12n
0058
(K12n
0058
)
A knot diagram
1
Linearized knot diagam
3 5 6 8 2 12 10 5 11 8 1 7
Solving Sequence
5,8 3,9
2 6 1
4,11
10 7 12
c
8
c
2
c
5
c
1
c
4
c
10
c
7
c
12
c
3
, c
6
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h6.96435 × 10
33
u
30
− 1.25405 × 10
34
u
29
+ ··· + 1.08242 × 10
37
d + 4.63583 × 10
36
,
9.28423 × 10
34
u
30
+ 2.43126 × 10
35
u
29
+ ··· + 2.16483 × 10
37
c − 1.72516 × 10
37
,
5.70526 × 10
35
u
30
+ 1.13115 × 10
36
u
29
+ ··· + 1.08242 × 10
37
b + 2.53478 × 10
37
,
− 4.91990 × 10
35
u
30
− 1.12026 × 10
36
u
29
+ ··· + 2.16483 × 10
37
a − 3.93806 × 10
37
,
u
31
+ 3u
30
+ ··· + 64u + 32i
I
u
2
= h38636161249u
22
c − 6684998365u
22
+ ··· − 212657671098c + 31359529106,
709294494705u
22
c − 467986206381u
22
+ ··· + 1120177291630c + 112735730394,
− 215916739835u
22
+ 130467973157u
21
+ ··· + 574976483848b − 314250588698,
− 153137520489u
22
+ 68036492975u
21
+ ··· + 1149952967696a − 806106649958,
u
23
− u
22
+ ··· + 8u + 4i
I
v
1
= ha, d, c − 1, b + v, v
2
− v + 1i
I
v
2
= ha, d + 1, av + c − a + 1, b + v, v
2
− v + 1i
I
v
3
= hc, d + 1, b, a + 1, v + 1i
I
v
4
= hc, d + 1, −v
2
ba + v
3
b − v
2
b + av − v
2
+ c, b
2
v
2
− bv + 1i
* 5 irreducible components of dim
C
= 0, with total 82 representations.
* 1 irreducible components of dim
C
= 1
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
1
I. I
u
1
= h6.96 × 10
33
u
30
− 1.25 × 10
34
u
29
+ · · · + 1.08 × 10
37
d + 4.64 ×
10
36
, 9.28 × 10
34
u
30
+ 2.43 × 10
35
u
29
+ · · · + 2.16 × 10
37
c − 1.73 × 10
37
, 5.71 ×
10
35
u
30
+ 1.13 × 10
36
u
29
+ · · · + 1.08 × 10
37
b + 2.53 × 10
37
, −4.92 × 10
35
u
30
−
1.12 × 10
36
u
29
+ · · · + 2.16 × 10
37
a − 3.94 × 10
37
, u
31
+ 3u
30
+ · · · + 64u + 32i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
3
=
0.0227265u
30
+ 0.0517482u
29
+ ··· + 2.69661u + 1.81911
−0.0527085u
30
− 0.104502u
29
+ ··· − 2.42240u − 2.34178
a
9
=
1
−u
2
a
2
=
0.0227265u
30
+ 0.0517482u
29
+ ··· + 2.69661u + 1.81911
−0.0423983u
30
− 0.0818074u
29
+ ··· − 2.09805u − 1.81598
a
6
=
0.0368633u
30
+ 0.0974729u
29
+ ··· + 0.270429u + 0.869375
−0.0613442u
30
− 0.159676u
29
+ ··· + 0.274410u − 2.98789
a
1
=
0.0244809u
30
+ 0.0622027u
29
+ ··· − 0.544839u + 2.11852
−0.0715195u
30
− 0.187609u
29
+ ··· + 0.338443u − 3.34757
a
4
=
−u
u
a
11
=
−0.00428866u
30
− 0.0112307u
29
+ ··· − 0.0728208u + 0.796905
−0.000643408u
30
+ 0.00115856u
29
+ ··· + 0.160798u − 0.428286
a
10
=
−0.00364526u
30
− 0. 0123893u
29
+ ··· − 0.233619u + 1.22519
−0.000643408u
30
+ 0.00115856u
29
+ ··· + 0.160798u − 0.428286
a
7
=
−0.00116998u
30
+ 0.000296647u
29
+ ··· + 0.120558u + 0.316290
−0.00311868u
30
− 0.0115274u
29
+ ··· − 0.193379u + 0.480614
a
12
=
0.0281261u
30
+ 0.0745920u
29
+ ··· − 0.311221u + 1.89333
−0.0708761u
30
− 0.188768u
29
+ ··· + 0.177645u − 2.91928
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0330834u
30
+ 0.0743041u
29
+ ··· + 9.35750u + 13.8824
