11a
99
(K11a
99
)
1
Arc Sequences
6 1 10 8 2 3 11 5 7 4 9
Solving Sequence
2,6
1 3
7,9
10 5 8 4 11
c
1
c
2
c
6
c
9
c
5
c
8
c
4
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= ha
12
+ 3a
11
3a
10
17a
9
6a
8
+ 9a
7
+ 14a
6
+ 18a
5
+ 24a
4
+ 53a
3
+ 39a
2
+ 3a + 1,
137a
11
+ 603b + ··· 3513a 541, 142a
11
+ 1809u + ··· + 13388a 9i
I
u
2
= ha
40
+ 4a
39
+ ··· + 5065101a + 759841,
6.88116 × 10
179
u 9.38038 × 10
174
a
39
+ ··· 6.48720 × 10
181
a 1.27844 × 10
181
,
8.96260 × 10
187
b + 2.34863 × 10
183
a
39
+ ··· + 1.66943 × 10
190
a + 3.27943 × 10
189
i
I
u
3
= hu
13
u
12
+ 4u
11
3u
10
+ 7u
9
4u
8
+ 5u
7
u
6
+ 2u
4
2u
3
+ 3u
2
u + 1,
u
11
u
10
+ 4u
9
3u
8
+ 7u
7
4u
6
+ 4u
5
u
3
+ 3u
2
+ b 2u + 3,
2u
12
+ u
11
6u
10
+ u
9
8u
8
u
7
2u
6
4u
5
+ u
4
2u
3
+ a 2u 2i
I
u
4
= hu
28
+ 6u
27
+ ··· + 26u + 4, 3u
27
26u
26
+ ··· + 2b 6, 9u
27
+ 72u
26
+ ··· + 4a + 84i
There are 4 irreducible components with 93 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
= ha
12
+ 3a
11
+ · · · + 3a + 1, 137a
11
+ 603b + · · · 3513a
541, 142a
11
+ 1809u + · · · + 13388a 9i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
0.0784964a
11
0.358762a
10
+ ··· 7.40077a + 0.00497512
a
1
=
1
0.0547264a
11
0.249862a
10
+ ··· 5.04754a 1.46158
a
3
=
0.0547264a
11
0.249862a
10
+ ··· 5.04754a 0.461581
0.133223a
11
+ 0.608624a
10
+ ··· + 12.4483a + 1.45661
a
7
=
0.0547264a
11
0.249862a
10
+ ··· 5.04754a 0.461581
0.0547264a
11
+ 0.249862a
10
+ ··· + 5.04754a + 1.46158
a
9
=
a
0.227197a
11
+ 0.611940a
10
+ ··· + 5.82587a + 0.897181
a
10
=
0.0298507a
11
+ 0.00497512a
10
+ ··· 1.37811a 0.839138
0.0110558a
11
+ 0.0845771a
10
+ ··· + 2.94251a + 2.10503
a
5
=
0.0784964a
11
+ 0.358762a
10
+ ··· + 7.40077a 0.00497512
0.0784964a
11
0.358762a
10
+ ··· 7.40077a + 0.00497512
a
8
=
0.435600a
11
1.13433a
10
+ ··· 10.0873a 0.528469
0.662797a
11
+ 1.74627a
10
+ ··· + 16.9132a + 1.42565
a
4
=
0.0243228a
11
0.213930a
10
+ ··· 5.59315a 0.546711
0.138198a
11
+ 0.665008a
10
+ ··· + 13.9409a + 1.79823
a
11
=
0.158098a
11
0.297955a
10
+ ··· 0.0961857a + 0.687120
0.0884467a
11
+ 0.175235a
10
+ ··· + 0.311774a 1.91432
a
11
=
0.158098a
11
0.297955a
10
+ ··· 0.0961857a + 0.687120
0.0884467a
11
+ 0.175235a
10
+ ··· + 0.311774a 1.91432
(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 = 0.682328
a = 2.33446 0.93114I
b = 0.500000 + 0.866025I
6.57974 2.02988I 8.00000 + 3.46410I
u = 0.682328
a = 2.33446 + 0.93114I
b = 0.500000 0.866025I
6.57974 + 2.02988I 8.00000 3.46410I
u = 0.341164 1.161541I
a = 1.034830 0.098333I
