11n
72
(K11n
72
)
1
Arc Sequences
4 1 8 2 11 9 4 6 8 5 10
Solving Sequence
5,11 2,6
4
1,8
3 10 9 7
c
5
c
4
c
1
c
3
c
10
c
9
c
6
c
2
, c
7
, c
8
, c
11
Representation Ideals
I =
8
\
i=1
I
u
i
\
I
v
1
1
The knot diagram image is adapter from “C. Livingston and A. H. Mo ore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I
u
1
= hu 1, c + 1, b + a, db + 2b 1i
I
u
2
= hc, u 1, a + 1, d + 1, b + 1i
I
u
3
= hu 1, a + 1, c + 1, b + 1, d + 2i
I
u
4
= ha + 1, c
4
+ 2c
3
+ 2c
2
+ c + b + 2, c
4
2c
3
3c
2
2c + u 2, c
6
+ 3c
5
+ 5c
4
+ 5c
3
+ 5c
2
+ 3c + 1,
c
5
2c
4
2c
3
c
2
+ d 2c + 1i
I
u
5
= hc 1, u
6
+ u
5
u
3
+ 2d + 2u 1, u
6
u
5
+ u
3
2u
2
+ 2a 2u 1, u
7
+ u
6
3u
4
+ 2u
2
+ 2b + 3u 2,
u
8
+ u
7
u
6
2u
5
+ 2u
4
+ 3u
3
+ u
2
2u + 1i
I
u
6
= hc 1, u
9
2u
7
2u
6
+ 2u
5
+ 2u
4
3u
2
+ b + 1, u
10
+ 2u
9
+ u
8
2u
7
u
6
+ 2u
5
+ 4u
4
2u
2
+ d u,
u
11
+ 2u
10
4u
8
2u
7
+ 4u
6
+ 5u
5
2u
4
5u
3
u
2
+ 3u + 1,
u
10
+ 2u
9
u
8
5u
7
u
6
+ 6u
5
+ 4u
4
4u
3
5u
2
+ a + u + 3i
I
u
7
= hu
9
2u
7
2u
6
+ 2u
5
+ 2u
4
3u
2
+ b + 1, u
11
+ 2u
10
4u
8
2u
7
+ 4u
6
+ 5u
5
2u
4
5u
3
u
2
+ 3u + 1,
u
10
u
9
+ u
8
+ 2u
7
u
6
2u
5
+ 2u
3
+ u
2
+ d u + 1,
u
10
+ 2u
9
u
8
5u
7
u
6
+ 6u
5
+ 4u
4
4u
3
5u
2
+ a + u + 3,
u
10
+ 2u
9
u
8
5u
7
u
6
+ 6u
5
+ 4u
4
4u
3
5u
2
+ c + u + 4i
I
u
8
= hu
11
3u
9
2u
8
+ 3u
7
+ 4u
6
2u
4
u
3
+ 3u
2
4,
109u
10
+ 198u
9
+ 163u
8
56u
7
503u
6
2u
5
+ 92u
4
+ 114u
3
319u
2
+ 344a 101u + 862,
41u
10
+ 166u
9
+ 55u
8
212u
7
347u
6
+ 146u
5
+ 164u
4
+ 106u
3
191u
2
+ 172b 109u + 542,
41u
10
6u
9
+ 55u
8
+ 132u
7
3u
6
198u
5
180u
4
+ 106u
3
+ 325u
2
+ 344c 109u + 26,
17u
10
+ 8u
9
+ 27u
8
4u
7
39u
6
+ 6u
5
+ 68u
4
+ 2u
3
+ 11u
2
+ 86d 41u + 80i
I
v
1
= hb, c, v 1, a + 1, d + 1i
There are 9 irreducible components with 50 representations.