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
31
+ 15u
30
+ ··· + 120u − 16
c
2
, c
5
u
31
+ u
30
+ ··· + 8u − 4
c
3
u
31
− u
30
+ ··· + 128u − 548
c
4
, c
8
u
31
− 3u
30
+ ··· + 64u − 32
c
6
, c
7
, c
10
c
12
u
31
+ 5u
30
+ ··· − 3u − 1
c
9
, c
11
u
31
− 11u
30
+ ··· + 21u − 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
31
+ 3y
30
+ ··· + 25888y − 256
c
2
, c
5
y
31
+ 15y
30
+ ··· + 120y − 16
c
3
y
31
− 9y
30
+ ··· + 4451896y − 300304
c
4
, c
8
y
31
+ 15y
30
+ ··· + 1024y − 1024
c
6
, c
7
, c
10
c
12
y
31
− 11y
30
+ ··· + 21y − 1
c
9
, c
11
y
31
+ 29y
30
+ ··· + 61y − 1
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.753219 + 0.379837I
a = −0.743282 − 0.874244I
b = 0.716703 + 0.640811I
c = 0.685053 − 0.287784I
d = −0.240774 − 0.521238I
−1.42006 + 1.96537I 1.93692 − 5.44006I
u = 0.753219 − 0.379837I
a = −0.743282 + 0.874244I
b = 0.716703 − 0.640811I
c = 0.685053 + 0.287784I
d = −0.240774 + 0.521238I
−1.42006 − 1.96537I 1.93692 + 5.44006I
u = −0.337564 + 1.132290I
a = −0.588580 + 0.817543I
b = −1.10048 + 1.34389I
c = 0.17117 − 1.61585I
d = 0.935169 − 0.612003I
0.45247 − 2.02679I 7.73031 + 3.42583I
u = −0.337564 − 1.132290I
a = −0.588580 − 0.817543I
b = −1.10048 − 1.34389I
c = 0.17117 + 1.61585I
d = 0.935169 + 0.612003I
0.45247 + 2.02679I 7.73031 − 3.42583I
u = 1.121020 + 0.424146I
a = −0.661458 + 0.037458I
b = 1.62605 + 0.80238I
c = 0.460731 + 0.138106I
d = −0.991521 + 0.596969I
1.55877 − 4.66712I 11.51750 + 4.56967I
u = 1.121020 − 0.424146I
a = −0.661458 − 0.037458I
b = 1.62605 − 0.80238I
c = 0.460731 − 0.138106I
d = −0.991521 − 0.596969I
1.55877 + 4.66712I 11.51750 − 4.56967I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.698083 + 0.364692I
a = 0.272982 − 1.147330I
b = −1.63704 + 2.06806I
c = 0.498679 + 0.078631I
d = −0.956651 + 0.308522I
3.68376 − 3.19069I 14.6846 + 5.1485I
u = 0.698083 − 0.364692I
a = 0.272982 + 1.147330I
b = −1.63704 − 2.06806I
c = 0.498679 − 0.078631I
d = −0.956651 − 0.308522I
3.68376 + 3.19069I 14.6846 − 5.1485I
u = −1.235540 + 0.189024I
a = 0.397076 − 0.873318I
b = −1.100320 + 0.790305I
c = 0.472913 − 0.179552I
d = −0.848142 − 0.701686I
−2.56816 + 1.34649I 5.38369 − 2.07194I
u = −1.235540 − 0.189024I
a = 0.397076 + 0.873318I
b = −1.100320 − 0.790305I
c = 0.472913 + 0.179552I
d = −0.848142 + 0.701686I
−2.56816 − 1.34649I 5.38369 + 2.07194I
u = 0.464557 + 1.163760I
a = −0.762353 + 0.385358I
b = 0.17520 + 1.91640I
c = −0.05406 + 1.60814I
d = 1.020880 + 0.621136I
1.15318 + 7.72517I 9.61403 − 8.29170I
u = 0.464557 − 1.163760I
a = −0.762353 − 0.385358I
b = 0.17520 − 1.91640I
c = −0.05406 − 1.60814I
d = 1.020880 − 0.621136I
1.15318 − 7.72517I 9.61403 + 8.29170I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.253240 + 0.506936I
a = 0.045977 + 0.940408I
b = −1.72925 − 0.22350I
c = 0.439439 − 0.143874I
d = −1.055310 − 0.672917I
−1.12377 + 9.51847I 8.01541 − 7.69926I
u = −1.253240 − 0.506936I
a = 0.045977 − 0.940408I
b = −1.72925 + 0.22350I
