12a
0694
(K12a
0694
)
A knot diagram
1
Linearized knot diagam
3 8 6 7 11 4 1 2 12 5 9 10
Solving Sequence
5,11 1,6,7
8 4 3 2 10 12 9
c
5
c
7
c
4
c
3
c
2
c
10
c
12
c
9
c
1
, c
6
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h3.71327 × 10
48
u
35
+ 4.04621 × 10
50
u
34
+ ··· + 1.08619 × 10
53
d − 2.28969 × 10
52
,
− 5.18177 × 10
49
u
35
− 5.63360 × 10
50
u
34
+ ··· + 2.17237 × 10
53
c − 2.07122 × 10
53
,
− 5.97435 × 10
50
u
35
− 1.74229 × 10
51
u
34
+ ··· + 1.08619 × 10
53
b + 9.47908 × 10
50
,
− 2.62593 × 10
51
u
35
− 7.78518 × 10
51
u
34
+ ··· + 2.17237 × 10
53
a + 6.90156 × 10
51
,
u
36
+ 3u
35
+ ··· + 64u + 32i
I
u
2
= h302671644024258u
27
a + 662808669960639u
27
+ ··· − 2916745959458060a − 4296331597385486,
5.46608 × 10
15
au
27
+ 5.56735 × 10
15
u
27
+ ··· − 2.36686 × 10
16
a − 1.71489 × 10
15
,
− 7.29186 × 10
14
au
27
− 8.99105 × 10
14
u
27
+ ··· + 4.25539 × 10
15
a + 3.18374 × 10
15
,
4247989817783u
27
a − 203084799592924u
27
+ ··· + 250742454402200a + 1119525361661648,
u
28
− u
27
+ ··· − 8u + 4i
I
v
1
= ha, d, c − 1, b + v + 1, v
2
+ v + 1i
I
v
2
= hc, d − 1, b, a − v, v
2
+ v + 1i
I
v
3
= ha, d − 1, c + a, b + 1, v + 1i
I
v
4
= hc, d − 1, a
2
v
2
− 2cav + v
2
a + c
2
− cv + v
2
, bv − 1i
* 5 irreducible components of dim
C
= 0, with total 97 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
= h3.71×10
48
u
35
+4.05×10
50
u
34
+· · ·+1.09×10
53
d−2.29×10
52
, −5.18×
10
49
u
35
− 5.63 × 10
50
u
34
+ · · · + 2.17 × 10
53
c − 2.07 × 10
53
, −5.97 × 10
50
u
35
−
1.74 × 10
51
u
34
+ · · · + 1.09 × 10
53
b + 9.48 × 10
50
, −2.63 × 10
51
u
35
− 7.79 ×
10
51
u
34
+ · · · + 2.17 × 10
53
a + 6.90 × 10
51
, u
36
+ 3u
35
+ · · · + 64u + 32i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
1
=
0.0120878u
35
+ 0.0358372u
34
+ ··· − 0.808374u − 0.0317697
0.00550031u
35
+ 0.0160404u
34
+ ··· + 0.725183u − 0.00872695
a
6
=
1
u
2
a
7
=
0.000238531u
35
+ 0.00259330u
34
+ ··· − 0.119290u + 0.953438
−0.0000341864u
35
− 0.00372516u
34
+ ··· + 0.444645u + 0.210801
a
8
=
0.00157086u
35
+ 0.0135938u
34
+ ··· − 1.44591u + 0.372386
0.00128903u
35
− 0.00127210u
34
+ ··· + 0.00984404u + 0.00259441
a
4
=
0.000238531u
35
+ 0.00259330u
34
+ ··· − 0.119290u + 0.953438
−0.000492763u
35
+ 0.00362002u
34
+ ··· − 0.572452u − 0.270888
a
3
=
0.000272717u
35
+ 0.00631846u
34
+ ··· − 0.563935u + 0.742637
−0.000426302u
35
+ 0.00445645u
34
+ ··· − 0.805392u − 0.386811
a
2
=
0.00896229u
35
+ 0.0251058u
34
+ ··· − 2.42424u − 0.0549226
0.0194270u
35
+ 0.0554189u
34
+ ··· + 0.0990461u + 0.00672681
a
10
=
u
u
a
12
=
0.00846525u
35
+ 0.0249030u
34
+ ··· − 0.595385u − 0.0306758
0.00187771u
35
+ 0.00510617u
34
+ ··· + 0.938172u − 0.00763298
a
9
=
−0.00658754u
35
− 0.0197968u
34
+ ··· + 1.53356u + 0.0230428
0.00187771u
35
+ 0.00510617u
34
+ ··· + 0.938172u − 0.00763298
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.0805025u
35
− 0.242112u
34
+ ··· − 5.72407u − 9.52193
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
36
+ 17u
35
+ ··· − 120u + 16
c
2
, c
8
u
36
+ u
35
+ ··· + 16u + 4
c
3
, c
4
, c
6
c
9
, c
11
, c
12
u
36
− 5u
35
+ ··· + 3u − 1
c
5
, c
10
u
36
+ 3u
35
+ ··· + 64u + 32
c
7
u
36
− u
35
+ ··· − 104u + 1252