There are 1 irreducible components of dim
C
= 1 for 11n
72
2
I. I
u
1
= hu 1, c + 1, b + a, db + 2b 1i
(i) Arc colorings
a
5
=
0
1
a
11
=
1
d
a
2
=
1
0
a
6
=
1
d + 1
a
4
=
1
1
a
1
=
0
1
a
8
=
b
b
a
3
=
1
1
a
10
=
1
d + 1
a
9
=
b 1
d + b + 1
a
7
=
b
b
a
7
=
b
b
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
3
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = ···
a = ···
b = ···
c = ···
d = ···
4.93480 14.7045 + 1.9603I
4
II. I
u
2
= hc, u 1, a + 1, d + 1, b + 1i
(i) Arc colorings
a
5
=
0
1
a
11
=
0
1
a
2
=
1
0
a
6
=
0
1
a
4
=
1
1
a
1
=
0
1
a
8
=
1
1
a
3
=
1
1
a
10
=
0
1
a
9
=
1
2
a
7
=
1
1
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.00000
c = 0
d = 1.00000
3.28987 12.0000
6
III. I
u
3
= hu 1, a + 1, c + 1, b + 1, d + 2i
(i) Arc colorings
a
5
=
0
1
a
11
=
1
2
a
2
=
1
0
a
6
=
1
1
a
4
=
1
1
a
1
=
0
1
a
8
=
1
1
a
3
=
1
1
a
10
=
1
1
a
9
=
1
1
a
7
=
1
1
a
7
=
1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.00000
a = 1.00000
b = 1.00000
c = 1.00000
d = 2.00000
3.28987 12.0000
8
IV. I
u
4
= ha + 1, c
4
+ 2c
3
+ 2c
2
+ c + b + 2, c
4
+ u + · · · 2c 2, c
6
+
3c
5
+ · · · + 3c + 1, c
5
+ d + · · · 2c + 1i
(i) Arc colorings
a
5
=
0
c
4
+ 2c
3
+ 3c
2
+ 2c + 2
a
11
=
c
c
5
+ 2c
4
+ 2c
3
+ c
2
+ 2c 1
a
2
=
1
0
a
6
=
c
5
+ 2c
4
+ 3c
3
+ 3c
2
+ 3c + 1
2c
5
+ 5c
4
+ 8c
3
+ 7c
2
+ 7c + 3
a
4
=
c
4
+ 2c
3
+ 3c
2
+ 2c + 2
c
4
+ 2c
3
+ 3c
2
+ 2c + 2
a
1
=
c
4
2c
3
2c
2
c 1
c
4
2c
3
2c
2
c 2
a
8
=
1
c
4
2c
3
2c
2
c 2
a
3
=
c
4
+ 2c
3
+ 3c
2
+ 2c + 3
2c
4
+ 4c
3
+ 5c
2
+ 3c + 4
a
10
=
c
1
a
9
=
c
5
2c
4
2c
3
c
2
c 1
2c
5
5c
4
7c
3
5c
2
5c 3
a
7
=
c
4
2c
3
3c
2
2c 1
c
2
c
a
7
=
c
4
2c
3
3c
2
2c 1
c
2
c
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
9
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.662359 + 0.562280I
a = 1.00000
b = 0.122561 + 0.744862I
c = 1.16236 0.98673I
d = 1.87744 + 0.74486I
1.64493 6.00000
u = 0.662359 0.562280I
a = 1.00000
b = 0.122561 0.744862I
c = 1.16236 + 0.98673I
d = 1.87744 0.74486I
1.64493 6.00000
u = 1.32472
a = 1.00000
b = 1.75488
c = 0.500000 0.424452I
d = 1.87744 0.74486I
1.64493 6.00000
u = 1.32472
a = 1.00000
b = 1.75488
c = 0.500000 + 0.424452I
d = 1.87744 + 0.74486I
1.64493 6.00000
u = 0.662359 0.562280I
a = 1.00000
b = 0.122561 0.744862I
c = 0.162359 0.986732I
d = 0.245122
1.64493 6.00000
u = 0.662359 + 0.562280I
a = 1.00000
b = 0.122561 + 0.744862I
c = 0.162359 + 0.986732I
