11a
277
(K11a
277
)
1
Arc Sequences
9 5 1 10 2 4 11 3 6 7 8
Solving Sequence
2,6
5
3,10
4 7 9 1 8 11
c
5
c
2
c
4
c
6
c
9
c
1
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
4
\
i=1
I
u
i
I
u
1
= ha
4
+ 3a
2
2a + 2, a
3
+ a
2
+ 2a + 2u, a
3
+ a
2
+ 2b 4a + 4i
I
u
2
= hu
12
6u
11
+ 20u
10
46u
9
+ 77u
8
98u
7
+ 95u
6
71u
5
+ 42u
4
21u
3
+ 10u
2
3u + 1,
u
11
+ 5u
10
14u
9
+ 26u
8
31u
7
+ 22u
6
u
5
15u
4
+ 15u
3
7u
2
+ a + u 2,
u
11
+ 6u
10
20u
9
+ 45u
8
72u
7
+ 85u
6
72u
5
+ 43u
4
18u
3
+ 6u
2
+ b 3ui
I
u
3
= h9a
48
9a
47
+ ··· 2a + 2, 1.21913 × 10
111
u 1.27326 × 10
112
a
47
+ ··· + 1.81903 × 10
112
a 2.03749 × 10
112
,
6.09567 × 10
110
b + 4.72246 × 10
112
a
47
+ ··· + 1.84803 × 10
112
a 6.43436 × 10
110
i
I
u
4
= hu
35
+ 9u
34
+ ··· + 129u + 8, 5.73272 × 10
21
u
34
+ 5.78933 × 10
22
u
33
+ ··· + 1.46127 × 10
23
b + 3.04671 × 10
23
,
1.58974 × 10
23
u
34
+ 1.57646 × 10
24
u
33
+ ··· + 1.16902 × 10
24
a + 1.93433 × 10
25
i
There are 4 irreducible components with 99 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
4
+ 3a
2
2a + 2, a
3
+ a
2
+ 2a + 2u, a
3
+ a
2
+ 2b 4a + 4i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
2
a
3
1
2
a
2
a
a
5
=
1
2
a
3
1
2
a
2
a
1
2
a
3
1
2
a
2
a
a
3
=
0
1
a
10
=
a
1
2
a
3
1
2
a
2
+ 2a 2
a
4
=
1
a
3
a
2
3a 2
a
7
=
1
2
a
3
+
1
2
a
2
+ a
a
3
+ 2a 3
a
9
=
a
1
2
a
3
1
2
a
2
+ a 2
a
1
=
1
2
a
3
1
2
a
2
a
a
3
2a + 3
a
8
=
a
1
2
a
3
1
2
a
2
+ 2a 2
a
11
=
1
2
a
3
1
2
a
2
1
2
a
3
1
2
a
2
+ 1
a
11
=
1
2
a
3
1
2
a
2
1
2
a
3
1
2
a
2
+ 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 = 1.00000I
a = 0.41880 1.69390I
b = 0.27510 2.11269I
1.64493 0
u = 1.00000I
a = 0.41880 + 1.69390I
b = 0.27510 + 2.11269I
1.64493 0
u = 1.00000I
a = 0.418797 0.693897I
b = 1.27510 1.11269I
1.64493 0
u = 1.00000I
a = 0.418797 + 0.693897I
b = 1.27510 + 1.11269I
1.64493 0
3
II.
