12a
0114
(K12a
0114
)
A knot diagram
1
Linearized knot diagam
3 5 8 2 12 9 4 10 7 1 6 11
Solving Sequence
3,8 2,4 5,10
9 1 11 7 6 12
c
3
c
4
c
8
c
1
c
10
c
7
c
6
c
12
c
2
, c
5
, c
9
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−2.04340 × 10
56
u
42
− 4.44323 × 10
56
u
41
+ ··· + 1.61592 × 10
58
d − 3.71857 × 10
57
,
− 7.08245 × 10
55
u
42
+ 2.18590 × 10
54
u
41
+ ··· + 3.23183 × 10
58
c + 1.16938 × 10
58
,
5.36649 × 10
55
u
42
+ 5.08814 × 10
55
u
41
+ ··· + 8.07958 × 10
57
b + 5.66596 × 10
56
,
1.77513 × 10
55
u
42
+ 8.50273 × 10
55
u
41
+ ··· + 3.23183 × 10
58
a − 3.36911 × 10
58
, u
43
+ 3u
42
+ ··· + 64u + 32i
I
u
2
= h−7.30862 × 10
18
au
34
− 1.42018 × 10
19
u
34
+ ··· − 3.97597 × 10
19
a + 1.41581 × 10
20
,
9.40640 × 10
18
au
34
− 1.54584 × 10
19
u
34
+ ··· − 4.98901 × 10
18
a + 5.34053 × 10
19
,
− 4.96996 × 10
18
au
34
+ 6.75491 × 10
18
u
34
+ ··· + 1.88128 × 10
19
a + 4.81090 × 10
19
,
− 5.09108 × 10
19
au
34
− 2.42015 × 10
19
u
34
+ ··· − 1.99866 × 10
19
a − 6.67500 × 10
19
, u
35
− u
34
+ ··· − 8u + 4i
I
v
1
= ha, d, c − v, b + 1, v
2
+ v + 1i
I
v
2
= hc, d + v + 1, b, a − 1, v
2
+ v + 1i
I
v
3
= ha, d + 1, c − a + 1, b + 1, v + 1i
I
v
4
= ha, a
2
d + c
2
v − 2da + 2ca + cv + d − 2c + a + v − 1, dv − 1,
c
2
v
2
+ 2cav + v
2
c − 2cv + a
2
+ av + v
2
− 2a − v + 1, b + 1i
* 5 irreducible components of dim
C
= 0, with total 118 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).
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−2.04 × 10
56
u
42
− 4.44 × 10
56
u
41
+ · · · + 1.62 × 10
58
d − 3.72 ×
10
57
, −7.08×10
55
u
42
+2.19× 10
54
u
41
+· · ·+ 3.23 ×10
58
c +1.17 ×10
58
, 5.37×
10
55
u
42
+ 5.09 × 10
55
u
41
+ · · · + 8.08 × 10
57
b + 5.67 × 10
56
, 1.78 × 10
55
u
42
+
8.50 × 10
55
u
41
+ · · · + 3.23 × 10
58
a − 3.37 × 10
58
, u
43
+ 3u
42
+ · · · + 64u + 32i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
−0.000549265u
42
− 0.00263093u
41
+ ··· − 0.260997u + 1.04248
−0.00664203u
42
− 0.00629753u
41
+ ··· − 0.502086u − 0.0701269
a
4
=
1
u
2
a
5
=
−0.000549265u
42
− 0.00263093u
41
+ ··· − 0.260997u + 1.04248
0.00262065u
42
+ 0.00310262u
41
+ ··· + 0.582583u + 0.101587
a
10
=
0.00219146u
42
− 0.0000676365u
41
+ ··· − 0.534860u − 0.361832
0.0126454u
42
+ 0.0274966u
41
+ ··· + 1.43259u + 0.230121
a
9
=
−0.00256786u
42
− 0.00870949u
41
+ ··· − 0.600995u − 0.445693
0.00192925u
42
+ 0.00197488u
41
+ ··· + 1.15804u − 0.0340955
a
1
=
−0.00719130u
42
− 0.00892846u
41
+ ··· − 0.763083u + 0.972348
−0.00664203u
42
− 0.00629753u
41
+ ··· − 0.502086u − 0.0701269
a
11
=
−0.0188325u
42
− 0.0568409u
41
+ ··· − 3.24630u − 0.805851
0.00514539u
42
+ 0.0189191u
41
+ ··· + 1.08816u + 0.00126900
a
7
=
u
u
3
+ u
a
6
=
0.0104540u
42
+ 0.0275643u
41
+ ··· + 1.96745u + 0.591953
0.00681841u
42
+ 0.0190556u
41
+ ··· + 1.34111u + 0.351645
a
12
=
−0.0163213u
42
− 0.0536714u
41
+ ··· − 3.05533u − 0.306156
−0.00108304u