b = 0.500000 0.866025I
6.57974 + 2.02988I 8.00000 3.46410I
u = 0.341164 + 1.161541I
a = 1.034830 + 0.098333I
b = 0.500000 + 0.866025I
6.57974 2.02988I 8.00000 + 3.46410I
u = 0.341164 1.161541I
a = 0.478220 1.030978I
b = 0.500000 + 0.866025I
6.57974 2.02988I 8.00000 + 3.46410I
u = 0.341164 + 1.161541I
a = 0.478220 + 1.030978I
b = 0.500000 0.866025I
6.57974 + 2.02988I 8.00000 3.46410I
u = 0.341164 + 1.161541I
a = 0.021780 0.164953I
b = 0.500000 0.866025I
6.57974 + 2.02988I 8.00000 3.46410I
u = 0.341164 1.161541I
a = 0.021780 + 0.164953I
b = 0.500000 + 0.866025I
6.57974 2.02988I 8.00000 + 3.46410I
u = 0.341164 + 1.161541I
a = 0.534830 0.964359I
b = 0.500000 + 0.866025I
6.57974 2.02988I 8.00000 + 3.46410I
u = 0.341164 1.161541I
a = 0.534830 + 0.964359I
b = 0.500000 0.866025I
6.57974 + 2.02988I 8.00000 3.46410I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.682328
a = 1.83446 0.06511I
b = 0.500000 0.866025I
6.57974 + 2.02988I 8.00000 3.46410I
u = 0.682328
a = 1.83446 + 0.06511I
b = 0.500000 + 0.866025I
6.57974 2.02988I 8.00000 + 3.46410I
4
II. I
u
2
= ha
40
+ 4a
39
+ · · · + 5065101a + 759841, 6.88 × 10
179
u 9.38 ×
10
174
a
39
+ · · · 6.49 × 10
181
a 1.28 × 10
181
, 8.96 × 10
187
b + 2.35 ×
10
183
a
39
+ · · · + 1.67 × 10
190
a + 3.28 × 10
189
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
0.0000136320a
39
+ 0.0000482406a
38
+ ··· + 94.2749a + 18.5789
a
1
=
1
0.0000143304a
39
+ 0.0000482792a
38
+ ··· + 82.6804a + 14.3165
a
3
=
0.0000143304a
39
+ 0.0000482792a
38
+ ··· + 82.6804a + 15.3165
4.19309 × 10
6
a
39
0.0000144340a
38
+ ··· 30.9910a 6.23645
a
7
=
0.0000189345a
39
0.0000644361a
38
+ ··· 107.893a 18.4001
0.0000120128a
39
+ 0.0000408703a
38
+ ··· + 74.7415a + 14.2643
a
9
=
a
0.0000262048a
39
0.0000932248a
38
+ ··· 186.266a 36.5902
a
10
=
0.0000128705a
39
+ 0.0000392978a
38
+ ··· + 62.5952a + 11.9291
0.0000293630a
39
0.000102767a
38
+ ··· 196.270a 38.0389
a
5
=
0.0000136320a
39
0.0000482406a
38
+ ··· 94.2749a 18.5789
0.0000136320a
39
+ 0.0000482406a
38
+ ··· + 94.2749a + 18.5789
a
8
=
7.88009 × 10
6
a
39
+ 0.0000294740a
38
+ ··· + 70.6898a + 15.5188
0.0000340849a
39
0.000122699a
38
+ ··· 255.956a 52.1090
a
4
=
1.42368 × 10
6
a
39
+ 1.42214 × 10
6
a
38
+ ··· + 28.8567a + 8.01645
0.0000330378a
39
0.000121020a
38
+ ··· 264.298a 55.1585
a
11
=
6.69353 × 10
6
a
39
+ 0.0000258980a
38
+ ··· + 61.2288a + 14.0408
2.72368 × 10
6
a
39
7.78605 × 10
7
a
38
+ ··· 66.7302a 22.0500
a
11
=
6.69353 × 10
6
a
39
+ 0.0000258980a
38
+ ··· + 61.2288a + 14.0408
2.72368 × 10
6
a
39
