11n
32
(K11n
32
)
1
Arc Sequences
4 1 7 2 8 4 10 5 11 7 9
Solving Sequence
7,10
8
4,11
3 6 5 9 1 2
c
7
c
10
c
3
c
6
c
5
c
9
c
11
c
2
c
1
, c
4
, c
8
Representation Ideals
I = I
u
1
\
I
v
1
I
u
1
= hu
38
+ 5u
37
+ ··· + 104u + 16,
4.56249 × 10
53
u
37
1.98366 × 10
54
u
36
+ ··· + 3.00630 × 10
54
b 1.18639 × 10
55
,
1.39340 × 10
54
u
37
+ 6.28549 × 10
54
u
36
+ ··· + 1.50315 × 10
54
a + 4.25205 × 10
55
i
I
v
1
= hb + v + 2, v
4
+ 5v
3
+ 7v
2
+ 2v + 1, ai
There are 2 irreducible components with 42 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
38
+5u
37
+· · ·+104u+16, 4.56×10
53
u
37
1.98×10
54
u
36
+· · ·+3.01×10
54
b
1.19 × 10
55
, 1.39 × 10
54
u
37
+ 6.29 × 10
54
u
36
+ · · · + 1.50 × 10
54
a + 4.25 × 10
55
i
(i) Arc colorings
a
7
=
0
u
a
10
=
0.926987u
37
4.18155u
36
+ ··· 135.593u 28.2876
0.151764u
37
+ 0.659836u
36
+ ··· + 18.5840u + 3.94634
a
8
=
1.22438u
37
+ 5.44528u
36
+ ··· + 159.909u + 34.0751
0.0453851u
37
+ 0.197052u
36
+ ··· + 8.02644u + 1.84760
a
4
=
1
0
a
11
=
0.926987u
37
4.18155u
36
+ ··· 135.593u 28.2876
0.0784391u
37
0.360238u
36
+ ··· 13.7357u 3.30772
a
3
=
1
u
2
a
6
=
u
u
a
5
=
0.471885u
37
2.14728u
36
+ ··· 70.9792u 17.1177
0.0642746u
37
0.280900u
36
+ ··· 9.18787u 2.15226
a
9
=
1.78274u
37
7.95424u
36
+ ··· 250.772u 53.4037
0.431125u
37
1.91026u
36
+ ··· 56.0313u 11.8301
a
1
=
0.536159u
37
+ 2.42818u
36
+ ··· + 80.1670u + 19.2700
0.0631382u
37
+ 0.279519u
36
+ ··· + 8.50618u + 1.88968
a
2
=
0.473021u
37
+ 2.14866u
36
+ ··· + 71.6609u + 17.3803
0.0631382u
37
+ 0.279519u
36
+ ··· + 8.50618u + 1.88968
a
2
=
0.473021u
37
+ 2.14866u
36
+ ··· + 71.6609u + 17.3803
0.0631382u
37
+ 0.279519u
36
+ ··· + 8.50618u + 1.88968
(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 = 1.52004 0.19492I
a = 0.483337 0.494284I
b = 0.12654 + 1.78294I
4.60338 2.49292I 7.66096 + 3.58742I
u = 1.52004 + 0.19492I
a = 0.483337 + 0.494284I
b = 0.12654 1.78294I
4.60338 + 2.49292I 7.66096 3.58742I
u = 1.45402 0.43836I
a = 0.183345 0.763715I
b = 0.51595 + 2.64583I
6.16601 + 6.56194I 4.09697 5.13849I
u = 1.45402 + 0.43836I
a = 0.183345 + 0.763715I
b = 0.51595 2.64583I
6.16601 6.56194I 4.09697 + 5.13849I
u = 1.43940 0.79817I
a = 0.050059 + 0.782526I
b = 0.16177 2.72225I
1.10073 + 13.93897I 0.18114 8.68220I
u = 1.43940 + 0.79817I
a = 0.050059 0.782526I
b = 0.16177 + 2.72225I
1.10073 13.93897I 0.18114 + 8.68220I
u = 1.32611 0.72615I
a = 0.689407 0.049253I
b = 0.149271 0.003685I
0.48850 + 8.10053I 2.17285 4.60397I
u = 1.32611 + 0.72615I
a = 0.689407 + 0.049253I
b = 0.149271 + 0.003685I