d = 0.245122
1.64493 6.00000
10
V. I
u
5
= hc 1, u
6
+ u
5
u
3
+ 2d + 2u 1, u
6
u
5
+ · · · + 2a 1, u
7
+
u
6
+ · · · + 2b 2, u
8
+ u
7
+ · · · 2u + 1i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
1
2
u
6
1
2
u
5
+
1
2
u
3
u +
1
2
a
2
=
1
0
a
6
=
u
1
2
u
7
+
1
2
u
6
1
2
u
4
+ u
2
+
1
2
u
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
8
=
1
2
u
6
+
1
2
u
5
+ ··· + u +
1
2
1
2
u
7
1
2
u
6
+ ···
3
2
u + 1
a
3
=
u
4
u
2
+ 1
u
4
a
10
=
1
1
2
u
6
1
2
u
5
+ ··· u +
1
2
a
9
=
1
2
u
6
+
1
2
u
5
1
2
u
3
+ u +
1
2
1
2
u
7
+
1
2
u
5
+ ···
1
2
u +
1
2
a
7
=
1
2
u
7
1
2
u
6
+ ··· u
2
3
2
u
1
2
u
6
+
1
2
u
5
+ ··· + u
1
2
a
7
=
1
2
u
7
1
2
u
6
+ ··· u
2
3
2
u
1
2
u
6
+
1
2
u
5
+ ··· + u
1
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
11
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.213441 0.663590I
a = 1.02473 + 1.24139I
b = 1.56585 + 2.17513I
c = 1.00000
d = 3.05682 + 0.36906I
0.8567 14.6934I 9.31845 + 9.04054I
u = 1.213441 + 0.663590I
a = 1.02473 1.24139I
b = 1.56585 2.17513I
c = 1.00000
d = 3.05682 0.36906I
0.8567 + 14.6934I 9.31845 9.04054I
u = 0.725725 0.895340I
a = 0.230638 + 0.784197I
b = 0.606091 0.153613I
c = 1.00000
d = 0.955681 + 0.515344I
6.13361 3.53925I 3.48597 + 4.52491I
u = 0.725725 + 0.895340I
a = 0.230638 0.784197I
b = 0.606091 + 0.153613I
c = 1.00000
d = 0.955681 0.515344I
6.13361 + 3.53925I 3.48597 4.52491I
u = 0.386400 0.333144I
a = 0.940610 0.519525I
b = 0.287449 + 0.715270I
c = 1.00000
d = 0.097710 + 0.262072I
0.441338 + 1.103721I 5.44788 6.54224I
u = 0.386400 + 0.333144I
a = 0.940610 + 0.519525I
b = 0.287449 0.715270I
c = 1.00000
d = 0.097710 0.262072I
0.441338 1.103721I 5.44788 + 6.54224I
12
Solution to I
u
5
1(vol +
1CS) Cusp shape
u = 1.052766 0.635427I
a = 0.68524 1.42536I
b = 0.17231 2.04087I
c = 1.00000
d = 2.38979 + 0.08745I
1.61416 + 7.63502I 9.74769 6.83193I
u = 1.052766 + 0.635427I
a = 0.68524 + 1.42536I
b = 0.17231 + 2.04087I
c = 1.00000
d = 2.38979 0.08745I
1.61416 7.63502I 9.74769 + 6.83193I
13
VI. I
u
6
= hc 1, u
9
2u
7
+ · · · + b + 1, u
10
+ 2u
9
+ · · · + d u, u
11
+
2u
10
+ · · · + 3u + 1, u
10
+ 2u
9
+ · · · + a + 3i
(i) Arc colorings
a
5
=
0
u
a
11
=
1
u
10
2u
9
u
8
+ 2u
7
+ u
6
2u
5
4u
4
+ 2u
2
+ u
a
2
=
1
0
a
6
=
u
u
9
+ 2u
8
+ u
7
2u
6
u
5
+ 2u
4
+ 3u
3
2u 1
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
8
=
u
10
2u
9
+ u
8
+ 5u
7
+ u
6
6u
5
4u
4
+ 4u
3