7.78605 × 10
7
a
38
+ ··· 66.7302a 22.0500
(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 = 0.248527 + 0.782547I
a = 2.16490 1.33388I
b = 2.78977 + 0.25266I
5.38286 0.79819I 6.90177 1.98497I
u = 0.248527 0.782547I
a = 2.16490 + 1.33388I
b = 2.78977 0.25266I
5.38286 + 0.79819I 6.90177 + 1.98497I
u = 0.449566 + 1.164785I
a = 1.75450 1.78926I
b = 2.08774 + 2.71705I
9.81146 2.11597I 10.98134 + 0.51190I
u = 0.449566 1.164785I
a = 1.75450 + 1.78926I
b = 2.08774 2.71705I
9.81146 + 2.11597I 10.98134 0.51190I
u = 0.584958 + 0.771492I
a = 1.63324 0.44978I
b = 0.783367 + 0.997354I
0.00239 4.33994I 1.13631 + 6.98543I
u = 0.584958 0.771492I
a = 1.63324 + 0.44978I
b = 0.783367 0.997354I
0.00239 + 4.33994I 1.13631 6.98543I
u = 0.524355 1.163405I
a = 1.43496 0.55642I
b = 1.51204 + 1.58158I
5.31595 6.25643I 6.17560 + 2.68471I
u = 0.524355 + 1.163405I
a = 1.43496 + 0.55642I
b = 1.51204 1.58158I
5.31595 + 6.25643I 6.17560 2.68471I
u = 0.524355 1.163405I
a = 1.20657 1.25082I
b = 0.33739 + 1.88156I
5.31595 10.31620I 6.17560 + 9.61291I
u = 0.524355 + 1.163405I
a = 1.20657 + 1.25082I
b = 0.33739 1.88156I
5.31595 + 10.31620I 6.17560 9.61291I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.761643 0.208049I
a = 1.109163 0.691872I
b = 0.405801 + 0.684900I
2.52120 + 1.44851I 2.80497 + 0.66896I
u = 0.761643 + 0.208049I
a = 1.109163 + 0.691872I
b = 0.405801 0.684900I
2.52120 1.44851I 2.80497 0.66896I
u = 0.761643 + 0.208049I
a = 0.888121 0.198095I
b = 0.169145 1.209713I
2.52120 5.50828I 2.80497 + 6.25925I
u = 0.761643 0.208049I
a = 0.888121 + 0.198095I
b = 0.169145 + 1.209713I
2.52120 + 5.50828I 2.80497 6.25925I
u = 0.584958 + 0.771492I
a = 0.811252 0.684607I
b = 0.326566 + 1.346246I
0.002387 0.280172I 1.136314 + 0.057227I
u = 0.584958 0.771492I
a = 0.811252 + 0.684607I
b = 0.326566 1.346246I
0.002387 + 0.280172I 1.136314 0.057227I
u = 0.248527 0.782547I
a = 0.77879 1.65055I
b = 0.1103874 + 0.0163537I
5.38286 + 0.79819I 6.90177 + 1.98497I
u = 0.248527 + 0.782547I
a = 0.77879 + 1.65055I
b = 0.1103874 0.0163537I
5.38286 0.79819I 6.90177 1.98497I
u = 0.248527 0.782547I
a = 0.528657 0.220233I
b = 0.80276 + 1.85708I
5.38286 3.26157I 6.90177 + 8.91318I
u = 0.248527 + 0.782547I
a = 0.528657 + 0.220233I
b = 0.80276 1.85708I
5.38286 + 3.26157I 6.90177 8.91318I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.761643 + 0.208049I
a = 0.465789 0.420142I
b = 0.307020 + 0.341147I
2.52120 1.44851I 2.80497 0.66896I
u = 0.761643 0.208049I
a = 0.465789 + 0.420142I
b = 0.307020 0.341147I