42
+ 0.00839531u
41
+ ··· + 0.726103u + 0.359337
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.141642u
42
− 0.373966u
41
+ ··· − 18.4912u − 10.3634
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
43
+ 19u
42
+ ··· + 11u + 1
c
2
, c
4
, c
6
c
9
u
43
− 5u
42
+ ··· − 5u + 1
c
3
, c
7
u
43
+ 3u
42
+ ··· + 64u + 32
c
5
, c
11
u
43
+ u
42
+ ··· + 8u + 4
c
10
, c
12
u
43
+ 15u
42
+ ··· + 88u − 16
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
43
+ 21y
42
+ ··· − 117y − 1
c
2
, c
4
, c
6
c
9
y
43
− 19y
42
+ ··· + 11y − 1
c
3
, c
7
y
43
+ 15y
42
+ ··· − 1024y − 1024
c
5
, c
11
y
43
+ 15y
42
+ ··· + 88y − 16
c
10
, c
12
y
43
+ 27y
42
+ ··· + 18208y − 256
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.083173 + 0.999400I
a = 0.72843 + 1.47481I
b = −0.236924 − 0.796663I
c = −0.811251 + 0.169551I
d = −0.636862 + 0.547617I
−0.05445 − 4.88438I −6.23953 + 8.26907I
u = 0.083173 − 0.999400I
a = 0.72843 − 1.47481I
b = −0.236924 + 0.796663I
c = −0.811251 − 0.169551I
d = −0.636862 − 0.547617I
−0.05445 + 4.88438I −6.23953 − 8.26907I
u = 0.853926 + 0.430623I
a = 0.481539 + 0.101502I
b = −0.801143 + 0.828451I
c = −0.357924 + 1.150660I
d = −0.673379 + 0.656482I
−2.38574 + 3.27178I −9.17419 − 4.94523I
u = 0.853926 − 0.430623I
a = 0.481539 − 0.101502I
b = −0.801143 − 0.828451I
c = −0.357924 − 1.150660I
d = −0.673379 − 0.656482I
−2.38574 − 3.27178I −9.17419 + 4.94523I
u = −1.033880 + 0.177916I
a = 0.555689 + 0.233546I
b = 0.132893 + 0.680601I
c = −0.014816 − 0.660848I
d = −0.874552 − 0.822608I
2.18783 − 1.46576I −4.39540 − 0.53246I
u = −1.033880 − 0.177916I
a = 0.555689 − 0.233546I
b = 0.132893 − 0.680601I
c = −0.014816 + 0.660848I
d = −0.874552 + 0.822608I
2.18783 + 1.46576I −4.39540 + 0.53246I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.073470 + 0.049653I
a = 0.530276 − 0.204737I
b = −0.009584 − 0.812539I
c = −0.043846 − 0.754897I
d = 0.609459 − 1.066160I
2.38615 − 4.03105I −4.49490 + 6.55598I
u = 1.073470 − 0.049653I
a = 0.530276 + 0.204737I
b = −0.009584 + 0.812539I
c = −0.043846 + 0.754897I
d = 0.609459 + 1.066160I
2.38615 + 4.03105I −4.49490 − 6.55598I
u = 0.118650 + 1.091750I
a = 0.665477 − 1.093120I
b = 0.093039 + 0.792480I
c = 0.726561 − 0.006259I
d = 0.418220 + 0.792440I
3.02575 + 1.21250I −0.81942 − 2.86814I
u = 0.118650 − 1.091750I
a = 0.665477 + 1.093120I
b = 0.093039 − 0.792480I
c = 0.726561 + 0.006259I
d = 0.418220 − 0.792440I
3.02575 − 1.21250I −0.81942 + 2.86814I
u = −0.359241 + 0.820253I
a = 0.870329 + 0.688965I
b = 0.226430 − 0.328392I
c = −0.437362 − 0.084500I
d = −0.689763 + 0.770087I
−0.40821 + 1.76300I −5.68682 − 2.17312I
u = −0.359241 − 0.820253I
a = 0.870329 − 0.688965I
b = 0.226430 + 0.328392I
c = −0.437362 + 0.084500I
d = −0.689763 − 0.770087I
−0.40821 − 1.76300I −5.68682 + 2.17312I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.910628 + 0.648287I
a = 0.449928 − 0.096871I