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
36
+ 5y
35
+ ··· − 27936y + 256
c
2
, c
8
y
36
+ 17y
35
+ ··· − 120y + 16
c
3
, c
4
, c
6
c
9
, c
11
, c
12
y
36
− 41y
35
+ ··· − 21y + 1
c
5
, c
10
y
36
− 15y
35
+ ··· − 1024y + 1024
c
7
y
36
− 7y
35
+ ··· − 22103608y + 1567504
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.956534 + 0.246505I
a = 0.245175 − 1.269220I
b = −0.346134 − 0.784654I
c = 0.587254 + 0.247408I
d = 0.446161 − 0.609262I
−2.56616 + 0.65266I −13.12638 − 3.31133I
u = −0.956534 − 0.246505I
a = 0.245175 + 1.269220I
b = −0.346134 + 0.784654I
c = 0.587254 − 0.247408I
d = 0.446161 + 0.609262I
−2.56616 − 0.65266I −13.12638 + 3.31133I
u = 0.935949 + 0.527292I
a = 0.386487 − 1.298670I
b = 0.910276 − 0.817885I
c = 0.601278 − 0.353058I
d = 0.236726 + 0.726179I
1.36964 − 3.10356I −5.16268 + 4.71165I
u = 0.935949 − 0.527292I
a = 0.386487 + 1.298670I
b = 0.910276 + 0.817885I
c = 0.601278 + 0.353058I
d = 0.236726 − 0.726179I
1.36964 + 3.10356I −5.16268 − 4.71165I
u = 0.651308 + 0.620650I
a = 0.626981 − 0.691158I
b = 1.099680 − 0.225491I
c = 0.730839 − 0.428002I
d = 0.018859 + 0.596676I
2.25394 − 1.43184I −2.05632 + 3.52848I
u = 0.651308 − 0.620650I
a = 0.626981 + 0.691158I
b = 1.099680 + 0.225491I
c = 0.730839 + 0.428002I
d = 0.018859 − 0.596676I
2.25394 + 1.43184I −2.05632 − 3.52848I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.134519 + 0.831817I
a = −0.333054 + 0.814839I
b = −0.168798 − 0.656332I
c = 0.444936 + 0.012138I
d = 1.245840 − 0.061269I
−4.07214 + 2.53804I −12.12047 − 3.16226I
u = 0.134519 − 0.831817I
a = −0.333054 − 0.814839I
b = −0.168798 + 0.656332I
c = 0.444936 − 0.012138I
d = 1.245840 + 0.061269I
−4.07214 − 2.53804I −12.12047 + 3.16226I
u = −0.488093 + 0.675929I
a = −0.729751 − 0.351432I
b = −1.163350 + 0.137978I
c = 0.831879 + 0.502397I
d = −0.119169 − 0.531960I
0.92725 − 3.15352I −4.07893 + 3.45921I
u = −0.488093 − 0.675929I
a = −0.729751 + 0.351432I
b = −1.163350 − 0.137978I
c = 0.831879 − 0.502397I
d = −0.119169 + 0.531960I
0.92725 + 3.15352I −4.07893 − 3.45921I
u = −1.066500 + 0.529753I
a = −0.36138 − 1.59734I
b = −0.887704 − 1.098310I
c = 0.554284 + 0.346614I
d = 0.296959 − 0.811036I
−0.85359 + 7.85577I −9.34096 − 8.43490I
u = −1.066500 − 0.529753I
a = −0.36138 + 1.59734I
b = −0.887704 + 1.098310I
c = 0.554284 − 0.346614I
d = 0.296959 + 0.811036I
−0.85359 − 7.85577I −9.34096 + 8.43490I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.471804 + 1.201650I
a = −1.033650 − 0.000390I
b = −0.795501 − 1.088210I
c = 0.409694 + 0.038448I
d = 1.41953 − 0.22707I
−6.92260 + 4.39379I −12.55418 − 2.40542I
u = 0.471804 − 1.201650I
a = −1.033650 + 0.000390I
b = −0.795501 + 1.088210I
c = 0.409694 − 0.038448I
d = 1.41953 + 0.22707I
−6.92260 − 4.39379I −12.55418 + 2.40542I
u = −1.232210 + 0.408112I
a = −0.074767 + 0.904861I
b = 1.02170 + 1.10904I
c = −1.91298 − 0.86265I
d = −1.43441 + 0.19589I
−8.11992 + 1.67660I −15.7568 − 0.9806I
u = −1.232210 − 0.408112I
a = −0.074767 − 0.904861I
b = 1.02170 − 1.10904I
c = −1.91298 + 0.86265I
d = −1.43441 − 0.19589I
−8.11992 − 1.67660I −15.7568 + 0.9806I
u = 1.223950 + 0.516090I
a = 0.037576 + 1.129580I
b = −1.02760 + 1.37545I