I
u
2
= hu
12
6u
11
+· · ·−3u+1, u
11
+5u
10
+· · ·+a2, u
11
+6u
10
+· · ·+b3ui
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
5
=
u
u
a
3
=
u
2
+ 1
u
2
a
10
=
u
11
5u
10
+ ··· u + 2
u
11
6u
10
+ ··· 6u
2
+ 3u
a
4
=
u
11
+ 6u
10
+ ··· 9u + 2
u
2
u + 1
a
7
=
u
11
6u
10
+ ··· + 7u 1
u
4
+ 2u
3
3u
2
+ 3u 1
a
9
=
u
11
5u
10
+ ··· u + 2
u
11
6u
10
+ ··· + 5u 1
a
1
=
u
11
7u
10
+ ··· + 13u 3
u
11
+ 5u
10
+ ··· u 1
a
8
=
u
11
4u
10
+ ··· 2u + 2
2u
11
11u
10
+ ··· + 6u 1
a
11
=
u
11
6u
10
+ ··· 15u
2
+ 6u
u
7
+ 3u
6
5u
5
+ 5u
4
u
3
2u
2
+ 2u 1
a
11
=
u
11
6u
10
+ ··· 15u
2
+ 6u
u
7
+ 3u
6
5u
5
+ 5u
4
u
3
2u
2
+ 2u 1
(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 = 0.224527 0.491967I
a = 1.80164 0.59128I
b = 0.362227 + 1.303827I
7.67039 6.40068I 6.43797 + 4.87755I
u = 0.224527 + 0.491967I
a = 1.80164 + 0.59128I
b = 0.362227 1.303827I
7.67039 + 6.40068I 6.43797 4.87755I
u = 0.160845 0.502812I
a = 2.14213 0.64819I
b = 0.609630 0.981964I
0.92209 2.24636I 7.11132 + 8.83230I
u = 0.160845 + 0.502812I
a = 2.14213 + 0.64819I
b = 0.609630 + 0.981964I
0.92209 + 2.24636I 7.11132 8.83230I
u = 0.38777 1.48567I
a = 0.293742 0.611093I
b = 0.51430 1.59184I
2.15077 + 6.80393I 5.48461 6.50411I
u = 0.38777 + 1.48567I
a = 0.293742 + 0.611093I
b = 0.51430 + 1.59184I
2.15077 6.80393I 5.48461 + 6.50411I
u = 0.454285 1.279883I
a = 0.278924 + 0.875366I
b = 0.42362 + 1.68359I
2.68926 + 5.20905I 1.24389 5.17860I
u = 0.454285 + 1.279883I
a = 0.278924 0.875366I
b = 0.42362 1.68359I
2.68926 5.20905I 1.24389 + 5.17860I
u = 0.803624 0.881445I
a = 0.856239 0.666314I
b = 0.443728 1.081148I
4.98090 + 3.00358I 6.27510 + 2.27848I
u = 0.803624 + 0.881445I
a = 0.856239 + 0.666314I
b = 0.443728 + 1.081148I
4.98090 3.00358I 6.27510 2.27848I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.25207
a = 0.349598
b = 0.110338
1.97860 21.2943
u = 1.58393
a = 0.347728
b = 0.321617
8.14019 6.83591
6
III. I
u
3
=
h9a
48
9a
47
+· · ·2a+2, 1.22×10
111
u1.27×10
112
a
47
+· · ·+1.82×10
112
a
2.04×10
112
, 6.10× 10
110
b+4.72× 10
112
a
47
+· · ·+1.85× 10
112
a6.43× 10
110
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
10.4439a
47
+ 13.8459a
46
+ ··· 14.9207a + 16.7126
a
5
=
10.4439a
47
+ 13.8459a
46
+ ··· 14.9207a + 16.7126
10.4439a
47
+ 13.8459a
46
+ ··· 14.9207a + 16.7126
a
3
=
2.79181a
47
+ 66.4590a
46
+ ··· 48.9804a + 34.7184