b = −1.05448 − 1.02817I
c = 0.235042 + 1.296410I
d = 1.27987 + 0.63257I
−6.78885 − 5.21532I −15.4874 + 4.9651I
u = −0.910628 − 0.648287I
a = 0.449928 + 0.096871I
b = −1.05448 + 1.02817I
c = 0.235042 − 1.296410I
d = 1.27987 − 0.63257I
−6.78885 + 5.21532I −15.4874 − 4.9651I
u = −0.653698 + 0.530431I
a = 0.474331 − 0.068978I
b = −1.043170 − 0.639245I
c = 0.48378 + 1.37044I
d = 0.747514 + 0.161233I
−4.07070 + 1.09789I −13.44053 − 1.40134I
u = −0.653698 − 0.530431I
a = 0.474331 + 0.068978I
b = −1.043170 + 0.639245I
c = 0.48378 − 1.37044I
d = 0.747514 − 0.161233I
−4.07070 − 1.09789I −13.44053 + 1.40134I
u = −0.576447 + 1.031310I
a = −0.28667 − 1.83591I
b = −0.89021 + 1.15174I
c = 1.218550 + 0.182083I
d = 1.38400 − 0.81935I
−2.58520 + 3.71825I −9.87585 − 4.37570I
u = −0.576447 − 1.031310I
a = −0.28667 + 1.83591I
b = −0.89021 − 1.15174I
c = 1.218550 − 0.182083I
d = 1.38400 + 0.81935I
−2.58520 − 3.71825I −9.87585 + 4.37570I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.098260 + 0.588414I
a = 0.444497 + 0.121481I
b = −0.86814 + 1.25108I
c = −0.139972 + 1.214140I
d = −1.27290 + 1.25814I
−0.56681 + 5.57701I −7.91552 − 3.90122I
u = 1.098260 − 0.588414I
a = 0.444497 − 0.121481I
b = −0.86814 − 1.25108I
c = −0.139972 − 1.214140I
d = −1.27290 − 1.25814I
−0.56681 − 5.57701I −7.91552 + 3.90122I
u = 0.614898 + 1.118930I
a = −0.31373 + 1.65536I
b = −0.89319 − 1.29520I
c = −1.225970 + 0.124533I
d = −1.14513 − 1.12900I
−0.28043 − 8.69625I −6.61034 + 7.94559I
u = 0.614898 − 1.118930I
a = −0.31373 − 1.65536I
b = −0.89319 + 1.29520I
c = −1.225970 − 0.124533I
d = −1.14513 + 1.12900I
−0.28043 + 8.69625I −6.61034 − 7.94559I
u = −1.109210 + 0.657844I
a = 0.436604 − 0.117557I
b = −0.95891 − 1.30595I
c = 0.122977 + 1.250300I
d = 1.51579 + 1.23538I
−1.67059 − 11.25340I −9.77881 + 8.46956I
u = −1.109210 − 0.657844I
a = 0.436604 + 0.117557I
b = −0.95891 + 1.30595I
c = 0.122977 − 1.250300I
d = 1.51579 − 1.23538I
−1.67059 + 11.25340I −9.77881 − 8.46956I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.724262 + 1.081360I
a = −0.51124 − 1.64089I
b = −1.06752 + 1.30329I
c = 1.288450 + 0.124239I
d = 1.50850 − 1.46270I
−5.40682 + 11.27400I −13.1483 − 8.7166I
u = −0.724262 − 1.081360I
a = −0.51124 + 1.64089I
b = −1.06752 − 1.30329I
c = 1.288450 − 0.124239I
d = 1.50850 + 1.46270I
−5.40682 − 11.27400I −13.1483 + 8.7166I
u = 0.460216 + 1.229810I
a = 0.522317 − 0.781774I
b = 0.614727 + 0.723655I
c = 0.680228 − 0.245304I
d = 0.59476 + 1.37160I
6.33622 − 1.07199I −1.20689 − 1.13710I
u = 0.460216 − 1.229810I
a = 0.522317 + 0.781774I
b = 0.614727 − 0.723655I
c = 0.680228 + 0.245304I
d = 0.59476 − 1.37160I
6.33622 + 1.07199I −1.20689 + 1.13710I
u = −0.548223 + 1.211710I
a = 0.521334 + 0.726495I
b = 0.704438 − 0.632367I
c = −0.651538 − 0.286578I
d = −0.78605 + 1.43368I
5.47474 + 6.91618I −2.74163 − 4.17963I
u = −0.548223 − 1.211710I
a = 0.521334 − 0.726495I
