 + 0.502421I
a = 0.142015 + 0.509292I
b = 0.433100 0.988087I
3.75291 + 3.24873I 5.67642 3.82013I
u = 0.905265 0.615337I
a = 1.72995 + 1.00752I
b = 0.15866 1.61313I
12.51666 3.55318I 3.48726 + 3.50374I
u = 0.905265 + 0.615337I
a = 1.72995 1.00752I
b = 0.15866 + 1.61313I
12.51666 + 3.55318I 3.48726 3.50374I
u = 0.780971 0.062434I
a = 0.402433 + 0.077190I
b = 0.309159 1.281953I
1.88408 + 2.74356I 0.924641 0.548389I
u = 0.780971 + 0.062434I
a = 0.402433 0.077190I
b = 0.309159 + 1.281953I
1.88408 2.74356I 0.924641 + 0.548389I
u = 0.705356 0.642035I
a = 0.20913 1.59187I
b = 0.08999 + 1.68712I
13.10850 1.33730I 2.96652 + 3.64874I
u = 0.705356 + 0.642035I
a = 0.20913 + 1.59187I
b = 0.08999 1.68712I
13.10850 + 1.33730I 2.96652 3.64874I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.630583 0.557769I
a = 1.37248 + 0.75536I
b = 0.493565 0.692270I
4.68147 1.04951I 4.16172 + 4.32794I
u = 0.630583 + 0.557769I
a = 1.37248 0.75536I
b = 0.493565 + 0.692270I
4.68147 + 1.04951I 4.16172 4.32794I
u = 0.388723 1.311466I
a = 0.06337 2.06962I
b = 0.10468 + 1.64228I
14.0417 + 7.2484I 3.17711 4.95121I
u = 0.388723 + 1.311466I
a = 0.06337 + 2.06962I
b = 0.10468 1.64228I
14.0417 7.2484I 3.17711 + 4.95121I
u = 0.295900 1.111291I
a = 0.073153 0.851180I
b = 0.376973 + 0.809467I
5.59371 + 5.41403I 4.14016 6.52359I
u = 0.295900 + 1.111291I
a = 0.073153 + 0.851180I
b = 0.376973 0.809467I
5.59371 5.41403I 4.14016 + 6.52359I
u = 0.252564 0.754785I
a = 0.227405 + 0.610176I
b = 0.535402 + 0.073202I
3.00953 + 2.35838I 8.15249 2.65728I
u = 0.252564 + 0.754785I
a = 0.227405 0.610176I
b = 0.535402 0.073202I
3.00953 2.35838I 8.15249 + 2.65728I
u = 0.227052 0.900508I
a = 0.24490 + 2.22849I
b = 0.08123 1.64771I
10.29886 + 3.16367I 6.11967 1.96636I
u = 0.227052 + 0.900508I
a = 0.24490 2.22849I
b = 0.08123 + 1.64771I
10.29886 3.16367I 6.11967 + 1.96636I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.109405 0.536765I
a = 0.614217 + 0.917044I
b = 0.249787 0.812726I
1.73380 + 1.81855I 6.35906 4.36354I
u = 0.109405 + 0.536765I
a = 0.614217 0.917044I
b = 0.249787 + 0.812726I
1.73380 1.81855I 6.35906 + 4.36354I
u = 0.221051
a = 1.14734
b = 0.295696
0.590385 17.0961
u = 0.810890 0.116476I
a = 4.65367 + 3.25743I
b = 0.02693 1.61334I
9.33157 + 0.28182I 8.77049 + 5.04634I
u = 0.810890 + 0.116476I
a = 4.65367 3.25743I
b = 0.02693 + 1.61334I
9.33157 0.28182I 8.77049 5.04634I
u = 0.853695 0.091512I
a = 2.12342 2.78746I
b = 0.128736 + 0.681128I
1.377801 + 0.247335I 11.41702 + 6.59841I
u = 0.853695 + 0.091512I
a = 2.12342 + 2.78746I