c = 0.439439 + 0.143874I
d = −1.055310 + 0.672917I
−1.12377 − 9.51847I 8.01541 + 7.69926I
u = 0.223678 + 1.371700I
a = 0.023144 − 0.618799I
b = −0.490393 − 0.901482I
c = 0.413752 − 0.939419I
d = 0.607334 − 0.891545I
−4.93468 − 0.57606I 5.79676 + 1.97891I
u = 0.223678 − 1.371700I
a = 0.023144 + 0.618799I
b = −0.490393 + 0.901482I
c = 0.413752 + 0.939419I
d = 0.607334 + 0.891545I
−4.93468 + 0.57606I 5.79676 − 1.97891I
u = −0.591801
a = 0.533366
b = −0.736939
c = 0.699591
d = −0.429406
0.834149 11.9720
u = −0.540907 + 0.236782I
a = −1.50466 + 1.00061I
b = 3.58655 − 2.56486I
c = 0.518602 − 0.047373I
d = −0.912302 − 0.174686I
3.12062 − 1.49349I 14.4230 + 1.8126I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.540907 − 0.236782I
a = −1.50466 − 1.00061I
b = 3.58655 + 2.56486I
c = 0.518602 + 0.047373I
d = −0.912302 + 0.174686I
3.12062 + 1.49349I 14.4230 − 1.8126I
u = 0.067118 + 0.557682I
a = 1.39023 + 1.20733I
b = 0.343697 + 0.692018I
c = 1.45537 − 0.23813I
d = 0.330807 − 0.109496I
0.46111 − 2.29513I 1.47827 + 3.85950I
u = 0.067118 − 0.557682I
a = 1.39023 − 1.20733I
b = 0.343697 − 0.692018I
c = 1.45537 + 0.23813I
d = 0.330807 + 0.109496I
0.46111 + 2.29513I 1.47827 − 3.85950I
u = 0.71578 + 1.28059I
a = 0.097632 − 0.639247I
b = −1.59966 − 0.59378I
c = −0.37486 + 1.39000I
d = 1.180860 + 0.670647I
−1.16605 + 11.32090I 10.43454 − 6.71502I
u = 0.71578 − 1.28059I
a = 0.097632 + 0.639247I
b = −1.59966 + 0.59378I
c = −0.37486 − 1.39000I
d = 1.180860 − 0.670647I
−1.16605 − 11.32090I 10.43454 + 6.71502I
u = −0.39077 + 1.46203I
a = −0.858408 − 0.114457I
b = 1.17073 − 1.58917I
c = 0.382686 + 0.821951I
d = 0.534475 + 0.999877I
−8.24554 − 4.31764I 2.71892 + 1.88458I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.39077 − 1.46203I
a = −0.858408 + 0.114457I
b = 1.17073 + 1.58917I
c = 0.382686 − 0.821951I
d = 0.534475 − 0.999877I
−8.24554 + 4.31764I 2.71892 − 1.88458I
u = −0.79393 + 1.30401I
a = −0.862730 + 0.059745I
b = 1.76369 − 2.19058I
c = −0.444220 − 1.327190I
d = 1.226790 − 0.677567I
−3.7041 − 16.8176I 8.02968 + 10.05725I
u = −0.79393 − 1.30401I
a = −0.862730 − 0.059745I
b = 1.76369 + 2.19058I
c = −0.444220 + 1.327190I
d = 1.226790 + 0.677567I
−3.7041 + 16.8176I 8.02968 − 10.05725I
u = −0.62073 + 1.40356I
a = 0.693155 − 0.448111I
b = −0.266136 + 0.105825I
c = −0.237422 − 1.289560I
d = 1.138090 − 0.750034I
−6.51517 − 8.00123I 4.81025 + 4.92455I
u = −0.62073 − 1.40356I
a = 0.693155 + 0.448111I
b = −0.266136 − 0.105825I
c = −0.237422 + 1.289560I
d = 1.138090 + 0.750034I
−6.51517 + 8.00123I 4.81025 − 4.92455I
u = −0.07489 + 1.53753I
a = 0.794591 − 0.282968I
b = −0.590866 − 0.831603I
c = 0.262372 + 0.979829I
d = 0.744999 + 0.952303I
−9.13328 + 4.81435I 2.44035 − 4.85668I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.07489 − 1.53753I
a = 0.794591 + 0.282968I
b = −0.590866 + 0.831603I
c = 0.262372 − 0.979829I
d = 0.744999 − 0.952303I
−9.13328 − 4.81435I 2.44035 + 4.85668I
10
II.