b = 0.704438 + 0.632367I
c = −0.651538 + 0.286578I
d = −0.78605 − 1.43368I
5.47474 − 6.91618I −2.74163 + 4.17963I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.168268 + 1.366960I
a = 0.219555 − 1.223470I
b = −0.108972 + 1.358650I
c = 0.988755 − 0.041994I
d = −0.203397 + 0.128416I
7.94604 + 2.88039I −2.40290 − 2.87135I
u = −0.168268 − 1.366960I
a = 0.219555 + 1.223470I
b = −0.108972 − 1.358650I
c = 0.988755 + 0.041994I
d = −0.203397 − 0.128416I
7.94604 − 2.88039I −2.40290 + 2.87135I
u = −0.620383
a = 0.635515
b = −0.328934
c = 0.530212
d = −0.190197
−1.07886 −8.06050
u = 0.256404 + 1.367180I
a = 0.141032 + 1.272300I
b = −0.23242 − 1.41922I
c = −1.033590 − 0.023839I
d = 0.177430 − 0.162620I
7.59831 − 8.92002I −3.37196 + 8.11870I
u = 0.256404 − 1.367180I
a = 0.141032 − 1.272300I
b = −0.23242 + 1.41922I
c = −1.033590 + 0.023839I
d = 0.177430 + 0.162620I
7.59831 + 8.92002I −3.37196 − 8.11870I
u = −0.170237 + 0.574659I
a = 1.248050 + 0.407611I
b = −0.0202482 − 0.1305180I
c = −0.199203 + 0.094247I
d = −0.368251 + 0.658395I
−0.37797 + 1.66748I −2.59196 − 2.78569I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.170237 − 0.574659I
a = 1.248050 − 0.407611I
b = −0.0202482 + 0.1305180I
c = −0.199203 − 0.094247I
d = −0.368251 − 0.658395I
−0.37797 − 1.66748I −2.59196 + 2.78569I
u = 0.766704 + 1.185140I
a = −0.48729 + 1.47075I
b = −1.07182 − 1.47408I
c = −1.289280 + 0.070307I
d = −1.19144 − 1.85032I
1.37987 − 12.30340I −8.00000 + 6.92563I
u = 0.766704 − 1.185140I
a = −0.48729 − 1.47075I
b = −1.07182 + 1.47408I
c = −1.289280 − 0.070307I
d = −1.19144 + 1.85032I
1.37987 + 12.30340I −8.00000 − 6.92563I
u = −0.80758 + 1.17123I
a = −0.54459 − 1.45657I
b = −1.13832 + 1.47599I
c = 1.308330 + 0.069788I
d = 1.33632 − 1.98675I
0.0200 + 18.1731I −8.00000 − 11.31467I
u = −0.80758 − 1.17123I
a = −0.54459 + 1.45657I
b = −1.13832 − 1.47599I
c = 1.308330 − 0.069788I
d = 1.33632 + 1.98675I
0.0200 − 18.1731I −8.00000 + 11.31467I
u = 0.546169 + 0.144967I
a = 0.536373 + 0.039062I
b = −0.711997 + 0.230827I
c = −1.113030 + 0.718056I
d = −0.135046 + 0.121945I
−2.99504 + 2.52590I −15.3721 − 4.9240I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.546169 − 0.144967I
a = 0.536373 − 0.039062I
b = −0.711997 − 0.230827I
c = −1.113030 − 0.718056I
d = −0.135046 − 0.121945I
−2.99504 − 2.52590I −15.3721 + 4.9240I
12
II. I
u
2
= h−7.31 × 10
18
au
34
− 1.42 × 10
19
u
34
+ · · · − 3.98 × 10
19
a + 1.42 ×
10
20
, 9.41×10
18
au
34
−1.55×10
19
u
34
+· · ·−4.99×10
18
a+5.34×10
19
, −4.97×
10
18
au
34
+6.75×10
18
u
34
+· · · + 1.88 × 10
19
a+4.81×10
19
, −5.09×10
19
au
34
−
2.42 × 10
19
u
34
+ · · · − 2.00 × 10
19
a − 6.67 × 10
19
, u
35
− u
34
+ · · · − 8u + 4i
(i) Arc colorings
a
3
=
1
0
a
8
=
0
u
a
2
=
a
0.410603au
34
− 0.558070u
34
+ ··· − 1.55425a − 3.97461
a
4
=
1
u
2
a
5
=
a
−0.410603au
34
+ 0.558070u
34
+ ··· + 1.55425a + 3.97461
a
10
=
−0.388564au
34
+ 0.638564u