c = −1.74112 + 1.00593I
d = −1.43061 − 0.24878I
−7.33125 − 7.52384I −14.0983 + 6.1679I
u = 1.223950 − 0.516090I
a = 0.037576 − 1.129580I
b = −1.02760 − 1.37545I
c = −1.74112 − 1.00593I
d = −1.43061 + 0.24878I
−7.33125 + 7.52384I −14.0983 − 6.1679I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.666134 + 0.068993I
a = −1.123260 + 0.576466I
b = −0.104353 + 0.169913I
c = 0.577923 + 0.067898I
d = 0.706776 − 0.200522I
−2.77509 + 2.72721I −16.6085 − 5.9652I
u = 0.666134 − 0.068993I
a = −1.123260 − 0.576466I
b = −0.104353 − 0.169913I
c = 0.577923 − 0.067898I
d = 0.706776 + 0.200522I
−2.77509 − 2.72721I −16.6085 + 5.9652I
u = −0.318666 + 1.335800I
a = 0.724523 − 0.313609I
b = 0.58164 − 1.39075I
c = 0.401008 − 0.024597I
d = 1.48437 + 0.15238I
−11.42670 − 0.95860I −17.6650 − 0.2050I
u = −0.318666 − 1.335800I
a = 0.724523 + 0.313609I
b = 0.58164 + 1.39075I
c = 0.401008 + 0.024597I
d = 1.48437 − 0.15238I
−11.42670 + 0.95860I −17.6650 + 0.2050I
u = −0.568640 + 1.285090I
a = 1.254760 − 0.150682I
b = 1.01253 − 1.18042I
c = 0.401346 − 0.044727I
d = 1.46105 + 0.27427I
−9.63713 − 9.42250I −15.4804 + 5.9490I
u = −0.568640 − 1.285090I
a = 1.254760 + 0.150682I
b = 1.01253 + 1.18042I
c = 0.401346 + 0.044727I
d = 1.46105 − 0.27427I
−9.63713 + 9.42250I −15.4804 − 5.9490I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.579877
a = 0.508844
b = −0.181813
c = 0.714033
d = 0.400496
−0.811618 −12.0290
u = 1.27702 + 0.74720I
a = 0.06527 + 1.61805I
b = −0.91000 + 1.90449I
c = −1.34025 + 1.05868I
d = −1.45945 − 0.36293I
−9.5381 − 11.3478I −13.0594 + 5.6672I
u = 1.27702 − 0.74720I
a = 0.06527 − 1.61805I
b = −0.91000 − 1.90449I
c = −1.34025 − 1.05868I
d = −1.45945 + 0.36293I
−9.5381 + 11.3478I −13.0594 − 5.6672I
u = −1.51924
a = −0.762049
b = 0.272206
c = −1.75045
d = −1.57128
−14.8609 −15.8600
u = −1.29117 + 0.81558I
a = −0.05855 + 1.76313I
b = 0.89290 + 2.05678I
c = −1.24306 − 1.05406I
d = −1.46798 + 0.39682I
−12.0349 + 16.8809I −15.3736 − 9.2575I
u = −1.29117 − 0.81558I
a = −0.05855 − 1.76313I
b = 0.89290 − 2.05678I
c = −1.24306 + 1.05406I
d = −1.46798 − 0.39682I
−12.0349 − 16.8809I −15.3736 + 9.2575I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.111921 + 0.451208I
a = −0.148541 + 0.145650I
b = −0.283161 + 0.602030I
c = 1.212710 + 0.167592I
d = −0.190856 − 0.111820I
−0.30692 + 1.79670I −2.13838 − 3.34715I
u = −0.111921 − 0.451208I
a = −0.148541 − 0.145650I
b = −0.283161 − 0.602030I
c = 1.212710 − 0.167592I
d = −0.190856 + 0.111820I
−0.30692 − 1.79670I −2.13838 + 3.34715I
u = −1.38860 + 0.67758I
a = −0.32966 + 1.52385I
b = 0.64328 + 1.76352I
c = −1.38705 − 0.88191I
d = −1.51341 + 0.32643I
−15.0030 + 8.0885I −18.3300 − 3.8436I
u = −1.38860 − 0.67758I
a = −0.32966 − 1.52385I
b = 0.64328 − 1.76352I
c = −1.38705 + 0.88191I
d = −1.51341 − 0.32643I
−15.0030 − 8.0885I −18.3300 + 3.8436I
u = 1.61122 + 0.12770I
a = 0.978439 + 0.310581I
b = −0.020607 + 0.352320I
c = −1.61050 + 0.15798I
d = −1.61501 − 0.06033I
−18.8051 − 4.7571I −19.1049 + 3.2273I
u = 1.61122 − 0.12770I
a = 0.978439 − 0.310581I
b = −0.020607 − 0.352320I
c = −1.61050 − 0.15798I
d = −1.61501 + 0.06033I
−18.8051 + 4.7571I −19.1049 − 3.2273I
10
II.