2.52120 + 1.44851I 2.80497 + 0.66896I
u = 0.584958 0.771492I
a = 0.13825 1.48131I
b = 0.856552 + 0.765235I
0.002387 + 0.280172I 1.136314 0.057227I
u = 0.584958 + 0.771492I
a = 0.13825 + 1.48131I
b = 0.856552 0.765235I
0.002387 0.280172I 1.136314 + 0.057227I
u = 0.449566 + 1.164785I
a = 0.152868 0.428323I
b = 1.107139 0.677603I
9.81146 2.11597I 10.98134 + 0.51190I
u = 0.449566 1.164785I
a = 0.152868 + 0.428323I
b = 1.107139 + 0.677603I
9.81146 + 2.11597I 10.98134 0.51190I
u = 0.524355 1.163405I
a = 0.740427 0.151085I
b = 0.650836 + 0.191721I
5.31595 6.25643I 6.17560 + 2.68471I
u = 0.524355 + 1.163405I
a = 0.740427 + 0.151085I
b = 0.650836 0.191721I
5.31595 + 6.25643I 6.17560 2.68471I
u = 0.449566 + 1.164785I
a = 0.79423 1.18245I
b = 0.42710 + 2.17011I
9.81146 6.17573I 10.98134 + 7.44010I
u = 0.449566 1.164785I
a = 0.79423 + 1.18245I
b = 0.42710 2.17011I
9.81146 + 6.17573I 10.98134 7.44010I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.584958 + 0.771492I
a = 1.41803 0.77086I
b = 1.87810 0.26325I
0.00239 4.33994I 1.13631 + 6.98543I
u = 0.584958 0.771492I
a = 1.41803 + 0.77086I
b = 1.87810 + 0.26325I
0.00239 + 4.33994I 1.13631 6.98543I
u = 0.761643 + 0.208049I
a = 1.44027 1.30172I
b = 0.177943 + 1.296043I
2.52120 5.50828I 2.80497 + 6.25925I
u = 0.761643 0.208049I
a = 1.44027 + 1.30172I
b = 0.177943 1.296043I
2.52120 + 5.50828I 2.80497 6.25925I
u = 0.449566 1.164785I
a = 1.92707 0.90418I
b = 1.82941 + 2.34062I
9.81146 + 6.17573I 10.98134 7.44010I
u = 0.449566 + 1.164785I
a = 1.92707 + 0.90418I
b = 1.82941 2.34062I
9.81146 6.17573I 10.98134 + 7.44010I
u = 0.524355 + 1.163405I
a = 2.16655 1.00309I
b = 2.30372 + 2.02238I
5.31595 + 10.31620I 6.17560 9.61291I
u = 0.524355 1.163405I
a = 2.16655 + 1.00309I
b = 2.30372 2.02238I
5.31595 10.31620I 6.17560 + 9.61291I
u = 0.248527 0.782547I
a = 2.27476 2.17074I
b = 1.93781 + 0.58149I
5.38286 3.26157I 6.90177 + 8.91318I
u = 0.248527 + 0.782547I
a = 2.27476 + 2.17074I
b = 1.93781 0.58149I
5.38286 + 3.26157I 6.90177 8.91318I
9
III.
I
u
3
= hu
13
u
12
+ · · · u + 1, u
11
u
10
+ · · · + b + 3, 2u
12
+ u
11
+ · · · + a 2i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
u
5
2u
3
u
u
7
u
5
+ u
a
9
=
2u
12
u
11
+ 6u
10
u
9
+ 8u
8
+ u
7
+ 2u
6
+ 4u
5
u
4
+ 2u
3
+ 2u + 2
u
11
+ u
10
4u
9
+ 3u
8
7u
7
+ 4u
6
4u
5
+ u
3
3u
2
+ 2u 3
a
10
=
2u
12
u
11
+ 6u
10
2u
9
+ 8u
8
u
7
+ 2u
6
+ 2u
5
u
4
+ 2u
3
+ 2u + 2
u
11
+ u
10
3u
9
+ 3u
8
5u
7
+ 4u
6
2u
5
+ u
3
2u
2
+ 2u 2
a
5
=
u
u
a
8
=
u
12
+ 3u
10
+ u
9
+ 4u
8
+ 3u
7
+ u
6
+ 3u
5
+ u
2
+ 2
u
12
2u
11