I
u
2
= h3.86 × 10
10
cu
22
− 6.68 × 10
9
u
22
+ · · · − 2.13 × 10
11
c + 3.14 × 10
10
, 7.09 ×
10
11
cu
22
− 4.68 × 10
11
u
22
+ · · · + 1.12 × 10
12
c + 1.13 × 10
11
, −2.16 ×
10
11
u
22
+ 1.30 × 10
11
u
21
+ · · · + 5.75 × 10
11
b − 3.14 × 10
11
, −1.53 × 10
11
u
22
+
6.80 × 10
10
u
21
+ · · · + 1.15 × 10
12
a − 8.06 × 10
11
, u
23
− u
22
+ · · · + 8u + 4i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
3
=
0.133169u
22
− 0.0591646u
21
+ ··· + 1.14807u + 0.700991
0.375523u
22
− 0.226910u
21
+ ··· + 3.58831u + 0.546545
a
9
=
1
−u
2
a
2
=
0.133169u
22
− 0.0591646u
21
+ ··· + 1.14807u + 0.700991
0.293213u
22
− 0. 236878u
21
+ ··· + 2.46360u + 0.250529
a
6
=
0.0322985u
22
− 0.252479u
21
+ ··· − 0.902295u + 0.301575
0.188074u
22
− 0.335831u
21
+ ··· + 0.0919786u − 0.580833
a
1
=
−0.220372u
22
+ 0. 588310u
21
+ ··· + 0.810316u + 0.279258
0.0232531u
22
+ 0.239196u
21
+ ··· + 2.15399u + 0.890919
a
4
=
−u
u
a
11
=
c
−0.134392cu
22
+ 0.0232531u
22
+ ··· + 0.739709c − 0.109081
a
10
=
0.134392cu
22
− 0.0232531u
22
+ ··· + 0.260291c + 0.109081
−0.134392cu
22
+ 0.0232531u
22
+ ··· + 0.739709c − 0.109081
a
7
=
−0.134392cu
22
+ 0.0232531u
22
+ ··· + 1.73971c − 0.109081
0.134392cu
22
− 0.0232531u
22
+ ··· − 0.739709c + 0.109081
a
12
=
0.0536818cu
22
− 0.109233u
22
+ ··· + 1.15888c − 1.35137
−0.0769349cu
22
− 0.0878859u
22
+ ··· − 1.04979c + 1.52155
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
173371509589
143744120962
u
22
−
241902270957
143744120962
u
21
+ ··· −
379864412243
143744120962
u +
545150434432
71872060481
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
23
+ 12u
22
+ ··· − 2u − 1)
2
c
2
, c
5
(u
23
+ 2u
22
+ ··· − 2u − 1)
2
c
3
(u
23
− 2u
22
+ ··· + 18u − 9)
2
c
4
, c
8
(u
23
+ u
22
+ ··· + 8u − 4)
2
c
6
, c
7
, c
10
c
12
u
46
+ 3u
45
+ ··· + 56u + 16
c
9
, c
11
u
46
− 23u
45
+ ··· − 288u + 256
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
23
+ 24y
21
+ ··· + 10y − 1)
2
c
2
, c
5
(y
23
+ 12y
22
+ ··· − 2y − 1)
2
c
3
(y
23
− 12y
22
+ ··· − 450y − 81)
2
c
4
, c
8
(y
23
+ 15y
22
+ ··· − 40y − 16)
2
c
6
, c
7
, c
10
c
12
y
46
− 23y
45
+ ··· − 288y + 256
c
9
, c
11
y
46
− 3y
45
+ ··· − 2449920y + 65536
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.969482
a = 0.635915
b = −1.38262
c = 0.546696 + 0.177229I
d = −0.655217 + 0.536590I
0.502753 9.67610
u = −0.969482
a = 0.635915
b = −1.38262
c = 0.546696 − 0.177229I
d = −0.655217 − 0.536590I
0.502753 9.67610
u = 0.308169 + 0.985429I
a = 0.004284 − 0.666189I
b = −0.572740 − 0.057611I
c = 0.430219 + 0.027076I
d = −1.315230 + 0.145711I
2.62555 + 2.00215I 10.76412 − 3.62705I
u = 0.308169 + 0.985429I
a = 0.004284 − 0.666189I
b = −0.572740 − 0.057611I
c = 0.35592 + 1.88659I
d = 0.903437 + 0.511840I
2.62555 + 2.00215I 10.76412 − 3.62705I
u = 0.308169 − 0.985429I
a = 0.004284 + 0.666189I
b = −0.572740 + 0.057611I
