12a
0208
(K12a
0208
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 11 2 9 4 1 12 5 10
Solving Sequence
1,9 4,10
8 5 7 3 2 6 12 11
c
9
c
8
c
4
c
7
c
3
c
1
c
6
c
12
c
10
c
2
, c
5
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−73876195581u
31
+ 635182095531u
30
+ ··· + 1260543449654b − 1153435624046,
− 324186211813u
31
+ 2767349300228u
30
+ ··· + 2521086899308a + 292251319739,
u
32
− 8u
31
+ ··· − 3u + 4i
I
u
2
= h−46u
26
a + 785u
26
+ ··· + 710a − 2547, 2u
26
a − 2u
26
+ ··· − 7a + 10, u
27
− 7u
26
+ ··· − 2u + 1i
I
u
3
= hb − u + 1, a − 1, u
2
− u + 1i
I
u
4
= hb
2
+ 1, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
* 4 irreducible components of dim
C
= 0, with total 94 representations.
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).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= h−7.39×10
10
u
31
+6.35×10
11
u
30
+· · ·+1.26×10
12
b−1.15×10
12
, −3.24×
10
11
u
31
+2.77×10
12
u
30
+· · ·+2.52×10
12
a+2.92×10
11
, u
32
−8u
31
+· · ·−3u+4i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
0.128590u
31
− 1.09768u
30
+ ··· + 5.24512u − 0.115923
0.0586066u
31
− 0.503895u
30
+ ··· − 1.40068u + 0.915030
a
10
=
1
u
2
a
8
=
0.0983513u
31
− 0.889506u
30
+ ··· + 3.00247u + 0.618797
0.0740836u
31
− 0.470529u
30
+ ··· − 1.24670u + 0.527414
a
5
=
0.146540u
31
− 1.26945u
30
+ ··· + 4.04903u + 0.702930
0.0976318u
31
− 0.820411u
30
+ ··· − 1.76926u + 1.02768
a
7
=
0.172435u
31
− 1.36004u
30
+ ··· + 1.75577u + 1.14621
0.0740836u
31
− 0.470529u
30
+ ··· − 1.24670u + 0.527414
a
3
=
0.131853u
31
− 1.12891u
30
+ ··· + 1.57311u + 0.851141
−0.0194438u
31
+ 0.129136u
30
+ ··· − 1.66352u + 0.689740
a
2
=
−0.0569748u
31
+ 0.488280u
30
+ ··· − 2.43533u + 0.0685016
−0.0390252u
31
+ 0.316515u
30
+ ··· + 0.368581u − 0.112645
a
6
=
0.256919u
31
− 2.15298u
30
+ ··· + 3.47300u + 0.998503
0.136486u
31
− 0.905042u
30
+ ··· − 2.46312u + 0.976685
a
12
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
=
204288482497
630271724827
u
31
−
1674264130767
630271724827
u
30
+ ··· +
8358771694435
630271724827
u +
744767795870
630271724827
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
32
+ 15u
31
+ ··· + 6u + 1
c
2
, c
4
, c
6
c
8
u
32
− u
31
+ ··· + 3u
2
+ 1
c
3
u
32
+ 4u
31
+ ··· + 192u + 128
c
5
, c
11
u
32
+ 2u
31
+ ··· − 3u + 2
c
9
, c
10
, c
12
u
32
+ 8u
31
+ ··· + 3u + 4
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
32
+ 11y
31
+ ··· + 2y + 1
c
2
, c
4
, c
6
c
8
y
32
+ 15y
31
+ ··· + 6y + 1
c
3
y
32
− 14y
31
+ ··· + 307200y + 16384
c
5
, c
11
y