+ ··· + 4u 3
a
4
=
u
12
u
11
2u
10
4u
9
2u
8
6u
7
3u
5
u
4
+ u
3
2u
2
3
2u
12
+ 3u
11
+ ··· 5u + 3
a
11
=
u
12
2u
11
+ ··· + 3u 2
2u
12
+ 2u
11
+ ··· 4u + 1
a
11
=
u
12
2u
11
+ ··· + 3u 2
2u
12
+ 2u
11
+ ··· 4u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.851574
a = 1.29542
b = 0.236834
5.58548 6.40048
u = 0.432945 1.190574I
a = 0.574206 0.848947I
b = 0.88235 + 1.94320I
9.24726 + 4.36417I 9.35230 3.32302I
u = 0.432945 + 1.190574I
a = 0.574206 + 0.848947I
b = 0.88235 1.94320I
9.24726 4.36417I 9.35230 + 3.32302I
u = 0.429348 0.836369I
a = 1.06443 + 0.95489I
b = 0.90233 1.19418I
1.50284 + 1.80144I 0.975171 0.624326I
u = 0.429348 + 0.836369I
a = 1.06443 0.95489I
b = 0.90233 + 1.19418I
1.50284 1.80144I 0.975171 + 0.624326I
u = 0.100465 0.707437I
a = 2.08183 1.26835I
b = 1.83693 0.64675I
5.50214 2.30256I 8.51436 + 0.38924I
u = 0.100465 + 0.707437I
a = 2.08183 + 1.26835I
b = 1.83693 + 0.64675I
5.50214 + 2.30256I 8.51436 0.38924I
u = 0.354755 1.099913I
a = 0.261043 + 1.280069I
b = 0.463549 0.404379I
7.44002 + 0.06234I 10.48891 + 0.49082I
u = 0.354755 + 1.099913I
a = 0.261043 1.280069I
b = 0.463549 + 0.404379I
7.44002 0.06234I 10.48891 0.49082I
u = 0.555159 1.145126I
a = 1.45591 0.17932I
b = 1.45752 + 1.05620I
5.89830 7.73676I 8.25887 + 7.75024I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.555159 + 1.145126I
a = 1.45591 + 0.17932I
b = 1.45752 1.05620I
5.89830 + 7.73676I 8.25887 7.75024I
u = 0.777700 0.380482I
a = 0.544452 0.841459I
b = 0.722544 + 0.675961I
3.52105 + 2.68668I 6.71015 2.69355I
u = 0.777700 + 0.380482I
a = 0.544452 + 0.841459I
b = 0.722544 0.675961I
3.52105 2.68668I 6.71015 + 2.69355I
12
IV. I
u
4
= hu
28
+ 6u
27
+ · · · + 26u + 4, 3u
27
26u
26
+ · · · + 2b 6, 9u
27
+
72u
26
+ · · · + 4a + 84i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
7
=
u
5
2u
3
u
u
7
u
5
+ u
a
9
=
9
4
u
27
18u
26
+ ···
513
4
u 21
3
2
u
27
+ 13u
26
+ ··· +
77
2
u + 3
a
10
=
11
4
u
27
+ 14u
26
+ ··· +
143
4
u + 5
5
2
u
27
15u
26
+ ···
127
2
u 11
a
5
=
u
u
a
8
=
21
4
u
27
29u
26
+ ···
449
4
u 19
9
2
u
27
+ 24u
26
+ ··· +
45
2
u + 1
a
4
=
1
2
u
27
3
2
u
26
+ ···
41
2
u
7
2
5
2
u
27
14u
26
+ ···
55
2
u 4
a
11
=
1
2
u
27
+
9
2
u
26
+ ··· +
73
2
u +
13
2
1
2
u
27
3u
26
+ ··· +
7
2
u + 2
a
11
=
1
2
u
27
+
9
2
u
26
+ ··· +
73
2
u +
13
2
1
2
u
27
3u
26
+ ··· +
7
2
u + 2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
13
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 1.007890 0.244456I
a = 0.648218 0.649776I
b = 0.484897 + 0.362346I
5.75558 1.16478I 9.81484 + 5.25007I