c = 0.430219 − 0.027076I
d = −1.315230 − 0.145711I
2.62555 − 2.00215I 10.76412 + 3.62705I
u = 0.308169 − 0.985429I
a = 0.004284 + 0.666189I
b = −0.572740 + 0.057611I
c = 0.35592 − 1.88659I
d = 0.903437 − 0.511840I
2.62555 − 2.00215I 10.76412 + 3.62705I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.107498 + 1.054050I
a = 0.832680 + 0.608094I
b = 0.35976 + 1.52792I
c = 0.716893 + 1.112390I
d = 0.590662 + 0.635162I
−0.12065 − 2.74438I 5.99863 + 3.42075I
u = −0.107498 + 1.054050I
a = 0.832680 + 0.608094I
b = 0.35976 + 1.52792I
c = 0.60269 − 1.46286I
d = 0.759232 − 0.584397I
−0.12065 − 2.74438I 5.99863 + 3.42075I
u = −0.107498 − 1.054050I
a = 0.832680 − 0.608094I
b = 0.35976 − 1.52792I
c = 0.716893 − 1.112390I
d = 0.590662 − 0.635162I
−0.12065 + 2.74438I 5.99863 − 3.42075I
u = −0.107498 − 1.054050I
a = 0.832680 − 0.608094I
b = 0.35976 − 1.52792I
c = 0.60269 + 1.46286I
d = 0.759232 + 0.584397I
−0.12065 + 2.74438I 5.99863 − 3.42075I
u = −0.000983 + 1.149400I
a = 0.974897 − 0.337516I
b = −1.35698 − 0.51540I
c = 0.547631 − 1.231120I
d = 0.698366 − 0.678096I
−0.86138 + 1.33135I 4.84050 − 0.67575I
u = −0.000983 + 1.149400I
a = 0.974897 − 0.337516I
b = −1.35698 − 0.51540I
c = 0.417486 − 0.000081I
d = −1.395290 − 0.000467I
−0.86138 + 1.33135I 4.84050 − 0.67575I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.000983 − 1.149400I
a = 0.974897 + 0.337516I
b = −1.35698 + 0.51540I
c = 0.547631 + 1.231120I
d = 0.698366 + 0.678096I
−0.86138 − 1.33135I 4.84050 + 0.67575I
u = −0.000983 − 1.149400I
a = 0.974897 + 0.337516I
b = −1.35698 + 0.51540I
c = 0.417486 + 0.000081I
d = −1.395290 + 0.000467I
−0.86138 − 1.33135I 4.84050 + 0.67575I
u = 1.222080 + 0.199525I
a = −0.209050 + 0.970065I
b = 1.41696 − 0.48835I
c = 0.508002 − 0.253270I
d = −0.576609 − 0.786036I
−2.55344 − 3.99588I 5.39099 + 3.49800I
u = 1.222080 + 0.199525I
a = −0.209050 + 0.970065I
b = 1.41696 − 0.48835I
c = 0.473795 + 0.176635I
d = −0.853067 + 0.690841I
−2.55344 − 3.99588I 5.39099 + 3.49800I
u = 1.222080 − 0.199525I
a = −0.209050 − 0.970065I
b = 1.41696 + 0.48835I
c = 0.508002 + 0.253270I
d = −0.576609 + 0.786036I
−2.55344 + 3.99588I 5.39099 − 3.49800I
u = 1.222080 − 0.199525I
a = −0.209050 − 0.970065I
b = 1.41696 + 0.48835I
c = 0.473795 − 0.176635I
d = −0.853067 − 0.690841I
−2.55344 + 3.99588I 5.39099 − 3.49800I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.383777 + 1.192290I
a = −0.986938 − 0.103224I
b = 1.68333 − 1.34680I
c = 0.06728 − 1.54278I
d = 0.971785 − 0.646950I
−0.03073 − 6.47771I 7.22220 + 6.52194I
u = −0.383777 + 1.192290I
a = −0.986938 − 0.103224I
b = 1.68333 − 1.34680I
c = 0.411691 − 0.031373I
d = −1.41498 − 0.18404I
−0.03073 − 6.47771I 7.22220 + 6.52194I
u = −0.383777 − 1.192290I
a = −0.986938 + 0.103224I
b = 1.68333 + 1.34680I
c = 0.06728 + 1.54278I
d = 0.971785 + 0.646950I
−0.03073 + 6.47771I 7.22220 − 6.52194I