32
+ 8y
31
+ ··· + 3y + 4
c
9
, c
10
, c
12
y
32
+ 32y
31
+ ··· + 239y + 16
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.999865 + 0.413471I
a = −0.208119 + 0.661905I
b = 0.483840 + 1.151180I
−7.03351 + 5.35323I −7.40440 − 3.59025I
u = 0.999865 − 0.413471I
a = −0.208119 − 0.661905I
b = 0.483840 − 1.151180I
−7.03351 − 5.35323I −7.40440 + 3.59025I
u = 0.689885 + 0.574928I
a = 0.507556 + 0.433180I
b = −0.644771 − 0.193099I
−0.67877 − 2.26339I 1.01658 + 3.94466I
u = 0.689885 − 0.574928I
a = 0.507556 − 0.433180I
b = −0.644771 + 0.193099I
−0.67877 + 2.26339I 1.01658 − 3.94466I
u = −0.071362 + 1.109170I
a = 0.066207 − 0.263550I
b = −0.462260 + 1.063600I
−0.59844 − 5.94993I −0.50554 + 7.47801I
u = −0.071362 − 1.109170I
a = 0.066207 + 0.263550I
b = −0.462260 − 1.063600I
−0.59844 + 5.94993I −0.50554 − 7.47801I
u = 0.856161 + 0.051151I
a = 0.159385 − 0.513993I
b = −0.308997 − 0.714151I
−2.68984 + 1.38889I −4.39846 − 4.80710I
u = 0.856161 − 0.051151I
a = 0.159385 + 0.513993I
b = −0.308997 + 0.714151I
−2.68984 − 1.38889I −4.39846 + 4.80710I
u = 0.926661 + 0.673958I
a = −1.33199 − 0.84627I
b = 0.530539 − 1.183740I
−6.27266 − 11.59750I −5.82560 + 10.02458I
u = 0.926661 − 0.673958I
a = −1.33199 + 0.84627I
b = 0.530539 + 1.183740I
−6.27266 + 11.59750I −5.82560 − 10.02458I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.284666 + 1.231480I
a = 0.003444 − 0.217087I
b = −0.044400 − 0.677264I
1.09703 − 2.68597I 3.28542 + 2.17424I
u = 0.284666 − 1.231480I
a = 0.003444 + 0.217087I
b = −0.044400 + 0.677264I
1.09703 + 2.68597I 3.28542 − 2.17424I
u = −0.134520 + 1.396800I
a = 1.98921 − 0.16991I
b = −0.578102 − 1.189990I
1.63545 + 10.10540I 0. − 5.69385I
u = −0.134520 − 1.396800I
a = 1.98921 + 0.16991I
b = −0.578102 + 1.189990I
1.63545 − 10.10540I 0. + 5.69385I
u = −0.02346 + 1.43595I
a = −1.030550 + 0.853034I
b = 0.790287 − 0.361253I
6.70077 − 0.35933I 6.32864 + 0.I
u = −0.02346 − 1.43595I
a = −1.030550 − 0.853034I
b = 0.790287 + 0.361253I
6.70077 + 0.35933I 6.32864 + 0.I
u = 0.41491 + 1.42277I
a = −0.149267 − 0.036799I
b = 0.429768 + 1.091750I
−1.327340 + 0.277330I 0
u = 0.41491 − 1.42277I
a = −0.149267 + 0.036799I
b = 0.429768 − 1.091750I
−1.327340 − 0.277330I 0
u = −0.142919 + 0.470061I
a = −1.90622 + 0.84746I
b = 0.540356 + 0.720045I
1.30044 + 2.16188I 5.01054 − 3.83056I
u = −0.142919 − 0.470061I
a = −1.90622 − 0.84746I
b = 0.540356 − 0.720045I
1.30044 − 2.16188I 5.01054 + 3.83056I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.03544 + 1.51856I
a = −1.68660 − 0.54922I