I
u
2
= h3.03 × 10
14
au
27
+6.63×10
14
u
27
+· · ·−2.92×10
15
a−4.30×10
15
, 5.47×
10
15
au
27
+ 5.57 × 10
15
u
27
+ · · · − 2.37 × 10
16
a − 1.71 × 10
15
, −7.29 ×
10
14
au
27
− 8.99 × 10
14
u
27
+ · · · + 4.26 × 10
15
a + 3.18 × 10
15
, 4.25 × 10
12
au
27
−
2.03 × 10
14
u
27
+ · · · + 2.51 × 10
14
a + 1.12 × 10
15
, u
28
− u
27
+ · · · − 8u + 4i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
1
=
a
2.82492au
27
+ 3.48319u
27
+ ··· − 16.4857a − 12.3340
a
6
=
1
u
2
a
7
=
−5.29398au
27
− 5.39206u
27
+ ··· + 22.9234a + 1.66090
−1.17257au
27
− 2.56776u
27
+ ··· + 11.2997a + 16.6443
a
8
=
−5.46593au
27
− 5.39206u
27
+ ··· + 21.5903a + 1.66090
−1.60474au
27
− 5.47431u
27
+ ··· + 15.1316a + 36.9788
a
4
=
−5.29398au
27
− 5.39206u
27
+ ··· + 22.9234a + 1.66090
−0.210350au
27
− 0.338787u
27
+ ··· + 1.35515a + 3.69028
a
3
=
−4.12142au
27
− 2.82430u
27
+ ··· + 11.6237a − 14.9834
−0.0843068u
27
+ 0.0893064u
26
+ ··· − 1.10305u + 0.0658279
a
2
=
−0.0154888au
27
− 1.33360u
27
+ ··· + 1.66131a − 4.83197
4.22120au
27
+ 4.90685u
27
+ ··· − 24.1466a − 20.2576
a
10
=
u
u
a
12
=
0.338787au
27
− 0.377991u
27
+ ··· − 3.69028a − 5.87532
3.16370au
27
+ 3.10520u
27
+ ··· − 21.1759a − 18.2093
a
9
=
2.82492au
27
+ 3.48319u
27
+ ··· − 17.4857a − 12.3340
3.16370au
27
+ 3.10520u
27
+ ··· − 21.1759a − 18.2093
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −
37274533074785
129063433504426
u
27
+
53621307092165
129063433504426
u
26
+ ··· −
660629047616669
129063433504426
u −
645502044434670
64531716752213
11
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
28
+ 14u
27
+ ··· + 2u + 1)
2
c
2
, c
8
(u
28
+ 2u
27
+ ··· + 2u + 1)
2
c
3
, c
4
, c
6
c
9
, c
11
, c
12
u
56
− 3u
55
+ ··· + 72u + 16
c
5
, c
10
(u
28
− u
27
+ ··· − 8u + 4)
2
c
7
(u
28
− 2u
27
+ ··· − 22u + 17)
2
12
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
28
+ 2y
27
+ ··· + 14y + 1)
2
c
2
, c
8
(y
28
+ 14y
27
+ ··· + 2y + 1)
2
c
3
, c
4
, c
6
c
9
, c
11
, c
12
y
56
− 43y
55
+ ··· + 736y + 256
c
5
, c
10
(y
28
− 15y
27
+ ··· − 88y + 16)
2
c
7
(y
28
− 10y
27
+ ··· − 246y + 289)
2
13
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910131 + 0.395689I
a = 0.577913 + 0.875653I
b = 1.83296 + 1.21612I
c = 0.614034 + 0.300820I
d = 0.313357 − 0.643423I
−1.72215 + 4.24816I −10.11355 − 6.97904I
u = −0.910131 + 0.395689I
a = −0.099220 − 1.209090I
b = −0.647282 − 0.740410I
c = −2.48219 − 1.67345I
d = −1.276980 + 0.186733I
−1.72215 + 4.24816I −10.11355 − 6.97904I
u = −0.910131 − 0.395689I
a = 0.577913 − 0.875653I
b = 1.83296 − 1.21612I
c = 0.614034 − 0.300820I
d = 0.313357 + 0.643423I
−1.72215 − 4.24816I −10.11355 + 6.97904I
u = −0.910131 − 0.395689I
a = −0.099220 + 1.209090I
b = −0.647282 + 0.740410I
c = −2.48219 + 1.67345I
d = −1.276980 − 0.186733I
−1.72215 − 4.24816I −10.11355 + 6.97904I
u = 0.017123 + 0.961380I
a = 1.23063 + 0.74510I
b = 1.77384 + 1.41897I
c = 0.433525 + 0.001501I
d = 1.306640 − 0.007988I
−4.61196 − 1.34593I −13.91932 + 0.66126I
u = 0.017123 + 0.961380I
a = −0.039967 + 0.519614I
b = −0.024073 − 0.839235I
c = 0.86981 − 1.28447I