2.79181a
47
+ 66.4590a
46
+ ··· 48.9804a + 33.7184
a
10
=
a
77.4723a
47
+ 105.008a
46
+ ··· 30.3171a + 1.05556
a
4
=
6.81210a
47
+ 31.2780a
46
+ ··· 27.0806a + 18.3678
19.7247a
47
11.4825a
46
+ ··· + 28.7076a 27.6460
a
7
=
115.871a
47
184.686a
46
+ ··· + 88.4241a 18.2027
75.7844a
47
53.6190a
46
+ ··· 0.583966a + 21.3311
a
9
=
a
8.22149a
47
+ 19.6573a
46
+ ··· + 4.02164a + 0.435161
a
1
=
11.4358a
47
6.54243a
46
+ ··· 1.39184a + 2.82700
45.4139a
47
+ 37.4469a
46
+ ··· 1.97136a 17.7667
a
8
=
146.406a
47
203.061a
46
+ ··· + 77.2759a 6.69116
137.238a
47
147.270a
46
+ ··· + 47.8737a + 11.8535
a
11
=
161.626a
47
+ 260.534a
46
+ ··· 130.560a + 28.4287
146.331a
47
+ 124.296a
46
+ ··· 21.9320a 36.1620
a
11
=
161.626a
47
+ 260.534a
46
+ ··· 130.560a + 28.4287
146.331a
47
+ 124.296a
46
+ ··· 21.9320a 36.1620
(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 = 0.263524 0.887339I
a = 1.86884 0.29175I
b = 0.879566 + 0.016951I
0.45153 3.90914I 4.05947 + 8.41437I
u = 0.263524 + 0.887339I
a = 1.86884 + 0.29175I
b = 0.879566 0.016951I
0.45153 + 3.90914I 4.05947 8.41437I
u = 0.387072 0.629729I
a = 1.76415 0.26748I
b = 0.284144 + 0.011865I
8.06651 + 4.88076I 7.61294 0.00229I
u = 0.387072 + 0.629729I
a = 1.76415 + 0.26748I
b = 0.284144 0.011865I
8.06651 4.88076I 7.61294 + 0.00229I
u = 0.887982 0.619939I
a = 0.546828 0.591593I
b = 0.595175 1.029694I
6.92221 + 3.07969I 9.61105 4.95105I
u = 0.887982 + 0.619939I
a = 0.546828 + 0.591593I
b = 0.595175 + 1.029694I
6.92221 3.07969I 9.61105 + 4.95105I
u = 0.34545 + 1.40335I
a = 0.519054 0.983590I
b = 1.02941 1.69817I
0.65429 7.12209I 0.24406 + 7.53717I
u = 0.34545 1.40335I
a = 0.519054 + 0.983590I
b = 1.02941 + 1.69817I
0.65429 + 7.12209I 0.24406 7.53717I
u = 0.263524 0.887339I
a = 0.486571 0.819066I
b = 0.96598 2.09565I
0.45153 3.90914I 4.05947 + 8.41437I
u = 0.263524 + 0.887339I
a = 0.486571 + 0.819066I
b = 0.96598 + 2.09565I
0.45153 + 3.90914I 4.05947 8.41437I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.66247 + 1.36339I
a = 0.345640 0.696381I
b = 0.658101 0.845108I
4.26677 6.65894I 7.66647 + 7.55605I
u = 0.66247 1.36339I
a = 0.345640 + 0.696381I
b = 0.658101 + 0.845108I
4.26677 + 6.65894I 7.66647 7.55605I
u = 0.387072 0.629729I
a = 0.29944 1.53355I
b = 1.33590 1.44688I
8.06651 + 4.88076I 7.61294 0.00229I
u = 0.387072 + 0.629729I
a = 0.29944 + 1.53355I