b = 0.699799 + 0.849942I
8.08214 + 2.19583I 0
u = 0.03544 − 1.51856I
a = −1.68660 + 0.54922I
b = 0.699799 − 0.849942I
8.08214 − 2.19583I 0
u = −0.454564 + 0.152446I
a = 0.84677 − 2.43519I
b = −0.530198 − 1.146870I
−3.38970 + 8.05749I −0.05529 − 6.30206I
u = −0.454564 − 0.152446I
a = 0.84677 + 2.43519I
b = −0.530198 + 1.146870I
−3.38970 − 8.05749I −0.05529 + 6.30206I
u = 0.25659 + 1.55249I
a = 1.018930 + 0.749304I
b = −0.804182 − 0.329406I
6.33684 − 5.84113I 0
u = 0.25659 − 1.55249I
a = 1.018930 − 0.749304I
b = −0.804182 + 0.329406I
6.33684 + 5.84113I 0
u = 0.16262 + 1.57088I
a = 1.62580 − 0.57249I
b = −0.694814 + 0.875920I
7.92044 − 8.51420I 0
u = 0.16262 − 1.57088I
a = 1.62580 + 0.57249I
b = −0.694814 − 0.875920I
7.92044 + 8.51420I 0
u = 0.34020 + 1.59071I
a = −1.81440 − 0.16181I
b = 0.574377 − 1.201010I
1.0251 − 16.3375I 0
u = 0.34020 − 1.59071I
a = −1.81440 + 0.16181I
b = 0.574377 + 1.201010I
1.0251 + 16.3375I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.140182 + 0.315362I
a = 0.784849 + 1.141860I
b = 0.518758 − 0.447984I
1.051570 − 0.810934I 6.74474 + 3.92362I
u = −0.140182 − 0.315362I
a = 0.784849 − 1.141860I
b = 0.518758 + 0.447984I
1.051570 + 0.810934I 6.74474 − 3.92362I
8
II. I
u
2
= h−46u
26
a + 785u
26
+ · · · + 710a − 2547, 2u
26
a − 2u
26
+ · · · − 7a +
10, u
27
− 7u
26
+ · · · − 2u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
a
0.0330223au
26
− 0.563532u
26
+ ··· − 0.509691a + 1.82843
a
10
=
1
u
2
a
8
=
0.563532au
26
− 1.98636u
26
+ ··· − 1.82843a + 3.96339
−0.0567121au
26
+ 0.0330223u
26
+ ··· + 0.310122a − 1.50969
a
5
=
−u
24
+ 6u
23
+ ··· − 4u + 1
u
24
− 6u
23
+ ··· − 8u
3
+ 4u
2
a
7
=
0.506820au
26
− 1.95334u
26
+ ··· − 1.51831a + 2.45370
−0.0567121au
26
+ 0.0330223u
26
+ ··· + 0.310122a − 1.50969
a
3
=
−0.310122au
26
− 0.490309u
26
+ ··· + 0.569275a + 0.263460
−0.124910au
26
− 0.433597u
26
+ ··· − 0.506820a + 1.95334
a
2
=
0.185212au
26
+ 0.0567121u
26
+ ··· − 1.07609a + 0.689878
0.152190au
26
+ 0.620244u
26
+ ··· + 0.433597a − 2.13855
a
6
=
−u
23
+ 6u
22
+ ··· + 8u
2
− 4u
−u
23
+ 6u
22
+ ··· + 4u
2
− u
a
12
=
u
u
3
+ u
a
11
=
u
2
+ 1
u
4
+ 2u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes
= 4u
26
−28u
25
+152u
24
−584u
23
+1880u
22
−5032u
21
+11712u
20
−23756u
19
+42652u
18
−
67860u
17
+ 96136u
16
− 120956u
15
+ 134900u
14
− 132208u
13
+ 112636u
12
− 81568u
11
+
48448u
10
−21704u
9
+5692u
8
+744u
7
−1464u
6
+528u
5
+136u
4
−188u
3
+76u
2
+12u −10
9
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
54
+ 31u
53
+ ··· + 16u