u = −0.383777 − 1.192290I
a = −0.986938 + 0.103224I
b = 1.68333 + 1.34680I
c = 0.411691 + 0.031373I
d = −1.41498 + 0.18404I
−0.03073 + 6.47771I 7.22220 − 6.52194I
u = 0.494865 + 0.507562I
a = −1.106230 − 0.139635I
b = 0.487880 + 0.827199I
c = 0.478200 + 0.048575I
d = −1.069820 + 0.210247I
4.00909 + 1.37448I 14.7018 − 4.3512I
u = 0.494865 + 0.507562I
a = −1.106230 − 0.139635I
b = 0.487880 + 0.827199I
c = −1.22900 + 4.29549I
d = 1.061570 + 0.215187I
4.00909 + 1.37448I 14.7018 − 4.3512I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.494865 − 0.507562I
a = −1.106230 + 0.139635I
b = 0.487880 − 0.827199I
c = 0.478200 − 0.048575I
d = −1.069820 − 0.210247I
4.00909 − 1.37448I 14.7018 + 4.3512I
u = 0.494865 − 0.507562I
a = −1.106230 + 0.139635I
b = 0.487880 − 0.827199I
c = −1.22900 − 4.29549I
d = 1.061570 − 0.215187I
4.00909 − 1.37448I 14.7018 + 4.3512I
u = −0.441227 + 0.551458I
a = 0.617455 − 0.819077I
b = −0.539142 + 1.070460I
c = 0.894756 + 0.404298I
d = 0.071873 + 0.419376I
1.18777 + 0.88878I 5.60709 + 0.92577I
u = −0.441227 + 0.551458I
a = 0.617455 − 0.819077I
b = −0.539142 + 1.070460I
c = 0.472778 − 0.042452I
d = −1.098240 − 0.188408I
1.18777 + 0.88878I 5.60709 + 0.92577I
u = −0.441227 − 0.551458I
a = 0.617455 + 0.819077I
b = −0.539142 − 1.070460I
c = 0.894756 − 0.404298I
d = 0.071873 − 0.419376I
1.18777 − 0.88878I 5.60709 − 0.92577I
u = −0.441227 − 0.551458I
a = 0.617455 + 0.819077I
b = −0.539142 − 1.070460I
c = 0.472778 + 0.042452I
d = −1.098240 + 0.188408I
1.18777 − 0.88878I 5.60709 − 0.92577I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.598699 + 0.195967I
a = 0.24768 + 1.68902I
b = −0.806895 − 0.050101I
c = 0.530888 − 0.055930I
d = −0.862960 − 0.196265I
3.01275 + 2.59653I 13.46303 − 3.78636I
u = −0.598699 + 0.195967I
a = 0.24768 + 1.68902I
b = −0.806895 − 0.050101I
c = −5.34285 − 3.08636I
d = 1.140340 − 0.081067I
3.01275 + 2.59653I 13.46303 − 3.78636I
u = −0.598699 − 0.195967I
a = 0.24768 − 1.68902I
b = −0.806895 + 0.050101I
c = 0.530888 + 0.055930I
d = −0.862960 + 0.196265I
3.01275 − 2.59653I 13.46303 + 3.78636I
u = −0.598699 − 0.195967I
a = 0.24768 − 1.68902I
b = −0.806895 + 0.050101I
c = −5.34285 + 3.08636I
d = 1.140340 + 0.081067I
3.01275 − 2.59653I 13.46303 + 3.78636I
u = −0.51611 + 1.32552I
a = −0.061894 − 0.631449I
b = 1.142220 − 0.744188I
c = 0.461233 + 0.756174I
d = 0.412094 + 0.963850I
−3.51902 − 5.35900I 7.50458 + 3.06793I
u = −0.51611 + 1.32552I
a = −0.061894 − 0.631449I
b = 1.142220 − 0.744188I
c = −0.132196 − 1.384640I
d = 1.068330 − 0.715684I
−3.51902 − 5.35900I 7.50458 + 3.06793I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.51611 − 1.32552I
a = −0.061894 + 0.631449I
b = 1.142220 + 0.744188I
c = 0.461233 − 0.756174I
d = 0.412094 − 0.963850I
−3.51902 + 5.35900I 7.50458 − 3.06793I
u = −0.51611 − 1.32552I
a = −0.061894 + 0.631449I
b = 1.142220 + 0.744188I