b = 1.33590 + 1.44688I
8.06651 4.88076I 7.61294 + 0.00229I
u = 1.24600
a = 0.189196 0.350223I
b = 0.529467 + 0.107348I
8.40649 13.8585
u = 1.24600
a = 0.189196 + 0.350223I
b = 0.529467 0.107348I
8.40649 13.8585
u = 0.334204 + 1.242177I
a = 0.181840 0.625293I
b = 0.66970 1.59883I
4.15748 4.71846I 5.79042 + 6.26335I
u = 0.334204 1.242177I
a = 0.181840 + 0.625293I
b = 0.66970 + 1.59883I
4.15748 + 4.71846I 5.79042 6.26335I
u = 0.510133 0.304616I
a = 0.159956 1.155296I
b = 0.399327 + 0.420233I
0.17657 + 1.63085I 4.99918 5.43978I
u = 0.510133 + 0.304616I
a = 0.159956 + 1.155296I
b = 0.399327 0.420233I
0.17657 1.63085I 4.99918 + 5.43978I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.887982 + 0.619939I
a = 0.142573 0.651331I
b = 0.192842 + 0.233907I
6.92221 3.07969I 9.61105 + 4.95105I
u = 0.887982 0.619939I
a = 0.142573 + 0.651331I
b = 0.192842 0.233907I
6.92221 + 3.07969I 9.61105 4.95105I
u = 0.54684 + 1.32589I
a = 0.073360 0.837723I
b = 0.48207 1.91865I
1.92307 5.70686I 7.16158 + 11.30466I
u = 0.54684 1.32589I
a = 0.073360 + 0.837723I
b = 0.48207 + 1.91865I
1.92307 + 5.70686I 7.16158 11.30466I
u = 0.66247 1.36339I
a = 0.029253 0.785736I
b = 0.65736 2.10113I
4.26677 + 6.65894I 7.66647 7.55605I
u = 0.66247 + 1.36339I
a = 0.029253 + 0.785736I
b = 0.65736 + 2.10113I
4.26677 6.65894I 7.66647 + 7.55605I
u = 0.277461 + 1.036230I
a = 0.07552 1.77654I
b = 0.45845 2.26217I
1.42987 1.40919I 2.00295 + 5.17297I
u = 0.277461 1.036230I
a = 0.07552 + 1.77654I
b = 0.45845 + 2.26217I
1.42987 + 1.40919I 2.00295 5.17297I
u = 0.34545 1.40335I
a = 0.110194 0.657429I
b = 0.35971 2.17763I
0.65429 + 7.12209I 0.24406 7.53717I
u = 0.34545 + 1.40335I
a = 0.110194 + 0.657429I
b = 0.35971 + 2.17763I
0.65429 7.12209I 0.24406 + 7.53717I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.06754
a = 0.119785 0.211933I
b = 0.264386 + 0.015281I
2.16765 17.3624
u = 1.06754
a = 0.119785 + 0.211933I
b = 0.264386 0.015281I
2.16765 17.3624
u = 0.333614 + 0.958581I
a = 0.281424 0.826584I
b = 1.27609 2.26621I
7.10793 + 8.02681I 5.10804 8.04729I
u = 0.333614 0.958581I
a = 0.281424 + 0.826584I
b = 1.27609 + 2.26621I
7.10793 8.02681I 5.10804 + 8.04729I
u = 0.277461 1.036230I
a = 0.285710 0.547276I
b = 1.26237 0.79589I
1.42987 + 1.40919I 2.00295 5.17297I
u = 0.277461 + 1.036230I
a = 0.285710 + 0.547276I
b = 1.26237 + 0.79589I