2
+ 1
c
2
, c
4
, c
6
c
8
u
54
− u
53
+ ··· − 2u + 1
c
3
(u
27
− u
26
+ ··· + 4u − 1)
2
c
5
, c
11
(u
27
− u
26
+ ··· − u
2
− 1)
2
c
9
, c
10
, c
12
(u
27
+ 7u
26
+ ··· − 2u − 1)
2
10
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
54
− 17y
53
+ ··· + 32y + 1
c
2
, c
4
, c
6
c
8
y
54
+ 31y
53
+ ··· + 16y
2
+ 1
c
3
(y
27
− 13y
26
+ ··· − 2y −1)
2
c
5
, c
11
(y
27
+ 7y
26
+ ··· − 2y −1)
2
c
9
, c
10
, c
12
(y
27
+ 27y
26
+ ··· + 14y −1)
2
11
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.851026 + 0.532141I
a = −0.307668 + 0.778974I
b = 0.344784 + 1.223910I
−7.58873 − 2.79673I −8.25981 + 4.61920I
u = 0.851026 + 0.532141I
a = −1.75724 − 0.97566I
b = 0.405628 − 1.159490I
−7.58873 − 2.79673I −8.25981 + 4.61920I
u = 0.851026 − 0.532141I
a = −0.307668 − 0.778974I
b = 0.344784 − 1.223910I
−7.58873 + 2.79673I −8.25981 − 4.61920I
u = 0.851026 − 0.532141I
a = −1.75724 + 0.97566I
b = 0.405628 + 1.159490I
−7.58873 + 2.79673I −8.25981 − 4.61920I
u = 0.881276 + 0.374809I
a = 0.289170 − 0.634254I
b = −0.382236 − 1.103440I
−4.11296 + 0.98697I −4.82659 + 0.25321I
u = 0.881276 + 0.374809I
a = −0.324670 − 0.523733I
b = 0.673840 − 0.103585I
−4.11296 + 0.98697I −4.82659 + 0.25321I
u = 0.881276 − 0.374809I
a = 0.289170 + 0.634254I
b = −0.382236 + 1.103440I
−4.11296 − 0.98697I −4.82659 − 0.25321I
u = 0.881276 − 0.374809I
a = −0.324670 + 0.523733I
b = 0.673840 + 0.103585I
−4.11296 − 0.98697I −4.82659 − 0.25321I
u = 0.845632 + 0.655604I
a = −0.394766 − 0.373032I
b = 0.812413 + 0.177201I
−3.30741 − 6.65682I −2.80212 + 7.22011I
u = 0.845632 + 0.655604I
a = 1.48008 + 0.72677I
b = −0.494977 + 1.127680I
−3.30741 − 6.65682I −2.80212 + 7.22011I
12
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.845632 − 0.655604I
a = −0.394766 + 0.373032I
b = 0.812413 − 0.177201I
−3.30741 + 6.65682I −2.80212 − 7.22011I
u = 0.845632 − 0.655604I
a = 1.48008 − 0.72677I
b = −0.494977 − 1.127680I
−3.30741 + 6.65682I −2.80212 − 7.22011I
u = 0.099061 + 0.685673I
a = −0.394947 + 0.815475I
b = 0.466586 − 0.799061I
1.05207 − 2.01066I 4.08108 + 3.90758I
u = 0.099061 + 0.685673I
a = 1.217330 − 0.183901I
b = −0.549070 − 0.485974I
1.05207 − 2.01066I 4.08108 + 3.90758I
u = 0.099061 − 0.685673I
a = −0.394947 − 0.815475I
b = 0.466586 + 0.799061I
1.05207 + 2.01066I 4.08108 − 3.90758I
u = 0.099061 − 0.685673I
a = 1.217330 + 0.183901I
b = −0.549070 + 0.485974I
1.05207 + 2.01066I 4.08108 − 3.90758I
u = −0.033645 + 1.357360I
a = −0.015470 − 0.150550I
b = −0.274844 + 1.278800I
−0.535824 + 0.961395I −1.27084 − 1.18503I