b = 0.128736 0.681128I
1.377801 0.247335I 11.41702 6.59841I
u = 0.97738 1.08187I
a = 0.75063 + 2.09644I
b = 0.06969 1.58540I
7.57583 + 5.34940I 7.06162 6.81779I
u = 0.97738 + 1.08187I
a = 0.75063 2.09644I
b = 0.06969 + 1.58540I
7.57583 5.34940I 7.06162 + 6.81779I
u = 1.005707 0.788996I
a = 0.399512 + 0.976707I
b = 0.328726 0.602476I
0.09032 + 4.00238I 9.47119 9.47766I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.005707 + 0.788996I
a = 0.399512 0.976707I
b = 0.328726 + 0.602476I
0.09032 4.00238I 9.47119 + 9.47766I
u = 1.111791 0.441573I
a = 0.060256 0.284505I
b = 0.339596 + 0.188204I
1.01423 + 1.50344I 14.02114 0.26378I
u = 1.111791 + 0.441573I
a = 0.060256 + 0.284505I
b = 0.339596 0.188204I
1.01423 1.50344I 14.02114 + 0.26378I
u = 1.143792 0.267385I
a = 0.828284 0.546247I
b = 0.235448 + 0.507844I
1.46138 + 0.98661I 12.15795 1.22039I
u = 1.143792 + 0.267385I
a = 0.828284 + 0.546247I
b = 0.235448 0.507844I
1.46138 0.98661I 12.15795 + 1.22039I
u = 1.194401 0.595818I
a = 1.21718 1.56119I
b = 0.04180 + 1.57969I
5.80181 + 1.83329I 10.40385 0.42256I
u = 1.194401 + 0.595818I
a = 1.21718 + 1.56119I
b = 0.04180 1.57969I
5.80181 1.83329I 10.40385 + 0.42256I
u = 1.345023 0.069345I
a = 0.435107 0.319469I
b = 0.271262 + 0.396700I
1.67074 + 1.07820I 12.01082 5.84608I
u = 1.345023 + 0.069345I
a = 0.435107 + 0.319469I
b = 0.271262 0.396700I
1.67074 1.07820I 12.01082 + 5.84608I
u = 1.61221 0.25894I
a = 0.414432 1.003153I
b = 0.01718 + 1.55667I
5.04838 + 1.69001I 10.14966 3.42632I
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.61221 + 0.25894I
a = 0.414432 + 1.003153I
b = 0.01718 1.55667I
5.04838 1.69001I 10.14966 + 3.42632I
9
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
3
(u
51
+ 4u
50
+ ··· 49u 25)
c
2
u
3
(u
51
+ u
50
+ ··· + 380u + 200)
c
3
(u + 1)
3
(u
51
+ 4u
50
+ ··· 49u 25)
c
4
(u
3
+ u
2
1)(u
51
+ 2u
50
+ ··· + 4u + 1)
c
5
(5u
3
+ 7u
2
+ 4u + 1)(5u
51
+ 28u
50
+ ··· 30u 857)
c
6
, c
7
(u
3
u
2
+ 2u 1)(u
51
+ 2u
50
+ ··· + u
2
1)
c
8
(u
3
u
2
+ 1)(u
51
+ 2u
50
+ ··· + 4u + 1)
c
9
(5u
3
+ 4u
2
u 1)(5u
51
+ 9u
50
+ ··· + 1703u 239)
c
10
, c
11
(u
3
+ u
2
+ 2u + 1)(u
51
+ 2u
50
+ ··· + u
2
1)
10
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
3
(y 1)
3
(y
51
26y
50
+ ··· + 17851y 625)
c
2
y
3
(y
51
+ 21y
50
+ ··· 118000y 40000)
c
4
, c
8
(y
3
y
2
+ 2y 1)(y
51
+ 28y
50
+ ··· + 2y 1)
c
5
(25y
3
9y
2
+ 2y 1)(25y
51
+ 176y
50
+ ··· 1375442y 734449)
c
6
, c
7
, c
10
c
11
(y
3
+ 3y
2
+ 2y 1)(y
51
+ 60y
50
+ ··· + 2y 1)
c
9
(25y
3
26y
2
+ 9y 1)(25y
51
+ 739y
50
+ ··· 637947y 57121)
11