c = −0.132196 + 1.384640I
d = 1.068330 + 0.715684I
−3.51902 + 5.35900I 7.50458 − 3.06793I
u = 0.63403 + 1.38420I
a = 0.865718 − 0.012325I
b = −1.50969 − 1.96886I
c = 0.425486 − 0.700704I
d = 0.366859 − 1.042680I
−6.36348 + 10.62070I 4.97373 − 6.45650I
u = 0.63403 + 1.38420I
a = 0.865718 − 0.012325I
b = −1.50969 − 1.96886I
c = −0.254465 + 1.306340I
d = 1.143660 + 0.737515I
−6.36348 + 10.62070I 4.97373 − 6.45650I
u = 0.63403 − 1.38420I
a = 0.865718 + 0.012325I
b = −1.50969 + 1.96886I
c = 0.425486 + 0.700704I
d = 0.366859 + 1.042680I
−6.36348 − 10.62070I 4.97373 + 6.45650I
u = 0.63403 − 1.38420I
a = 0.865718 + 0.012325I
b = −1.50969 + 1.96886I
c = −0.254465 − 1.306340I
d = 1.143660 − 0.737515I
−6.36348 − 10.62070I 4.97373 + 6.45650I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.37388 + 1.47842I
a = −0.746559 − 0.380105I
b = 0.386598 − 0.300673I
c = 0.371907 − 0.829286I
d = 0.549766 − 1.003940I
−8.32991 + 1.64388I 2.69530 − 0.40272I
u = 0.37388 + 1.47842I
a = −0.746559 − 0.380105I
b = 0.386598 − 0.300673I
c = −0.005040 + 1.210940I
d = 1.003440 + 0.825793I
−8.32991 + 1.64388I 2.69530 − 0.40272I
u = 0.37388 − 1.47842I
a = −0.746559 + 0.380105I
b = 0.386598 + 0.300673I
c = 0.371907 + 0.829286I
d = 0.549766 + 1.003940I
−8.32991 − 1.64388I 2.69530 + 0.40272I
u = 0.37388 − 1.47842I
a = −0.746559 + 0.380105I
b = 0.386598 + 0.300673I
c = −0.005040 − 1.210940I
d = 1.003440 − 0.825793I
−8.32991 − 1.64388I 2.69530 + 0.40272I
21
III. I
v
1
= ha, d, c − 1, b + v, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
3
=
0
−v
a
9
=
1
0
a
2
=
−1
−v
a
6
=
1
1
a
1
=
−1
−1
a
4
=
v
0
a
11
=
1
0
a
10
=
1
0
a
7
=
1
0
a
12
=
0
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 7
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
7
, c
8
c
9
, c
10
u
2
c
6
, c
11
(u + 1)
2
c
12
(u − 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
7
, c
8
c
9
, c
10
y
2
c
6
, c
11
, c
12
(y − 1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
c = 1.00000
d = 0
1.64493 − 2.02988I 9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = 1.00000
d = 0
1.64493 + 2.02988I 9.00000 − 3.46410I
25
IV. I
v
2
= ha, d + 1, av + c − a + 1, b + v, v
2
− v + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
3
=
0
−v
a
9
=
1
0
a
2
=
−1
−v
a
6
=
1
1
a
1
=
−1
−1
a
4
=
v
0
a
11
=
−1
−1
a
10
=
0
−1
a
7
=
1
1
a
12
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v + 7
26
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
3
, c
5
u
2
− u + 1
c
2
u
2
+ u + 1
c
4
, c
6
, c
8
c
11
, c
12
u
2
c
7
, c
9
(u + 1)
2
c
10
(u − 1)
2
27
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
5
y
2
+ y + 1
c
4
, c
6
, c
8
c
11
, c
12
y
2
c
7
, c
9
, c
10
(y − 1)
2
28
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = 0.500000 + 0.866025I
a = 0
b = −0.500000 − 0.866025I
c = −1.00000
d = −1.00000