u = −0.033645 + 1.357360I
a = 2.44863 + 0.04055I
b = −0.464129 − 1.077600I
−0.535824 + 0.961395I −1.27084 − 1.18503I
u = −0.033645 − 1.357360I
a = −0.015470 + 0.150550I
b = −0.274844 − 1.278800I
−0.535824 − 0.961395I −1.27084 + 1.18503I
u = −0.033645 − 1.357360I
a = 2.44863 − 0.04055I
b = −0.464129 + 1.077600I
−0.535824 − 0.961395I −1.27084 + 1.18503I
13
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.119558 + 1.364110I
a = 0.76183 − 1.36750I
b = −0.344719 + 0.341856I
1.58939 − 2.83072I 1.79804 + 3.74350I
u = 0.119558 + 1.364110I
a = 0.0108437 + 0.0806079I
b = 0.084381 − 1.175530I
1.58939 − 2.83072I 1.79804 + 3.74350I
u = 0.119558 − 1.364110I
a = 0.76183 + 1.36750I
b = −0.344719 − 0.341856I
1.58939 + 2.83072I 1.79804 − 3.74350I
u = 0.119558 − 1.364110I
a = 0.0108437 − 0.0806079I
b = 0.084381 + 1.175530I
1.58939 + 2.83072I 1.79804 − 3.74350I
u = −0.08960 + 1.41179I
a = 0.960076 − 0.790976I
b = −0.884320 + 0.254207I
4.44628 + 4.75862I 3.32590 − 2.41055I
u = −0.08960 + 1.41179I
a = −2.05371 + 0.00645I
b = 0.577308 + 1.120420I
4.44628 + 4.75862I 3.32590 − 2.41055I
u = −0.08960 − 1.41179I
a = 0.960076 + 0.790976I
b = −0.884320 − 0.254207I
4.44628 − 4.75862I 3.32590 + 2.41055I
u = −0.08960 − 1.41179I
a = −2.05371 − 0.00645I
b = 0.577308 − 1.120420I
4.44628 − 4.75862I 3.32590 + 2.41055I
u = 0.25231 + 1.41767I
a = −0.704744 − 1.061140I
b = 0.433641 + 0.198875I
1.41036 − 3.05015I 0. + 1.99178I
u = 0.25231 + 1.41767I
a = 0.0734789 + 0.0398264I
b = −0.155570 − 1.155430I
1.41036 − 3.05015I 0. + 1.99178I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.25231 − 1.41767I
a = −0.704744 + 1.061140I
b = 0.433641 − 0.198875I
1.41036 + 3.05015I 0. − 1.99178I
u = 0.25231 − 1.41767I
a = 0.0734789 − 0.0398264I
b = −0.155570 + 1.155430I
1.41036 + 3.05015I 0. − 1.99178I
u = 0.10205 + 1.54134I
a = 1.46611 + 0.70019I
b = −0.732596 − 0.699246I
8.43216 − 3.15301I 5.82291 + 0.I
u = 0.10205 + 1.54134I
a = −1.44220 + 0.75303I
b = 0.722594 − 0.728691I
8.43216 − 3.15301I 5.82291 + 0.I
u = 0.10205 − 1.54134I
a = 1.46611 − 0.70019I
b = −0.732596 + 0.699246I
8.43216 + 3.15301I 5.82291 + 0.I
u = 0.10205 − 1.54134I
a = −1.44220 − 0.75303I
b = 0.722594 + 0.728691I
8.43216 + 3.15301I 5.82291 + 0.I
u = 0.30604 + 1.51914I
a = −0.1073610 − 0.0682683I
b = 0.294293 + 1.287200I
−0.99741 − 7.02686I 0. + 6.08794I
u = 0.30604 + 1.51914I
a = −2.24569 − 0.03447I
b = 0.474570 − 1.100580I
−0.99741 − 7.02686I 0. + 6.08794I
u = 0.30604 − 1.51914I
a = −0.1073610 + 0.0682683I
b = 0.294293 − 1.287200I