u = 1.007890 + 0.244456I
a = 0.648218 + 0.649776I
b = 0.484897 0.362346I
5.75558 + 1.16478I 9.81484 5.25007I
u = 0.877743 0.205256I
a = 1.36751 + 0.95489I
b = 0.332382 1.109600I
7.91511 11.38135I 4.44423 + 5.90932I
u = 0.877743 + 0.205256I
a = 1.36751 0.95489I
b = 0.332382 + 1.109600I
7.91511 + 11.38135I 4.44423 5.90932I
u = 0.608424 0.177740I
a = 0.665110 + 0.192137I
b = 0.474963 + 0.907755I
1.04620 1.66789I 3.14449 + 2.66380I
u = 0.608424 + 0.177740I
a = 0.665110 0.192137I
b = 0.474963 0.907755I
1.04620 + 1.66789I 3.14449 2.66380I
u = 0.586363 1.242355I
a = 1.064323 0.381059I
b = 1.41368 + 1.21973I
8.88695 + 6.88314I 9.37455 6.80974I
u = 0.586363 + 1.242355I
a = 1.064323 + 0.381059I
b = 1.41368 1.21973I
8.88695 6.88314I 9.37455 + 6.80974I
u = 0.554721 1.203484I
a = 1.83799 + 0.92930I
b = 1.96223 2.11484I
10.9151 + 16.6086I 7.19926 9.00617I
u = 0.554721 + 1.203484I
a = 1.83799 0.92930I
b = 1.96223 + 2.11484I
10.9151 16.6086I 7.19926 + 9.00617I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.483475 1.130605I
a = 1.03565 1.24896I
b = 0.38060 + 1.45896I
1.61917 + 5.94948I 1.73292 6.08838I
u = 0.483475 + 1.130605I
a = 1.03565 + 1.24896I
b = 0.38060 1.45896I
1.61917 5.94948I 1.73292 + 6.08838I
u = 0.417630 1.105257I
a = 0.990060 + 0.503261I
b = 0.343945 0.624215I
2.12382 + 1.70105I 2.95787 0.05705I
u = 0.417630 + 1.105257I
a = 0.990060 0.503261I
b = 0.343945 + 0.624215I
2.12382 1.70105I 2.95787 + 0.05705I
u = 0.315106 1.262771I
a = 0.488001 0.002907I
b = 0.100408 1.021430I
12.6068 7.4137I 9.32623 + 3.45211I
u = 0.315106 + 1.262771I
a = 0.488001 + 0.002907I
b = 0.100408 + 1.021430I
12.6068 + 7.4137I 9.32623 3.45211I
u = 0.305330 0.675911I
a = 0.630555 0.172210I
b = 0.360299 0.412592I
0.257625 + 1.154957I 2.96071 5.77634I
u = 0.305330 + 0.675911I
a = 0.630555 + 0.172210I
b = 0.360299 + 0.412592I
0.257625 1.154957I 2.96071 + 5.77634I
u = 0.243939 1.326512I
a = 0.0674133 0.0418679I
b = 0.033141 + 1.007615I
11.26133 + 3.02152I 13.62827 2.14467I
u = 0.243939 + 1.326512I
a = 0.0674133 + 0.0418679I
b = 0.033141 1.007615I
11.26133 3.02152I 13.62827 + 2.14467I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.433444 0.634083I
a = 1.80511 + 0.76581I
b = 1.031196 0.788265I
2.24308 1.31021I 4.48172 2.40271I
u = 0.433444 + 0.634083I
a = 1.80511 0.76581I
b = 1.031196 + 0.788265I
2.24308 + 1.31021I 4.48172 + 2.40271I
u = 0.450069 0.945327I
a = 0.97063 + 1.16479I
b = 0.92359 1.77022I
1.30775 2.44749I 4.69640 + 9.53101I
u = 0.450069 + 0.945327I
a = 0.97063 1.16479I
b = 0.92359 + 1.77022I