0.48850 8.10053I 2.17285 + 4.60397I
u = 1.233006 0.050062I
a = 0.516758 + 0.875767I
b = 0.79276 1.84419I
2.77951 1.18659I 2.30827 0.46017I
u = 1.233006 + 0.050062I
a = 0.516758 0.875767I
b = 0.79276 + 1.84419I
2.77951 + 1.18659I 2.30827 + 0.46017I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.156071 0.287792I
a = 0.609116 0.482021I
b = 0.088892 + 0.144996I
0.57801 + 4.07433I 1.00107 5.21688I
u = 1.156071 + 0.287792I
a = 0.609116 + 0.482021I
b = 0.088892 0.144996I
0.57801 4.07433I 1.00107 + 5.21688I
u = 0.55366 1.35876I
a = 0.289945 + 0.580664I
b = 0.34598 1.37942I
3.24288 0.91080I 5.85440 + 2.87226I
u = 0.55366 + 1.35876I
a = 0.289945 0.580664I
b = 0.34598 + 1.37942I
3.24288 + 0.91080I 5.85440 2.87226I
u = 0.533786 0.030166I
a = 1.54034 + 1.80642I
b = 0.289563 0.253759I
8.01967 + 3.23855I 7.49106 4.17157I
u = 0.533786 + 0.030166I
a = 1.54034 1.80642I
b = 0.289563 + 0.253759I
8.01967 3.23855I 7.49106 + 4.17157I
u = 0.391833 0.533554I
a = 0.481578 0.104361I
b = 1.014341 0.314495I
1.88768 0.79705I 5.20475 0.93842I
u = 0.391833 + 0.533554I
a = 0.481578 + 0.104361I
b = 1.014341 + 0.314495I
1.88768 + 0.79705I 5.20475 + 0.93842I
u = 0.26079 1.59013I
a = 0.641426 + 0.289977I
b = 1.099622 0.719781I
2.54932 5.85938I 3.38157 + 9.01726I
u = 0.26079 + 1.59013I
a = 0.641426 0.289977I
b = 1.099622 + 0.719781I
2.54932 + 5.85938I 3.38157 9.01726I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.230395 0.298664I
a = 2.30144 + 0.56503I
b = 0.108722 0.621711I
0.31225 1.54508I 2.23777 + 4.87383I
u = 0.230395 + 0.298664I
a = 2.30144 0.56503I
b = 0.108722 + 0.621711I
0.31225 + 1.54508I 2.23777 4.87383I
u = 0.162866 0.630461I
a = 1.58426 0.48425I
b = 0.86678 + 1.49705I
1.35379 + 2.75023I 1.67570 + 2.67847I
u = 0.162866 + 0.630461I
a = 1.58426 + 0.48425I
b = 0.86678 1.49705I
1.35379 2.75023I 1.67570 2.67847I
u = 0.275945 0.814062I
a = 0.852519 0.312379I
b = 0.698335 0.334641I
0.77944 1.52604I 4.36193 + 4.60900I
u = 0.275945 + 0.814062I
a = 0.852519 + 0.312379I
b = 0.698335 + 0.334641I
0.77944 + 1.52604I 4.36193 4.60900I
u = 0.278602 0.363866I
a = 0.68703 1.96808I
b = 1.48828 + 2.95029I
1.79987 1.63683I 0.6342 + 22.3814I
u = 0.278602 + 0.363866I
a = 0.68703 + 1.96808I
b = 1.48828 2.95029I
1.79987 + 1.63683I 0.6342 22.3814I
u = 1.139293 0.198092I
a = 0.800512 + 0.400559I
b = 0.008420 + 0.191321I
0.789901 0.872417I 0.203682 + 1.029460I
u = 1.139293 + 0.198092I
a = 0.800512 0.400559I
b = 0.008420 0.191321I
0.789901 + 0.872417I 0.203682 1.029460I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.259828 0.356568I