−0.99741 + 7.02686I 0. − 6.08794I
u = 0.30604 − 1.51914I
a = −2.24569 + 0.03447I
b = 0.474570 + 1.100580I
−0.99741 + 7.02686I 0. − 6.08794I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.357506 + 0.271060I
a = 1.255620 + 0.003386I
b = −0.067219 − 1.140920I
−3.64210 − 0.95364I −2.23281 + 7.10310I
u = 0.357506 + 0.271060I
a = 2.29905 − 3.35138I
b = −0.179781 + 0.840004I
−3.64210 − 0.95364I −2.23281 + 7.10310I
u = 0.357506 − 0.271060I
a = 1.255620 − 0.003386I
b = −0.067219 + 1.140920I
−3.64210 + 0.95364I −2.23281 − 7.10310I
u = 0.357506 − 0.271060I
a = 2.29905 + 3.35138I
b = −0.179781 − 0.840004I
−3.64210 + 0.95364I −2.23281 − 7.10310I
u = −0.351036 + 0.182657I
a = −0.976869 − 0.429852I
b = −0.738069 + 0.235848I
−0.74562 + 3.27708I 3.27794 − 2.87566I
u = −0.351036 + 0.182657I
a = −1.40048 + 2.62389I
b = 0.480202 + 1.056470I
−0.74562 + 3.27708I 3.27794 − 2.87566I
u = −0.351036 − 0.182657I
a = −0.976869 + 0.429852I
b = −0.738069 − 0.235848I
−0.74562 − 3.27708I 3.27794 + 2.87566I
u = −0.351036 − 0.182657I
a = −1.40048 − 2.62389I
b = 0.480202 − 1.056470I
−0.74562 − 3.27708I 3.27794 + 2.87566I
u = 0.30716 + 1.57661I
a = −0.950516 − 0.672058I
b = 0.895765 + 0.235028I
3.93318 − 10.97750I 0
u = 0.30716 + 1.57661I
a = 1.89805 + 0.02059I
b = −0.573651 + 1.137950I
3.93318 − 10.97750I 0
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.30716 − 1.57661I
a = −0.950516 + 0.672058I
b = 0.895765 − 0.235028I
3.93318 + 10.97750I 0
u = 0.30716 − 1.57661I
a = 1.89805 − 0.02059I
b = −0.573651 − 1.137950I
3.93318 + 10.97750I 0
u = −0.294686
a = 0.41605 + 3.96773I
b = −0.324823 + 1.147400I
−4.80157 −2.25830
u = −0.294686
a = 0.41605 − 3.96773I
b = −0.324823 − 1.147400I
−4.80157 −2.25830
17
III. I
u
3
= hb − u + 1, a − 1, u
2
− u + 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
1
u − 1
a
10
=
1
u − 1
a
8
=
u
−u
a
5
=
0
u
a
7
=
0
−u
a
3
=
1
0
a
2
=
−u
u
a
6
=
−1
−u + 1
a
12
=
u
u − 1
a
11
=
u
u − 2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 12u − 6
18
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
4
c
5
, c
6
, c
7
c
8
, c
9
, c
10
c
11
, c
12
u
2
+ u + 1
c
3
u
2
− u + 1
19
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
6
c
7
, c
8
, c
9
c
10
, c
11
, c
12
y
2
+ y + 1
20
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.500000 + 0.866025I
a = 1.00000
b = −0.500000 + 0.866025I
− 6.08965I 0. + 10.39230I
u = 0.500000 − 0.866025I
a = 1.00000
b = −0.500000 − 0.866025I
6.08965I 0. − 10.39230I
21
IV. I
u
4
= hb
2
+ 1, u
2
+ a − u + 2, u
3
− u
2
+ 2u − 1i