1.64493 − 2.02988I 9.00000 + 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = −0.500000 + 0.866025I
c = −1.00000
d = −1.00000
1.64493 + 2.02988I 9.00000 − 3.46410I
29
V. I
v
3
= hc, d + 1, b, a + 1, v + 1i
(i) Arc colorings
a
5
=
−1
0
a
8
=
1
0
a
3
=
−1
0
a
9
=
1
0
a
2
=
−1
0
a
6
=
−1
0
a
1
=
−1
0
a
4
=
−1
0
a
11
=
0
−1
a
10
=
1
−1
a
7
=
0
1
a
12
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
u
c
6
, c
10
u − 1
c
7
, c
9
, c
11
c
12
u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
8
y
c
6
, c
7
, c
9
c
10
, c
11
, c
12
y − 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = −1.00000
b = 0
c = 0
d = −1.00000
3.28987 12.0000
33
VI. I
v
4
= hc, d + 1, −v
2
ba + v
3
b − v
2
b + av − v
2
+ c, b
2
v
2
− bv + 1i
(i) Arc colorings
a
5
=
v
0
a
8
=
1
0
a
3
=
a
b
a
9
=
1
0
a
2
=
−av + v
2
+ a − v
b
a
6
=
1
−ba − b + a − v + 1
a
1
=
−1
ba + b − a + v − 1
a
4
=
v
0
a
11
=
0
−1
a
10
=
1
−1
a
7
=
0
1
a
12
=
−1
ba + b − a + v − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
2
a + b
2
− ba −v
2
− b − 3a + 3v + 13
(iv) u-Polynomials at the component : It cannot be defined for a positive
dimension component.
(v) Riley Polynomials at the component : It cannot be defined for a positive
dimension component.
34
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
3.28987 + 2.02988I 12.82409 − 3.19607I
35
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
23
+ 12u
22
+ ··· − 2u − 1)
2
· (u
31
+ 15u
30
+ ··· + 120u − 16)
c
2
u(u
2
+ u + 1)
2
(u
23
+ 2u
22
+ ··· − 2u − 1)
2
(u
31
+ u
30
+ ··· + 8u − 4)
c
3
u(u
2
− u + 1)
2
(u
23
− 2u
22
+ ··· + 18u − 9)
2
· (u
31
− u
30
+ ··· + 128u − 548)
c
4
, c
8
u
5
(u
23
+ u
22
+ ··· + 8u − 4)
2
(u
31
− 3u
30
+ ··· + 64u − 32)
c
5
u(u
2
− u + 1)
2
(u
23
+ 2u
22
+ ··· − 2u − 1)
2
(u
31
+ u
30
+ ··· + 8u − 4)
c
6
u
2
(u − 1)(u + 1)
2
(u
31
+ 5u
30
+ ··· − 3u − 1)
· (u
46
+ 3u
45
+ ··· + 56u + 16)
c
7
u
2
(u + 1)
3
(u
31
+ 5u
30
+ ··· − 3u − 1)(u
46
+ 3u
45
+ ··· + 56u + 16)
c
9
, c
11
u
2
(u + 1)
3
(u
31
− 11u
30
+ ··· + 21u − 1)
· (u
46
− 23u
45
+ ··· − 288u + 256)
c
10
u
2
(u − 1)
3
(u
31
+ 5u
30
+ ··· − 3u − 1)(u
46
+ 3u
45
+ ··· + 56u + 16)
c
12
u
2
(u − 1)
2
(u + 1)(u
31
+ 5u
30
+ ··· − 3u − 1)
· (u
46
+ 3u
45
+ ··· + 56u + 16)
36
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
23
+ 24y
21
+ ··· + 10y − 1)
2
· (y
31
+ 3y
30
+ ··· + 25888y − 256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
23
+ 12y
22
+ ··· − 2y − 1)
2
· (y
31
+ 15y
30
+ ··· + 120y − 16)
c
3
y(y
2
+ y + 1)
2
(y
23
− 12y
22
+ ··· − 450y − 81)
2
· (y
31
− 9y
30
+ ··· + 4451896y − 300304)
c
4
, c
8
y
5
(y
23
+ 15y
22
+ ··· − 40y − 16)
2
· (y
31
+ 15y
30
+ ··· + 1024y − 1024)
c
6
, c
7
, c
10
c
12
y
2
(y − 1)
3
(y
31
− 11y
30
+ ··· + 21y − 1)
· (y
46
− 23y
45
+ ··· − 288y + 256)
c
9
, c
11
y
2
(y − 1)
3
(y
31
+ 29y
30
+ ··· + 61y − 1)
· (y
46
− 3y
45
+ ··· − 2449920y + 65536)
37