+ 5u
2
u 3
u
9
+ 2u
7
+ 2u
6
2u
5
2u
4
+ 3u
2
1
a
3
=
u
4
u
2
+ 1
u
4
a
10
=
1
u
10
2u
9
u
8
+ 2u
7
+ u
6
2u
5
4u
4
+ u
2
+ u
a
9
=
2u
10
3u
9
+ 2u
8
+ 7u
7
8u
5
4u
4
+ 6u
3
+ 6u
2
2u 3
2u
10
4u
9
+ 6u
7
+ 2u
6
7u
5
6u
4
+ 3u
3
+ 6u
2
u 2
a
7
=
2u
10
+ 3u
9
2u
8
7u
7
+ 9u
5
+ 5u
4
7u
3
7u
2
+ 3u + 4
u
10
+ 2u
9
u
8
4u
7
u
6
+ 5u
5
+ 3u
4
3u
3
5u
2
+ 2u + 2
a
7
=
2u
10
+ 3u
9
2u
8
7u
7
+ 9u
5
+ 5u
4
7u
3
7u
2
+ 3u + 4
u
10
+ 2u
9
u
8
4u
7
u
6
+ 5u
5
+ 3u
4
3u
3
5u
2
+ 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
14
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 1.126055 0.711355I
a = 0.824956 0.783251I
b = 1.42691 1.70719I
c = 1.00000
d = 2.58050 + 0.38061I
3.47965 8.65115I 6.21430 + 5.57892I
u = 1.126055 + 0.711355I
a = 0.824956 + 0.783251I
b = 1.42691 + 1.70719I
c = 1.00000
d = 2.58050 0.38061I
3.47965 + 8.65115I 6.21430 5.57892I
u = 0.978643 0.595733I
a = 0.060657 + 0.770160I
b = 0.58821 + 1.57894I
c = 1.00000
d = 2.07935 0.37091I
2.61864 4.69742I 9.08124 + 5.88322I
u = 0.978643 + 0.595733I
a = 0.060657 0.770160I
b = 0.58821 1.57894I
c = 1.00000
d = 2.07935 + 0.37091I
2.61864 + 4.69742I 9.08124 5.88322I
u = 0.523691 0.948055I
a = 0.815992 1.141805I
b = 0.100710 0.183890I
c = 1.00000
d = 0.479183 + 0.445156I
5.32590 + 2.58451I 3.80806 1.01660I
u = 0.523691 + 0.948055I
a = 0.815992 + 1.141805I
b = 0.100710 + 0.183890I
c = 1.00000
d = 0.479183 0.445156I
5.32590 2.58451I 3.80806 + 1.01660I
15
Solution to I
u
6
1(vol +
1CS) Cusp shape
u = 0.347303
a = 2.24600
b = 0.654769
c = 1.00000
d = 0.153709
2.16369 2.57056
u = 0.850023 0.614930I
a = 1.007368 + 0.850380I
b = 0.21555 + 1.59147I
c = 1.00000
d = 1.48329 + 0.32770I
0.08426 + 2.41892I 7.07184 2.88947I
u = 0.850023 + 0.614930I
a = 1.007368 0.850380I
b = 0.21555 1.59147I
c = 1.00000
d = 1.48329 0.32770I
0.08426 2.41892I 7.07184 + 2.88947I
u = 0.952018 0.226513I
a = 0.085971 0.401284I
b = 0.373838 0.904801I
c = 1.00000
d = 1.45453 + 3.73523I
5.02081 + 0.74196I 15.5393 1.1191I
u = 0.952018 + 0.226513I
a = 0.085971 + 0.401284I
b = 0.373838 + 0.904801I
c = 1.00000
d = 1.45453 3.73523I
5.02081 0.74196I 15.5393 + 1.1191I
16
VII. I
u
7
= hu
9
2u
7
+ · · · + b + 1, u
11
+ 2u
10
+ · · · + 3u + 1, u
10
u
9
+
· · · + d + 1, u
10
+ 2u
9
+ · · · + a + 3, u
10
+ 2u
9
+ · · · + c + 4i
(i) Arc colorings
a
5
=
0
u
a
11
=
u
10
2u
9
+ u
8
+ 5u
7
+ u
6
6u
5
4u
4
+ 4u
3
+ 5u
2
u 4
u