1.42987 1.40919I 2.00295 + 5.17297I
u = 0.54684 1.32589I
a = 0.294249 0.754696I
b = 0.453062 1.229740I
1.92307 + 5.70686I 7.16158 11.30466I
u = 0.54684 + 1.32589I
a = 0.294249 + 0.754696I
b = 0.453062 + 1.229740I
1.92307 5.70686I 7.16158 + 11.30466I
u = 0.334204 1.242177I
a = 0.349024 1.260520I
b = 0.83020 1.94926I
4.15748 + 4.71846I 5.79042 6.26335I
u = 0.334204 + 1.242177I
a = 0.349024 + 1.260520I
b = 0.83020 + 1.94926I
4.15748 4.71846I 5.79042 + 6.26335I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.237103 + 0.737994I
a = 0.78897 1.24768I
b = 1.02029 1.57644I
0.89648 1.35600I 6.20233 1.19503I
u = 0.237103 0.737994I
a = 0.78897 + 1.24768I
b = 1.02029 + 1.57644I
0.89648 + 1.35600I 6.20233 + 1.19503I
u = 0.510133 + 0.304616I
a = 1.373165 0.277947I
b = 0.117208 0.920853I
0.17657 1.63085I 4.99918 + 5.43978I
u = 0.510133 0.304616I
a = 1.373165 + 0.277947I
b = 0.117208 + 0.920853I
0.17657 + 1.63085I 4.99918 5.43978I
u = 0.237103 + 0.737994I
a = 1.60517 0.24700I
b = 0.136720 0.436976I
0.89648 1.35600I 6.20233 1.19503I
u = 0.237103 0.737994I
a = 1.60517 + 0.24700I
b = 0.136720 + 0.436976I
0.89648 + 1.35600I 6.20233 + 1.19503I
u = 0.333614 + 0.958581I
a = 1.82350 0.09201I
b = 0.833015 + 0.546460I
7.10793 + 8.02681I 5.10804 8.04729I
u = 0.333614 0.958581I
a = 1.82350 + 0.09201I
b = 0.833015 0.546460I
7.10793 8.02681I 5.10804 + 8.04729I
12
IV. I
u
4
=
hu
35
+9u
34
+· · ·+129u+8, 5.73×10
21
u
34
+5.79×10
22
u
33
+· · ·+1.46×10
23
b+
3.05 × 10
23
, 1.59 × 10
23
u
34
+ 1.58 × 10
24
u
33
+ · · · + 1.17 × 10
24
a + 1.93 × 10
25
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
5
=
u
u
a
3
=
u
2
+ 1
u
2
a
10
=
0.135989u
34
1.34853u
33
+ ··· 110.856u 16.5466
0.0392310u
34
0.396184u
33
+ ··· 18.1615u 2.08497
a
4
=
0.226399u
34
+ 1.78191u
33
+ ··· + 64.9143u + 11.3787
0.0718538u
34
+ 0.380306u
33
+ ··· 12.3443u 0.234219
a
7
=
0.0185758u
34
0.224592u
33
+ ··· + 37.7643u + 7.33120
0.107422u
34
0.980585u
33
+ ··· 13.6650u 0.522268
a
9
=
0.135989u
34
1.34853u
33
+ ··· 110.856u 16.5466
0.124632u
34
+ 0.957827u
33
+ ··· 0.995973u 1.08791
a
1
=
0.0878378u
34
0.551320u
33
+ ··· + 70.1500u + 13.5898
0.239219u
34
2.22799u
33
+ ··· 23.9209u 0.702702
a
8
=
0.0148592u
34
0.341708u
33
+ ··· 101.394u 15.1034
0.327289u
34
+ 2.78204u
33
+ ··· + 10.4461u 0.418777
a
11
=
0.0716655u
34
+ 0.719375u
33