(i) Arc colorings
a
1
=
0
u
a
9
=
1
0
a
4
=
−u
2
+ u − 2
b
a
10
=
1
u
2
a
8
=
−u
2
b + bu − 2b + 1
−1
a
5
=
b
0
a
7
=
−u
2
b + bu − 2b
−1
a
3
=
−u
2
+ u − 2
b
a
2
=
−u
2
+ u − 2
b + u
a
6
=
0
−bu
a
12
=
u
u
2
− u + 1
a
11
=
u
2
+ 1
u
2
− u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4u
2
+ 4u − 12
22
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
(u − 1)
6
c
2
, c
4
, c
6
c
8
(u
2
+ 1)
3
c
3
u
6
c
5
, c
11
u
6
+ u
4
+ 2u
2
+ 1
c
9
, c
10
(u
3
− u
2
+ 2u − 1)
2
c
12
(u
3
+ u
2
+ 2u + 1)
2
23
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y −1)
6
c
2
, c
4
, c
6
c
8
(y + 1)
6
c
3
y
6
c
5
, c
11
(y
3
+ y
2
+ 2y + 1)
2
c
9
, c
10
, c
12
(y
3
+ 3y
2
+ 2y −1)
2
24
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = 1.000000I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = 0.215080 + 1.307140I
a = −0.122561 + 0.744862I
b = − 1.000000I
−0.26574 − 2.82812I −4.49024 + 2.97945I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = 1.000000I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = 0.215080 − 1.307140I
a = −0.122561 − 0.744862I
b = − 1.000000I
−0.26574 + 2.82812I −4.49024 − 2.97945I
u = 0.569840
a = −1.75488
b = 1.000000I
−4.40332 −11.0200
u = 0.569840
a = −1.75488
b = − 1.000000I
−4.40332 −11.0200
25
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
7
((u − 1)
6
)(u
2
+ u + 1)(u
32
+ 15u
31
+ ··· + 6u + 1)
· (u
54
+ 31u
53
+ ··· + 16u
2
+ 1)
c
2
, c
4
, c
6
c
8
((u
2
+ 1)
3
)(u
2
+ u + 1)(u
32
− u
31
+ ··· + 3u
2
+ 1)(u
54
− u
53
+ ··· − 2u + 1)
c
3
u
6
(u
2
− u + 1)(u
27
− u
26
+ ··· + 4u − 1)
2
· (u
32
+ 4u
31
+ ··· + 192u + 128)
c
5
, c
11
(u
2
+ u + 1)(u
6
+ u
4
+ 2u
2
+ 1)(u
27
− u
26
+ ··· − u
2
− 1)
2
· (u
32
+ 2u
31
+ ··· − 3u + 2)
c
9
, c
10
(u
2
+ u + 1)(u
3
− u
2
+ 2u − 1)
2
(u
27
+ 7u
26
+ ··· − 2u − 1)
2
· (u
32
+ 8u
31
+ ··· + 3u + 4)
c
12
(u
2
+ u + 1)(u
3
+ u
2
+ 2u + 1)
2
(u
27
+ 7u
26
+ ··· − 2u − 1)
2
· (u
32
+ 8u
31
+ ··· + 3u + 4)
26
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
((y −1)
6
)(y
2
+ y + 1)(y
32
+ 11y
31
+ ··· + 2y + 1)
· (y
54
− 17y
53
+ ··· + 32y + 1)
c
2
, c
4
, c
6
c
8
((y + 1)
6
)(y
2
+ y + 1)(y
32
+ 15y
31
+ ··· + 6y + 1)
· (y
54
+ 31y
53
+ ··· + 16y
2
+ 1)
c
3
y
6
(y
2
+ y + 1)(y
27
− 13y
26
+ ··· − 2y −1)
2
· (y
32
− 14y
31
+ ··· + 307200y + 16384)
c
5
, c
11
(y
2
+ y + 1)(y
3
+ y
2
+ 2y + 1)
2
(y
27
+ 7y
26
+ ··· − 2y −1)
2
· (y
32
+ 8y
31
+ ··· + 3y + 4)
c
9
, c
10
, c
12
(y
2
+ y + 1)(y
3
+ 3y
2
+ 2y −1)
2
(y
27
+ 27y
26
+ ··· + 14y −1)
2
· (y
32
+ 32y
31
+ ··· + 239y + 16)
27