10
+ u
9
u
8
2u
7
+ u
6
+ 2u
5
2u
3
u
2
+ u 1
a
2
=
1
0
a
6
=
u
10
+ 3u
9
+ u
8
5u
7
4u
6
+ 5u
5
+ 7u
4
2u
3
7u
2
u + 4
u
10
+ 3u
8
+ 2u
7
4u
6
4u
5
+ 2u
4
+ 5u
3
4u
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
8
=
u
10
2u
9
+ u
8
+ 5u
7
+ u
6
6u
5
4u
4
+ 4u
3
+ 5u
2
u 3
u
9
+ 2u
7
+ 2u
6
2u
5
2u
4
+ 3u
2
1
a
3
=
u
4
u
2
+ 1
u
4
a
10
=
u
10
2u
9
+ u
8
+ 5u
7
+ u
6
6u
5
4u
4
+ 4u
3
+ 5u
2
u 4
1
a
9
=
u
9
+ 3u
7
+ 2u
6
4u
5
4u
4
+ 2u
3
+ 5u
2
4
2u
10
+ 2u
9
2u
8
4u
7
+ 2u
6
+ 5u
5
+ u
4
5u
3
2u
2
+ 3u
a
7
=
2u
10
+ 3u
9
2u
8
7u
7
+ 9u
5
+ 5u
4
7u
3
7u
2
+ 3u + 4
u
10
+ 2u
9
u
8
4u
7
u
6
+ 5u
5
+ 3u
4
3u
3
5u
2
+ 2u + 2
a
7
=
2u
10
+ 3u
9
2u
8
7u
7
+ 9u
5
+ 5u
4
7u
3
7u
2
+ 3u + 4
u
10
+ 2u
9
u
8
4u
7
u
6
+ 5u
5
+ 3u
4
3u
3
5u
2
+ 2u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
17
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 1.126055 0.711355I
a = 0.824956 0.783251I
b = 1.42691 1.70719I
c = 0.175044 0.783251I
d = 0.121429 0.877245I
3.47965 8.65115I 6.21430 + 5.57892I
u = 1.126055 + 0.711355I
a = 0.824956 + 0.783251I
b = 1.42691 + 1.70719I
c = 0.175044 + 0.783251I
d = 0.121429 + 0.877245I
3.47965 + 8.65115I 6.21430 5.57892I
u = 0.978643 0.595733I
a = 0.060657 + 0.770160I
b = 0.58821 + 1.57894I
c = 0.939343 + 0.770160I
d = 2.46430 0.63101I
2.61864 4.69742I 9.08124 + 5.88322I
u = 0.978643 + 0.595733I
a = 0.060657 0.770160I
b = 0.58821 1.57894I
c = 0.939343 0.770160I
d = 2.46430 + 0.63101I
2.61864 + 4.69742I 9.08124 5.88322I
u = 0.523691 0.948055I
a = 0.815992 1.141805I
b = 0.100710 0.183890I
c = 0.184008 1.141805I
d = 0.248710 + 0.530406I
5.32590 + 2.58451I 3.80806 1.01660I
u = 0.523691 + 0.948055I
a = 0.815992 + 1.141805I
b = 0.100710 + 0.183890I
c = 0.184008 + 1.141805I
d = 0.248710 0.530406I
5.32590 2.58451I 3.80806 + 1.01660I
18
Solution to I
u
7
1(vol +
1CS) Cusp shape
u = 0.347303
a = 2.24600
b = 0.654769
c = 3.24600
d = 1.39153
2.16369 2.57056
u = 0.850023 0.614930I
a = 1.007368 + 0.850380I
b = 0.21555 + 1.59147I
c = 0.007368 + 0.850380I
d = 0.108468 + 0.285167I
0.08426 + 2.41892I 7.07184 2.88947I
u = 0.850023 + 0.614930I
a = 1.007368 0.850380I
b = 0.21555 1.59147I
c = 0.007368 0.850380I
d = 0.108468 0.285167I
0.08426 2.41892I 7.07184 + 2.88947I
u = 0.952018 0.226513I
a = 0.085971 0.401284I
b = 0.373838 0.904801I
c = 1.085971 0.401284I
d = 2.10161 + 0.12526I
5.02081 + 0.74196I 15.5393 1.1191I