+ ··· 13.6441u 3.60651
0.0372386u
34
0.0561449u
33
+ ··· + 21.9167u + 0.926166
a
11
=
0.0716655u
34
+ 0.719375u
33
+ ··· 13.6441u 3.60651
0.0372386u
34
0.0561449u
33
+ ··· + 21.9167u + 0.926166
(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 = 1.204478 0.248072I
a = 0.887964 + 0.392532I
b = 0.026853 0.382884I
7.58044 + 10.41688I 6.58450 6.84896I
u = 1.204478 + 0.248072I
a = 0.887964 0.392532I
b = 0.026853 + 0.382884I
7.58044 10.41688I 6.58450 + 6.84896I
u = 1.032064 0.216151I
a = 1.036124 0.458384I
b = 0.119556 + 0.232074I
0.31706 + 7.01027I 3.82014 7.79890I
u = 1.032064 + 0.216151I
a = 1.036124 + 0.458384I
b = 0.119556 0.232074I
0.31706 7.01027I 3.82014 + 7.79890I
u = 0.746671 0.829900I
a = 1.286683 + 0.556421I
b = 0.901751 + 1.015274I
5.09357 3.39425I 14.2242 + 15.5417I
u = 0.746671 + 0.829900I
a = 1.286683 0.556421I
b = 0.901751 1.015274I
5.09357 + 3.39425I 14.2242 15.5417I
u = 0.719504 0.276631I
a = 1.42702 + 0.47857I
b = 0.455319 0.040096I
0.64524 + 2.18197I 1.66363 5.31437I
u = 0.719504 + 0.276631I
a = 1.42702 0.47857I
b = 0.455319 + 0.040096I
0.64524 2.18197I 1.66363 + 5.31437I
u = 0.64890 1.31702I
a = 0.143192 1.130503I
b = 0.72438 2.16230I
4.1620 16.9207I 4.65236 + 8.62196I
u = 0.64890 + 1.31702I
a = 0.143192 + 1.130503I
b = 0.72438 + 2.16230I
4.1620 + 16.9207I 4.65236 8.62196I
14
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.648498 0.961930I
a = 0.31867 + 1.39500I
b = 0.03103 + 1.69984I
4.64663 2.02674I 10.39702 3.31188I
u = 0.648498 + 0.961930I
a = 0.31867 1.39500I
b = 0.03103 1.69984I
4.64663 + 2.02674I 10.39702 + 3.31188I
u = 0.595757 1.264358I
a = 0.174530 + 1.201298I
b = 0.61192 + 2.16745I
2.94252 12.83480I 1.59518 + 9.50250I
u = 0.595757 + 1.264358I
a = 0.174530 1.201298I
b = 0.61192 2.16745I
2.94252 + 12.83480I 1.59518 9.50250I
u = 0.548826 1.162058I
a = 0.195398 1.363500I
b = 0.46697 2.15669I
3.22979 7.07568I 1.38313 + 9.02703I
u = 0.548826 + 1.162058I
a = 0.195398 + 1.363500I
b = 0.46697 + 2.15669I
3.22979 + 7.07568I 1.38313 9.02703I
u = 0.405669 1.141420I
a = 0.196196 0.886051I
b = 0.49372 1.32576I
4.39987 1.11837I 2.66422 + 2.51524I
u = 0.405669 + 1.141420I
a = 0.196196 + 0.886051I
b = 0.49372 + 1.32576I
4.39987 + 1.11837I 2.66422 2.51524I
u = 0.271698 1.365605I
a = 0.044130 + 0.649233I
b = 0.495853 + 1.311691I
5.18517 + 2.44630I 3.60455 4.73123I