1.30775 + 2.44749I 4.69640 9.53101I
u = 0.693563 0.915180I
a = 1.289003 + 0.358838I
b = 1.64479 + 0.73716I
3.67868 9.29135I 4.02619 + 9.42557I
u = 0.693563 + 0.915180I
a = 1.289003 0.358838I
b = 1.64479 0.73716I
3.67868 + 9.29135I 4.02619 9.42557I
u = 0.823545 0.669603I
a = 0.244511 1.089613I
b = 0.807023 + 0.636285I
2.90686 + 3.71581I 3.96472 7.21162I
u = 0.823545 + 0.669603I
a = 0.244511 + 1.089613I
b = 0.807023 0.636285I
2.90686 3.71581I 3.96472 + 7.21162I
16
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
3
+ u + 1)
4
(u
10
u
9
+ 3u
8
3u
7
+ 5u
6
5u
5
+ 4u
4
4u
3
+ 3u
2
2u + 1)
4
(u
13
u
12
+ ··· u + 1)(u
28
+ 6u
27
+ ··· + 26u + 4)
c
2
(u
3
+ 2u
2
+ u 1)
4
(u
10
+ 5u
9
+ 13u
8
+ 19u
7
+ 17u
6
+ 7u
5
2u
3
+ u
2
+ 2u + 1)
4
(u
13
+ 7u
12
+ ··· 5u 1)(u
28
+ 14u
27
+ ··· + 36u + 16)
c
3
, c
8
(u
12
6u
10
+ ··· + 8u + 1)(u
13
u
12
+ ··· + 3u + 1)
(u
28
+ u
27
+ ··· + 3u + 1)(u
40
u
39
+ ··· 18u
2
+ 1)
c
4
, c
10
(u
12
6u
10
+ ··· + 8u + 1)(u
13
+ u
12
+ ··· + 3u 1)
(u
28
+ u
27
+ ··· + 3u + 1)(u
40
u
39
+ ··· 18u
2
+ 1)
c
5
(u
3
+ u + 1)
4
(u
10
u
9
+ 3u
8
3u
7
+ 5u
6
5u
5
+ 4u
4
4u
3
+ 3u
2
2u + 1)
4
(u
13
+ u
12
+ ··· u 1)(u
28
+ 6u
27
+ ··· + 26u + 4)
c
6
(u 1)
12
(u
10
+ 2u
9
u
8
5u
7
3u
6
+ 4u
5
+ 12u
4
+ 13u
3
+ 5u
2
+ u + 2)
4
(u
13
u
12
+ ··· + u 1)(u
28
+ 6u
27
+ ··· + 1800u + 712)
c
7
(u
2
u + 1)
26
(u
13
2u
12
+ ··· + 2u 1)
(u
28
+ 29u
27
+ ··· + 118784u + 8192)
c
9
, c
11
(u
12
+ 4u
11
+ ··· + 32u + 13)(u
13
+ 2u
12
+ ··· + 2u + 1)
(u
28
2u
27
+ ··· 2u + 1)(u
40
+ 11u
39
+ ··· + 644u + 61)
17
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
3
+ 2y
2
+ y 1)
4
(y
10
+ 5y
9
+ 13y
8
+ 19y
7
+ 17y
6
+ 7y
5
2y
3
+ y
2
+ 2y + 1)
4
(y
13
+ 7y
12
+ ··· 5y 1)(y
28
+ 14y
27
+ ··· + 36y + 16)
c
2
(y
3
2y
2
+ 5y 1)
4
(y
10
+ y
9
+ 13y
8
+ 11y
7
+ 45y
6
+ 35y
5
+ 12y
4
+ 2y
3
+ 9y
2
2y + 1)
4
(y
13
y
12
+ ··· + 7y 1)(y
28
2y
27
+ ··· 240y + 256)
c
3
, c
10
(y
12
12y
11
+ ··· 36y + 1)(y
13
15y
12
+ ··· 9y 1)
(y
28
23y
27
+ ··· + 3y + 1)(y
40
33y
39
+ ··· 36y + 1)
c
4
, c
8
(y
12
12y
11
+ ··· 36y + 1)(y
13
15y
12
+ ··· 9y 1)
(y
28
23y
27
+ ··· + 3y + 1)(y
40
33y
39
+ ··· 36y + 1)
c
6
(y 1)
12
(4 + 19y + 47y
2
69y
3
+ 16y
4
+ 32y
5
17y
6
11y
7
+ 15y
8
6y
9
+ y
10
)
4
(y
13
9y
12
+ ··· 11y 1)(y
28
18y
27
+ ··· + 1943360y + 506944)
c
7
(y
2
+ y + 1)
26
(y
13
+ 2y
12
+ ··· 2y 1)
(y
28
+ 3y
27
+ ··· + 486539264y + 67108864)
c
9
, c
11
(y
12
+ 8y
11
+ ··· + 848y + 169)(y
13
+ 2y
12
+ ··· 2y 1)
(y
28
+ 6y
27
+ ··· + 40y + 1)(y
40
+ 11y
39
+ ··· + 62528y + 3721)
18