u = 0.952018 + 0.226513I
a = 0.085971 + 0.401284I
b = 0.373838 + 0.904801I
c = 1.085971 + 0.401284I
d = 2.10161 0.12526I
5.02081 0.74196I 15.5393 + 1.1191I
19
VIII. I
u
8
=
hu
11
3u
9
+· · ·+3u
2
4, 109u
10
+198u
9
+· · ·+344a+862, 41u
10
+166u
9
+
· · ·+ 172b +542, 41u
10
6u
9
+· · · + 344c+26, 17u
10
+8u
9
+· · · + 86d+80i
(i) Arc colorings
a
5
=
0
u
a
11
=
0.119186u
10
+ 0.0174419u
9
+ ··· + 0.316860u 0.0755814
0.197674u
10
0.0930233u
9
+ ··· + 0.476744u 0.930233
a
2
=
1
0
a
6
=
0.232558u
10
+ 0.197674u
9
+ ··· + 0.174419u + 0.476744
0.0755814u
10
+ 0.476744u
9
+ ··· 0.00581395u + 1.26744
a
4
=
u
u
a
1
=
u
2
+ 1
u
2
a
8
=
0.316860u
10
0.575581u
9
+ ··· + 0.293605u 2.50581
0.238372u
10
0.965116u
9
+ ··· + 0.633721u 3.15116
a
3
=
u
4
u
2
+ 1
u
4
a
10
=
0.119186u
10
+ 0.0174419u
9
+ ··· + 0.316860u 0.0755814
1
a
9
=
0.197674u
10
0.593023u
9
+ ··· 0.0232558u 1.43023
0.0406977u
10
0.872093u
9
+ ··· + 0.156977u 2.22093
a
7
=
0.398256u
10
+ 0.319767u
9
+ ··· 0.607558u + 0.947674
0.319767u
10
+ 0.709302u
9
+ ··· 0.947674u + 1.59302
a
7
=
0.398256u
10
+ 0.319767u
9
+ ··· 0.607558u + 0.947674
0.319767u
10
+ 0.709302u
9
+ ··· 0.947674u + 1.59302
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
20
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 1.124760 0.136043I
a = 0.92290 + 3.49565I
b = 0.70111 + 4.04126I
c = 0.810207 + 0.299385I
d = 2.10161 + 0.12526I
5.02081 + 0.74196I 15.5393 1.1191I
u = 1.124760 + 0.136043I
a = 0.92290 3.49565I
b = 0.70111 4.04126I
c = 0.810207 0.299385I
d = 2.10161 0.12526I
5.02081 0.74196I 15.5393 + 1.1191I
u = 0.986131 0.772404I
a = 0.453369 + 0.163918I
b = 1.14497 + 1.07823I
c = 0.137568 0.853636I
d = 0.248710 0.530406I
5.32590 2.58451I 3.80806 + 1.01660I
u = 0.986131 + 0.772404I
a = 0.453369 0.163918I
b = 1.14497 1.07823I
c = 0.137568 + 0.853636I
d = 0.248710 + 0.530406I
5.32590 + 2.58451I 3.80806 1.01660I
u = 0.360061 1.006502I
a = 1.26283 + 1.32725I
b = 0.302906 + 0.344192I
c = 0.271755 1.215997I
d = 0.121429 + 0.877245I
3.47965 + 8.65115I 6.21430 5.57892I
u = 0.360061 + 1.006502I
a = 1.26283 1.32725I
b = 0.302906 0.344192I
c = 0.271755 + 1.215997I
d = 0.121429 0.877245I
3.47965 8.65115I 6.21430 + 5.57892I
21
Solution to I
u
8
1(vol +
1CS) Cusp shape
u = 0.529187 0.718311I
a = 1.61599 0.14933I
b = 0.752639 1.087938I
c = 0.010188 + 1.175857I
d = 0.108468 0.285167I
0.08426 2.41892I 7.07184 + 2.88947I