u = 0.271698 + 1.365605I
a = 0.044130 0.649233I
b = 0.495853 1.311691I
5.18517 2.44630I 3.60455 + 4.73123I
15
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.15479 1.53945I
a = 0.009969 0.509978I
b = 0.517106 1.285916I
0.87578 + 5.04274I 1.43283 3.64618I
u = 0.15479 + 1.53945I
a = 0.009969 + 0.509978I
b = 0.517106 + 1.285916I
0.87578 5.04274I 1.43283 + 3.64618I
u = 0.100849
a = 8.56933
b = 0.777057
3.33456 1.41011
u = 0.030627 1.114570I
a = 0.609593 + 0.947255I
b = 0.21574 + 1.84268I
0.301669 0.553139I 3.58187 + 1.60443I
u = 0.030627 + 1.114570I
a = 0.609593 0.947255I
b = 0.21574 1.84268I
0.301669 + 0.553139I 3.58187 1.60443I
u = 0.029467 1.005662I
a = 0.504374 1.097913I
b = 0.67440 1.61420I
3.33325 + 0.06783I 5.95235 + 0.12495I
u = 0.029467 + 1.005662I
a = 0.504374 + 1.097913I
b = 0.67440 + 1.61420I
3.33325 0.06783I 5.95235 0.12495I
u = 0.160155 0.940171I
a = 0.678022 + 1.180067I
b = 0.99150 + 1.66546I
1.89744 + 0.70933I 2.29610 + 0.18489I
u = 0.160155 + 0.940171I
a = 0.678022 1.180067I
b = 0.99150 1.66546I
1.89744 0.70933I 2.29610 0.18489I
u = 0.308052 0.545459I
a = 0.762564 0.126969I
b = 0.031534 + 0.685600I
0.241930 + 1.296498I 3.54219 4.67694I
16
Solution to I
u
4
1(vol +
1CS) Cusp shape
u = 0.308052 + 0.545459I
a = 0.762564 + 0.126969I
b = 0.031534 0.685600I
0.241930 1.296498I 3.54219 + 4.67694I
u = 0.795787 0.881934I
a = 0.329420 0.075312I
b = 0.386670 0.703873I
6.54898 + 2.97371I 10.02830 2.31900I
u = 0.795787 + 0.881934I
a = 0.329420 + 0.075312I
b = 0.386670 + 0.703873I
6.54898 2.97371I 10.02830 + 2.31900I
u = 1.11586
a = 0.111819
b = 0.264005
2.17258 20.5005
u = 1.41303
a = 0.153347
b = 0.522862
8.46698 18.1287
17
V. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
9
(u
4
+ 2u
3
u
2
2u + 2)(u
12
+ 2u
11
+ ··· u 1)
(u
35
+ 2u
34
+ ··· u 1)(u
48
+ u
47
+ ··· + 16u
2
+ 2)
c
2
(u
2
+ 1)
2
(u
12
6u
11
+ ··· 3u + 1)
(3 + 15u + 49u
2
+ 129u
3
+ 295u
4
+ 583u
5
+ 1044u
6
+ 1689u
7
+ 2504u
8
+ 3409u
9
+ 4273u
10
+ 4939u
11
+ 5260u
12
+ 5156u
13
+ 4636u
14
+ 3812u
15
+ 2847u
16
+ 1919u
17
+ 1153u
18
+ 609u
19
+ 277u
20
+ 105u
21
+ 32u
22
+ 7u
23
+ u
24
)
2
(u
35
9u
34
+ ··· + 129u 8)
c
3
(u
2
+ 1)
2
(u
12
+ 2u
11
+ ··· + 2u + 1)(u
35
+ 2u
34
+ ··· 7u + 2)
(u
48
+ 7u
47
+ ··· + 28u + 8)
c
4
(u
4
+ 3u
2
+ 2u + 2)
(u
12
u
10
+ u
9
+ 2u
8
4u
7
+ 2u
6
u
5
+ 3u
4
u
3
u
2
u 1)
(u
35
+ 5u
33