d = −0.638546 + 0.533764I
−4.61196 − 1.34593I −13.91932 + 0.66126I
14
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.017123 − 0.961380I
a = 1.23063 − 0.74510I
b = 1.77384 − 1.41897I
c = 0.433525 − 0.001501I
d = 1.306640 + 0.007988I
−4.61196 + 1.34593I −13.91932 − 0.66126I
u = 0.017123 − 0.961380I
a = −0.039967 − 0.519614I
b = −0.024073 + 0.839235I
c = 0.86981 + 1.28447I
d = −0.638546 − 0.533764I
−4.61196 + 1.34593I −13.91932 − 0.66126I
u = 0.907099 + 0.252760I
a = −0.216978 − 1.161080I
b = 0.375545 − 0.694496I
c = 0.507453 + 0.124235I
d = 0.859190 − 0.455166I
−2.63794 − 3.28147I −13.2327 + 4.9939I
u = 0.907099 + 0.252760I
a = −1.21470 + 1.14721I
b = −0.465509 + 0.436668I
c = 0.605754 − 0.244512I
d = 0.419544 + 0.572998I
−2.63794 − 3.28147I −13.2327 + 4.9939I
u = 0.907099 − 0.252760I
a = −0.216978 + 1.161080I
b = 0.375545 + 0.694496I
c = 0.507453 − 0.124235I
d = 0.859190 + 0.455166I
−2.63794 + 3.28147I −13.2327 − 4.9939I
u = 0.907099 − 0.252760I
a = −1.21470 − 1.14721I
b = −0.465509 − 0.436668I
c = 0.605754 + 0.244512I
d = 0.419544 − 0.572998I
−2.63794 + 3.28147I −13.2327 − 4.9939I
15
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.387411 + 0.832689I
a = −1.036680 − 0.102202I
b = −1.48423 + 0.44182I
c = 0.443674 − 0.035750I
d = 1.239370 + 0.180444I
−1.43770 − 1.40144I −7.30053 + 1.74630I
u = −0.387411 + 0.832689I
a = 0.879401 + 0.727615I
b = 0.488283 − 0.578810I
c = 0.838293 + 0.678920I
d = −0.279611 − 0.583432I
−1.43770 − 1.40144I −7.30053 + 1.74630I
u = −0.387411 − 0.832689I
a = −1.036680 + 0.102202I
b = −1.48423 − 0.44182I
c = 0.443674 + 0.035750I
d = 1.239370 − 0.180444I
−1.43770 + 1.40144I −7.30053 − 1.74630I
u = −0.387411 − 0.832689I
a = 0.879401 − 0.727615I
b = 0.488283 + 0.578810I
c = 0.838293 − 0.678920I
d = −0.279611 + 0.583432I
−1.43770 + 1.40144I −7.30053 − 1.74630I
u = 0.387502 + 1.047530I
a = −0.847760 + 0.306836I
b = −0.585544 − 0.879512I
c = 0.669242 − 0.797085I
d = −0.382179 + 0.735842I
−3.70255 + 5.75423I −11.89302 − 5.96655I
u = 0.387502 + 1.047530I
a = 1.51403 − 0.04211I
b = 2.01322 + 0.50738I
c = 0.423917 + 0.033459I
d = 1.344350 − 0.185032I
−3.70255 + 5.75423I −11.89302 − 5.96655I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.387502 − 1.047530I
a = −0.847760 − 0.306836I
b = −0.585544 + 0.879512I
c = 0.669242 + 0.797085I
d = −0.382179 − 0.735842I
−3.70255 − 5.75423I −11.89302 + 5.96655I
u = 0.387502 − 1.047530I
a = 1.51403 + 0.04211I
b = 2.01322 − 0.50738I
c = 0.423917 − 0.033459I
d = 1.344350 + 0.185032I
−3.70255 − 5.75423I −11.89302 + 5.96655I
u = 0.802767 + 0.244916I
a = −0.844969 + 0.599643I
b = −2.28532 + 0.90013I
c = 0.647474 − 0.227775I
d = 0.374376 + 0.483492I
−2.32218 + 0.90628I −12.59768 + 1.67094I
u = 0.802767 + 0.244916I
a = −0.201313 − 0.924926I
b = 0.393435 − 0.504095I
c = −3.52128 + 1.70882I
d = −1.229860 − 0.111546I
−2.32218 + 0.90628I −12.59768 + 1.67094I
u = 0.802767 − 0.244916I
a = −0.844969 − 0.599643I
b = −2.28532 − 0.90013I
c = 0.647474 + 0.227775I
d = 0.374376 − 0.483492I
−2.32218 − 0.90628I −12.59768 − 1.67094I
u = 0.802767 − 0.244916I