a = 0.295658 0.923203I
b = 0.84185 + 1.97914I
2.13442 6.62776I 1.31703 + 5.48212I
u = 1.259828 + 0.356568I
a = 0.295658 + 0.923203I
b = 0.84185 1.97914I
2.13442 + 6.62776I 1.31703 5.48212I
u = 1.32367 0.54173I
a = 0.590584 0.104768I
b = 0.168421 + 0.170029I
1.89024 2.00477I 0.55164 + 1.57531I
u = 1.32367 + 0.54173I
a = 0.590584 + 0.104768I
b = 0.168421 0.170029I
1.89024 + 2.00477I 0.55164 1.57531I
u = 1.53818 0.08244I
a = 0.078634 0.734504I
b = 0.51262 + 2.63453I
7.11789 0.13853I 5.96603 0.12241I
u = 1.53818 + 0.08244I
a = 0.078634 + 0.734504I
b = 0.51262 2.63453I
7.11789 + 0.13853I 5.96603 + 0.12241I
u = 1.62072 0.63223I
a = 0.110732 + 0.695721I
b = 0.19294 2.63595I
3.58657 7.12992I 2.46388 + 6.33493I
u = 1.62072 + 0.63223I
a = 0.110732 0.695721I
b = 0.19294 + 2.63595I
3.58657 + 7.12992I 2.46388 6.33493I
6
II. I
v
1
= hb + v + 2, v
4
+ 5v
3
+ 7v
2
+ 2v + 1, ai
(i) Arc colorings
a
7
=
v
0
a
10
=
0
v 2
a
8
=
v
v
3
+ 4v
2
+ 4v
a
4
=
1
0
a
11
=
v
3
+ 2v
2
v 2
a
3
=
1
0
a
6
=
v
0
a
5
=
2v
3
+ 5v
2
+ 2v + 1
1
a
9
=
2v
3
+ 6v
2
+ 2v + 1
v
2
+ 2v 1
a
1
=
2v
3
5v
2
2v 1
1
a
2
=
2v
3
5v
2
2v
1
a
2
=
2v
3
5v
2
2v
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 2.39923 0.32564I
a = 0
b = 0.399232 + 0.325640I
8.43568 3.16396I 11.64142 + 1.04769I
v = 2.39923 + 0.32564I
a = 0
b = 0.399232 0.325640I
8.43568 + 3.16396I 11.64142 1.04769I
v = 0.100768 0.400532I
a = 0
b = 1.89923 + 0.40053I
1.43393 1.41510I 3.14142 + 7.60220I
v = 0.100768 + 0.400532I
a = 0
b = 1.89923 0.40053I
1.43393 + 1.41510I 3.14142 7.60220I
8
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
4
(u
38
+ 5u
37
+ ··· u + 1)
c
2
(u + 1)
4
(u
38
+ 15u
37
+ ··· 81u + 1)
c
3
, c
6
u
4
(u
38
+ 5u
37
+ ··· + 104u + 16)
c
4
(u + 1)
4
(u
38
+ 5u
37
+ ··· u + 1)
c
5
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
38
+ 2u
37
+ ··· + u + 1)
c
7
(u
4
+ u
3
+ u
2
+ 1)(u
38
+ 2u
37
+ ··· 3u + 1)
c
8
(u
4
u
3
+ 3u
2
2u + 1)(u
38
+ 2u
37
+ ··· + u + 1)
c
9
(u
4
+ u
3
+ 3u
2
+ 2u + 1)(u
38
+ 14u
37
+ ··· + 7u + 1)
c
10
(u
4
u
3
+ u
2
+ 1)(u
38
+ 2u
37
+ ··· 3u + 1)
c
11
(u
4
u
3
+ 3u
2
2u + 1)(u
38
+ 14u
37
+ ··· + 7u + 1)
9
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y 1)
4
(y
38
15y
37
+ ··· + 81y + 1)
c
2
(y 1)
4
(y
38
+ 21y
37
+ ··· 2859y + 1)
c
3
, c
6
y
4
(y
38
27y
37
+ ··· 320y + 256)
c
5
, c
8
(y
4
+ 5y
3
+ ··· + 2y + 1)(y
38
+ 10y
37
+ ··· + 7y + 1)
c
7
, c
10
(y
4
+ y
3
+ 3y
2
+ 2y + 1)(y
38
+ 14y
37
+ ··· + 7y + 1)
c
9
, c
11
(y
4
+ 5y
3
+ ··· + 2y + 1)(y
38
+ 22y
37
+ ··· + 179y + 1)
10