+ ··· 10u 4)(u
48
+ u
47
+ ··· 48u + 32)
c
5
(u
2
+ 1)
2
(u
12
+ 6u
11
+ ··· + 3u + 1)
(3 + 15u + 49u
2
+ 129u
3
+ 295u
4
+ 583u
5
+ 1044u
6
+ 1689u
7
+ 2504u
8
+ 3409u
9
+ 4273u
10
+ 4939u
11
+ 5260u
12
+ 5156u
13
+ 4636u
14
+ 3812u
15
+ 2847u
16
+ 1919u
17
+ 1153u
18
+ 609u
19
+ 277u
20
+ 105u
21
+ 32u
22
+ 7u
23
+ u
24
)
2
(u
35
9u
34
+ ··· + 129u 8)
c
6
(u
2
+ 1)
2
(u
12
+ 2u
11
+ ··· + 2u + 1)(u
35
+ 2u
34
+ ··· 7u + 2)
(u
48
+ 7u
47
+ ··· + 28u + 8)
c
7
(u 1)
4
(u
12
+ 3u
11
+ ··· + u 1)
(1 + 3u + 3u
2
5u
3
27u
4
7u
5
+ 72u
6
+ 159u
7
+ 4u
8
339u
9
305u
10
+ 259u
11
+ 556u
12
+ 28u
13
496u
14
216u
15
+ 263u
16
+ 203u
17
97u
18
101u
19
+ 31u
20
+ 27u
21
8u
22
3u
23
+ u
24
)
2
(u
35
+ 10u
34
+ ··· 7u 2)
c
8
(u
4
+ 3u
2
+ 2u + 2)
(u
12
u
10
+ u
9
+ 2u
8
4u
7
+ 2u
6
u
5
+ 3u
4
u
3
u
2
u 1)
(u
35
+ 5u
33
+ ··· 10u 4)(u
48
+ u
47
+ ··· 48u + 32)
c
10
, c
11
(u + 1)
4
(u
12
3u
11
+ ··· u 1)
(1 + 3u + 3u
2
5u
3
27u
4
7u
5
+ 72u
6
+ 159u
7
+ 4u
8
339u
9
305u
10
+ 259u
11
+ 556u
12
+ 28u
13
496u
14
216u
15
+ 263u
16
+ 203u
17
97u
18
101u
19
+ 31u
20
+ 27u
21
8u
22
3u
23
+ u
24
)
2
(u
35
+ 10u
34
+ ··· 7u 2)
18
VI. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
9
(y
4
6y
3
+ ··· 8y + 4)(y
12
2y
10
+ ··· 7y + 1)
(y
35
28y
34
+ ··· + 97y 1)(y
48
+ y
47
+ ··· + 64y + 4)
c
2
, c
5
(y + 1)
4
(y
12
+ 4y
11
+ ··· + 11y + 1)
(9 + 69y + 301y
2
+ 1043y
3
+ 3277y
4
+ 9069y
5
+ 2.05 × 10
4
y
6
+ 3.62 × 10
4
y
7
+ 4.78 × 10
4
y
8
+ 4.50 × 10
4
y
9
+ 2.57 × 10
4
y
10
899y
11
2.23 × 10
4
y
12
3.17 × 10
4
y
13
2.91 × 10
4
y
14
1.88 × 10
4
y
15
6835y
16
+ 1229y
17
+ 3825y
18
+ 3003y
19
+ 1459y
20
+ 483y
21
+ 108y
22
+ 15y
23
+ y
24
)
2
(y
35
+ 17y
34
+ ··· + 5825y 64)
c
3
(y + 1)
4
(y
12
12y
11
+ ··· 10y
2
+ 1)(y
35
+ 4y
34
+ ··· 35y 4)
(y
48
21y
47
+ ··· + 176y + 64)
c
4
(y
4
+ 6y
3
+ ··· + 8y + 4)(y
12
2y
11
+ ··· + y + 1)
(y
35
+ 10y
34
+ ··· 68y 16)(y
48
+ 9y
47
+ ··· + 20736y + 1024)
c
6
(y + 1)
4
(y
12
12y
11
+ ··· 10y
2
+ 1)(y
35
+ 4y
34
+ ··· 35y 4)
(y
48
21y
47
+ ··· + 176y + 64)
c
7
, c
11
(y 1)
4
(y
12
15y
11
+ ··· + y + 1)(y
35
38y
34
+ ··· 63y 4)
(y
48
50y
47
+ ··· 30y + 1)
c
8
(y
4
+ 6y
3
+ ··· + 8y + 4)(y
12
2y
11
+ ··· + y + 1)
(y
35
+ 10y
34
+ ··· 68y 16)(y
48
+ 9y
47
+ ··· + 20736y + 1024)
c
10
(y 1)
4
(y
12
15y
11
+ ··· + y + 1)(y
35
38y
34
+ ··· 63y 4)
(y
48
50y
47
+ ··· 30y + 1)
19