a = −0.201313 + 0.924926I
b = 0.393435 + 0.504095I
c = −3.52128 − 1.70882I
d = −1.229860 + 0.111546I
−2.32218 − 0.90628I −12.59768 − 1.67094I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.147340 + 0.340892I
a = −0.098527 + 0.753717I
b = −1.25317 + 0.95465I
c = 0.467659 + 0.149971I
d = 0.938913 − 0.621780I
−5.81300 − 1.47542I −13.29345 + 0.59666I
u = 1.147340 + 0.340892I
a = −1.40778 + 1.44620I
b = −0.803773 + 0.724816I
c = −2.16974 + 0.89969I
d = −1.393270 − 0.163069I
−5.81300 − 1.47542I −13.29345 + 0.59666I
u = 1.147340 − 0.340892I
a = −0.098527 − 0.753717I
b = −1.25317 − 0.95465I
c = 0.467659 − 0.149971I
d = 0.938913 + 0.621780I
−5.81300 + 1.47542I −13.29345 − 0.59666I
u = 1.147340 − 0.340892I
a = −1.40778 − 1.44620I
b = −0.803773 − 0.724816I
c = −2.16974 − 0.89969I
d = −1.393270 + 0.163069I
−5.81300 + 1.47542I −13.29345 − 0.59666I
u = −0.611767 + 0.458091I
a = −0.302684 − 0.597006I
b = −0.775693 − 0.182328I
c = 0.484849 − 0.064041I
d = 1.027130 + 0.267751I
−0.887541 − 0.644142I −7.64602 − 1.30683I
u = −0.611767 + 0.458091I
a = 1.34953 + 1.04053I
b = 0.483743 − 0.045437I
c = 0.768846 + 0.328940I
d = 0.099411 − 0.470368I
−0.887541 − 0.644142I −7.64602 − 1.30683I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.611767 − 0.458091I
a = −0.302684 + 0.597006I
b = −0.775693 + 0.182328I
c = 0.484849 + 0.064041I
d = 1.027130 − 0.267751I
−0.887541 + 0.644142I −7.64602 + 1.30683I
u = −0.611767 − 0.458091I
a = 1.34953 − 1.04053I
b = 0.483743 + 0.045437I
c = 0.768846 − 0.328940I
d = 0.099411 + 0.470368I
−0.887541 + 0.644142I −7.64602 + 1.30683I
u = −1.175470 + 0.589984I
a = 0.078447 + 1.266970I
b = 1.13190 + 1.55275I
c = 0.517297 + 0.357727I
d = 0.307742 − 0.904345I
−3.88965 + 6.77427I −10.22594 − 4.95962I
u = −1.175470 + 0.589984I
a = −0.47336 − 1.86947I
b = −0.99093 − 1.35989I
c = −1.64648 − 1.15561I
d = −1.40691 + 0.28559I
−3.88965 + 6.77427I −10.22594 − 4.95962I
u = −1.175470 − 0.589984I
a = 0.078447 − 1.266970I
b = 1.13190 − 1.55275I
c = 0.517297 − 0.357727I
d = 0.307742 + 0.904345I
−3.88965 − 6.77427I −10.22594 + 4.95962I
u = −1.175470 − 0.589984I
a = −0.47336 + 1.86947I
b = −0.99093 + 1.35989I
c = −1.64648 + 1.15561I
d = −1.40691 − 0.28559I
−3.88965 − 6.77427I −10.22594 + 4.95962I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.312590 + 0.177484I
a = −0.275200 + 0.404719I
b = 0.835435 + 0.490381I
c = 0.462683 − 0.188428I
d = 0.853841 + 0.754977I
−9.90219 − 2.08114I −17.7960 + 2.7886I
u = −1.312590 + 0.177484I
a = 1.24331 + 1.82011I
b = 0.680869 + 1.168880I
c = −2.04845 − 0.36673I
d = −1.47301 + 0.08468I
−9.90219 − 2.08114I −17.7960 + 2.7886I
u = −1.312590 − 0.177484I
a = −0.275200 − 0.404719I
b = 0.835435 − 0.490381I
c = 0.462683 + 0.188428I
d = 0.853841 − 0.754977I
−9.90219 + 2.08114I −17.7960 − 2.7886I
u = −1.312590 − 0.177484I
a = 1.24331 − 1.82011I
b = 0.680869 − 1.168880I
c = −2.04845 + 0.36673I
d = −1.47301 − 0.08468I
−9.90219 + 2.08114I −17.7960 − 2.7886I
u = −1.262900 + 0.460239I
a = −0.130945 + 1.020930I
b = 0.93861 + 1.23552I
c = 0.442858 − 0.149307I
d = 1.027590 + 0.683591I