u = 0.529187 + 0.718311I
a = 1.61599 + 0.14933I
b = 0.752639 + 1.087938I
c = 0.010188 1.175857I
d = 0.108468 + 0.285167I
0.08426 + 2.41892I 7.07184 2.88947I
u = 1.12735
a = 0.392584
b = 0.882797
c = 0.308071
d = 1.39153
2.16369 2.57056
u = 1.378091 0.194114I
a = 1.105574 0.729726I
b = 1.94081 0.90593I
c = 0.636622 0.521961I
d = 2.46430 0.63101I
2.61864 4.69742I 9.08124 + 5.88322I
u = 1.378091 + 0.194114I
a = 1.105574 + 0.729726I
b = 1.94081 + 0.90593I
c = 0.636622 + 0.521961I
d = 2.46430 + 0.63101I
2.61864 + 4.69742I 9.08124 5.88322I
22
IX. I
v
1
= hb, c, v 1, a + 1, d + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
1
a
2
=
1
0
a
6
=
1
1
a
4
=
1
0
a
1
=
1
0
a
8
=
1
0
a
3
=
1
0
a
10
=
1
1
a
9
=
2
1
a
7
=
1
0
a
7
=
1
0
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
23
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 1.00000
a = 1.00000
b = 0
c = 0
d = 1.00000
3.28987 12.0000
24
X. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u)(u 1)
3
(u
3
u 1)
2
(u
8
+ u
7
+ ··· 2u + 1)
(u
11
3u
9
2u
8
+ 3u
7
+ 4u
6
2u
4
u
3
+ 3u
2
4)
(u
11
+ 2u
10
4u
8
2u
7
+ 4u
6
+ 5u
5
2u
4
5u
3
u
2
+ 3u + 1)
2
c
2
, c
9
, c
11
u(u + 1)
3
(u
3
+ 2u
2
+ u + 1)
2
(u
8
+ 3u
7
+ 9u
6
+ 12u
5
+ 20u
4
+ 15u
3
+ 17u
2
+ 2u + 1)
(1 + 11u + 27u
2
+ 43u
3
+ 50u
4
+ 49u
5
+ 42u
6
+ 34u
7
+ 22u
8
+ 12u
9
+ 4u
10
+ u
11
)
2
(u
11
+ 6u
10
+ ··· + 24u + 16)
c
3
, c
7
u
4
(u 1)
6
(u
8
+ u
7
u
6
5u
5
4u
4
+ 8u
2
+ 4u + 4)
(u
11
+ 2u
10
u
9
3u
8
+ u
7
+ 2u
6
+ 4u
5
+ 11u
4
+ 9u
3
+ u
2
2u 2)
3
c
4
, c
5
, c
8
c
10
u(u 1)(u + 1)
2
(u
3
u 1)
2
(u
8
+ u
7
u
6
2u
5
+ 2u
4
+ 3u
3
+ u
2
2u + 1)
(u
11
3u
9
2u
8
+ 3u
7
+ 4u
6
2u
4
u
3
+ 3u
2
4)
(u
11
+ 2u
10
4u
8
2u
7
+ 4u
6
+ 5u
5
2u
4
5u
3
u
2
+ 3u + 1)
2
25
XI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
, c
5
c
6
, c
8
, c
10
y(y 1)
3
(y
3
2y
2
+ y 1)
2
(y
8
3y
7
+ 9y
6
12y
5
+ 20y
4
15y
3
+ 17y
2
2y + 1)
(y
11
6y
10
+ ··· + 24y 16)
(1 + 11y 27y
2
+ 43y
3
50y
4
+ 49y
5
42y
6
+ 34y
7
22y
8
+ 12y
9
4y
10
+ y
11
)
2
c
2
, c
9
, c
11
y(y 1)
3
(y
3
2y
2
3y 1)
2
(y
8
+ 9y
7
+ 49y
6
+ 160y
5
+ 336y
4
+ 425y
3
+ 269y
2
+ 30y + 1)
(y
11
6y
10
+ ··· 224y 256)
(1 + 67y + 117y
2
+ 143y
3
+ 150y
4
+ 193y
5
+ 206y
6
+ 170y
7
+ 94y
8
+ 36y
9
+ 8y
10
+ y
11
)
2
c
3
, c
7
y
4
(y 1)
6
(y
8
3y
7
+ 3y
6
y
5
32y
3
+ 32y
2
+ 48y + 16)
(4 + 8y + 7y
2
+ 51y
3
69y
4
+ 8y
5
+ 44y
6
21y
7
11y
8
+ 15y
9
6y
10
+ y
11
)
3
26