−8.61088 + 6.23266I −16.1498 − 4.3008I
u = −1.262900 + 0.460239I
a = 1.66593 + 1.52234I
b = 1.121790 + 0.782747I
c = −1.79085 − 0.88148I
d = −1.44949 + 0.22125I
−8.61088 + 6.23266I −16.1498 − 4.3008I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.262900 − 0.460239I
a = −0.130945 − 1.020930I
b = 0.93861 − 1.23552I
c = 0.442858 + 0.149307I
d = 1.027590 − 0.683591I
−8.61088 − 6.23266I −16.1498 + 4.3008I
u = −1.262900 − 0.460239I
a = 1.66593 − 1.52234I
b = 1.121790 − 0.782747I
c = −1.79085 + 0.88148I
d = −1.44949 − 0.22125I
−8.61088 − 6.23266I −16.1498 + 4.3008I
u = 1.280370 + 0.446560I
a = 0.170945 + 0.995242I
b = −0.89636 + 1.19996I
c = 0.496590 − 0.314623I
d = 0.436936 + 0.910395I
−8.68474 − 3.62399I −16.2087 + 2.7619I
u = 1.280370 + 0.446560I
a = 0.09808 − 2.06965I
b = 0.62342 − 1.54184I
c = −1.79070 + 0.83874I
d = −1.45797 − 0.21451I
−8.68474 − 3.62399I −16.2087 + 2.7619I
u = 1.280370 − 0.446560I
a = 0.170945 − 0.995242I
b = −0.89636 − 1.19996I
c = 0.496590 + 0.314623I
d = 0.436936 − 0.910395I
−8.68474 + 3.62399I −16.2087 − 2.7619I
u = 1.280370 − 0.446560I
a = 0.09808 + 2.06965I
b = 0.62342 + 1.54184I
c = −1.79070 − 0.83874I
d = −1.45797 + 0.21451I
−8.68474 + 3.62399I −16.2087 − 2.7619I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.376924 + 0.508425I
a = −1.15170 + 1.28261I
b = −0.324622 − 0.238361I
c = 0.01916 + 5.10656I
d = −0.999265 − 0.195824I
−3.51302 − 1.43304I −13.5823 + 4.9760I
u = 0.376924 + 0.508425I
a = −1.12316 + 1.43233I
b = −2.31200 + 2.51639I
c = 0.477044 + 0.034956I
d = 1.085050 − 0.152783I
−3.51302 − 1.43304I −13.5823 + 4.9760I
u = 0.376924 − 0.508425I
a = −1.15170 − 1.28261I
b = −0.324622 + 0.238361I
c = 0.01916 − 5.10656I
d = −0.999265 + 0.195824I
−3.51302 + 1.43304I −13.5823 − 4.9760I
u = 0.376924 − 0.508425I
a = −1.12316 − 1.43233I
b = −2.31200 − 2.51639I
c = 0.477044 − 0.034956I
d = 1.085050 + 0.152783I
−3.51302 + 1.43304I −13.5823 − 4.9760I
u = 1.241130 + 0.661367I
a = 0.02947 + 1.43015I
b = −0.98154 + 1.71054I
c = 0.493724 − 0.371241I
d = 0.293882 + 0.972896I
−6.41692 − 11.95450I −13.0412 + 8.3222I
u = 1.241130 + 0.661367I
a = 0.62725 − 2.04833I
b = 1.13700 − 1.53608I
c = −1.48418 + 1.08099I
d = −1.44024 − 0.32064I
−6.41692 − 11.95450I −13.0412 + 8.3222I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.241130 − 0.661367I
a = 0.02947 − 1.43015I
b = −0.98154 − 1.71054I
c = 0.493724 + 0.371241I
d = 0.293882 − 0.972896I
−6.41692 + 11.95450I −13.0412 − 8.3222I
u = 1.241130 − 0.661367I
a = 0.62725 + 2.04833I
b = 1.13700 + 1.53608I
c = −1.48418 − 1.08099I
d = −1.44024 + 0.32064I
−6.41692 + 11.95450I −13.0412 − 8.3222I
23
III. I
v
1
= ha, d, c − 1, b + v + 1, v
2
+ v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
1
=
0
−v − 1
a
6
=
1
0
a
7
=
1
0
a
8
=
1
v
a
4
=
1
0
a
3
=
1
0
a
2
=
v + 1
−v − 1
a
10
=
v
0
a
12
=
v
−v − 1
a
9
=
0
v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 7
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
− u + 1
c
2
, c
7
u
2
+ u + 1
c
3
, c
4
, c
5
c
6
, c
10
u
2
c
9
(u − 1)
2
c
11
, c
12
(u + 1)
2
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
2
+ y + 1
c
3
, c
4
, c
5
c
6
, c
10
y
2
c
9
, c
11
, c
12
(y − 1)
2
26
(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
27
IV. I
v
2
= hc, d − 1, b, a − v, v
2
+ v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
1
=
v
0
a
6
=
1
0
a
7
=
0
1
a
8
=
v + 1
1
a
4
=
1
−1
a
3
=
0
−1
a
2
=
v
v
a
10
=
v
0
a
12
=
v
0
a
9
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v − 11
28
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
7
u
2
− u + 1
c
3
, c
4
(u − 1)
2
c
5
, c
9
, c
10
c
11
, c
12
u
2
c
6
(u + 1)
2
c
8
u
2
+ u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
7
c
8
y
2
+ y + 1
c
3
, c
4
, c
6
(y − 1)
2
c
5
, c
9
, c
10
c
11
, c
12
y
2
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = −0.500000 + 0.866025I
b = 0
c = 0
d = 1.00000
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = −0.500000 − 0.866025I
b = 0
c = 0
d = 1.00000
−1.64493 − 2.02988I −9.00000 + 3.46410I
31
V. I
v
3
= ha, d − 1, c + a, b + 1, v + 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
−1
0
a
1
=
0
−1
a
6
=
1
0
a
7
=
0
1
a
8
=
0
1
a
4
=
1
−1
a
3
=
0
−1
a
2
=
0
−1
a
10
=
−1
0
a
12
=
−1
−1
a
9
=
0
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
10
u
c
3
, c
4
, c
9
u − 1
c
6
, c
11
, c
12
u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
7
, c
8
, c
10
y
c
3
, c
4
, c
6
c
9
, c
11
, c
12
y − 1
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
3
√
−1(vol +
√
−1CS) Cusp shape
v = −1.00000
a = 0
b = −1.00000
c = 0
d = 1.00000
−3.28987 −12.0000
35
VI. I
v
4
= hc, d − 1, a
2
v
2
− 2cav + v
2
a + c
2
− cv + v
2
, bv − 1i
(i) Arc colorings
a
5
=
1
0
a
11
=
v
0
a
1
=
a
b
a
6
=
1
0
a
7
=
0
1
a
8
=
a + 1
−ba + 1
a
4
=
1
−1
a
3
=
0
−1
a
2
=
a
b + a
a
10
=
v
0
a
12
=
a + v
b
a
9
=
−a
−b
(ii) Obstruction class = −1
(iii) Cusp Shapes = b
2
+ v
2
− 4a − 16
(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.
36
(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 −15.4701 − 3.5093I
37
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
28
+ 14u
27
+ ··· + 2u + 1)
2
· (u
36
+ 17u
35
+ ··· − 120u + 16)
c
2
, c
8
u(u
2
− u + 1)(u
2
+ u + 1)(u
28
+ 2u
27
+ ··· + 2u + 1)
2
· (u
36
+ u
35
+ ··· + 16u + 4)
c
3
, c
4
, c
9
u
2
(u − 1)
3
(u
36
− 5u
35
+ ··· + 3u − 1)(u
56
− 3u
55
+ ··· + 72u + 16)
c
5
, c
10
u
5
(u
28
− u
27
+ ··· − 8u + 4)
2
(u
36
+ 3u
35
+ ··· + 64u + 32)
c
6
, c
11
, c
12
u
2
(u + 1)
3
(u
36
− 5u
35
+ ··· + 3u − 1)(u
56
− 3u
55
+ ··· + 72u + 16)
c
7
u(u
2
− u + 1)(u
2
+ u + 1)(u
28
− 2u
27
+ ··· − 22u + 17)
2
· (u
36
− u
35
+ ··· − 104u + 1252)
38
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
28
+ 2y
27
+ ··· + 14y + 1)
2
· (y
36
+ 5y
35
+ ··· − 27936y + 256)
c
2
, c
8
y(y
2
+ y + 1)
2
(y
28
+ 14y
27
+ ··· + 2y + 1)
2
· (y
36
+ 17y
35
+ ··· − 120y + 16)
c
3
, c
4
, c
6
c
9
, c
11
, c
12
y
2
(y − 1)
3
(y
36
− 41y
35
+ ··· − 21y + 1)
· (y
56
− 43y
55
+ ··· + 736y + 256)
c
5
, c
10
y
5
(y
28
− 15y
27
+ ··· − 88y + 16)
2
· (y
36
− 15y
35
+ ··· − 1024y + 1024)
c
7
y(y
2
+ y + 1)
2
(y
28
− 10y
27
+ ··· − 246y + 289)
2
· (y
36
− 7y
35
+ ··· − 22103608y + 1567504)
39