34
+ ··· + 0.206088a − 2.20609
0.301908au
34
+ 0.586656u
34
+ ··· + 1.64241a − 5.84850
a
9
=
−0.690471au
34
+ 0.638564u
34
+ ··· − 1.43632a − 2.20609
−0.238077au
34
+ 0.586656u
34
+ ··· + 3.02481a − 5.84850
a
1
=
0.410603au
34
− 0.558070u
34
+ ··· − 0.554254a − 3.97461
0.410603au
34
− 0.558070u
34
+ ··· − 1.55425a − 3.97461
a
11
=
−0.683790au
34
+ 0.400487u
34
+ ··· − 6.75397a + 0.818722
−0.546198au
34
+ 0.348579u
34
+ ··· − 0.00923237a − 2.82369
a
7
=
u
u
3
+ u
a
6
=
0.690471au
34
− 0.0519078u
34
+ ··· + 1.43632a − 3.64241
0.238077au
34
+ 0.348579u
34
+ ··· − 3.02481a − 2.82369
a
12
=
−1.36731au
34
+ 0.710589u
34
+ ··· + 1.55907a − 3.21365
0.360100au
34
− 0.905750u
34
+ ··· + 0.00164563a − 1.70543
(ii) Obstruction class = −1
(iii) Cusp Shapes =
22672372767718895251
6052032860907500938
u
34
−
26762652226596727431
6052032860907500938
u
33
+ ··· +
270510416900889983975
6052032860907500938
u −
78654406032569267566
3026016430453750469
13
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
u
70
+ 39u
69
+ ··· + 2336u + 256
c
2
, c
6
u
70
− 3u
69
+ ··· − 56u + 16
c
3
(u
35
− u
34
+ ··· − 8u + 4)
2
c
4
, c
9
u
70
+ 3u
69
+ ··· + 56u + 16
c
5
(u
35
+ 2u
34
+ ··· − 2u
2
+ 1)
2
c
7
(u
35
+ u
34
+ ··· − 8u − 4)
2
c
10
, c
12
(u
35
− 12u
34
+ ··· + 4u + 1)
2
c
11
(u
35
− 2u
34
+ ··· + 2u
2
− 1)
2
14
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
70
− 19y
69
+ ··· − 1270272y + 65536
c
2
, c
4
, c
6
c
9
y
70
− 39y
69
+ ··· − 2336y + 256
c
3
, c
7
(y
35
+ 15y
34
+ ··· − 72y − 16)
2
c
5
, c
11
(y
35
+ 12y
34
+ ··· + 4y − 1)
2
c
10
, c
12
(y
35
+ 24y
34
+ ··· + 40y − 1)
2
15
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.207372 + 0.975503I
a = 0.810975 + 0.957053I
b = 0.135002 − 0.589507I
c = 0.10620 + 1.73197I
d = 0.532443 − 1.191670I
0.32534 − 1.86508I −3.98051 + 2.70414I
u = −0.207372 + 0.975503I
a = 0.431780 − 0.018192I
b = −1.71157 − 0.25557I
c = −0.606330 − 0.009498I
d = −0.554711 + 0.846584I
0.32534 − 1.86508I −3.98051 + 2.70414I
u = −0.207372 − 0.975503I
a = 0.810975 − 0.957053I
b = 0.135002 + 0.589507I
c = 0.10620 − 1.73197I
d = 0.532443 + 1.191670I
0.32534 + 1.86508I −3.98051 − 2.70414I
u = −0.207372 − 0.975503I
a = 0.431780 + 0.018192I
b = −1.71157 + 0.25557I
c = −0.606330 + 0.009498I
d = −0.554711 − 0.846584I
0.32534 + 1.86508I −3.98051 − 2.70414I
u = 0.325740 + 0.904391I
a = 0.825073 − 0.782270I
b = 0.235348 + 0.437813I
c = −1.032100 + 0.325792I
d = −1.254530 + 0.220950I
−0.525136 + 0.811264I −5.97406 + 0.21615I
u = 0.325740 + 0.904391I
a = 0.40485 + 2.13305I
b = −0.630839 − 0.827296I
c = 0.511473 − 0.076007I
d = 0.656946 + 0.846832I
−0.525136 + 0.811264I −5.97406 + 0.21615I
16
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.325740 − 0.904391I
a = 0.825073 + 0.782270I
b = 0.235348 − 0.437813I
c = −1.032100 − 0.325792I
d = −1.254530 − 0.220950I
−0.525136 − 0.811264I −5.97406 − 0.21615I
u = 0.325740 − 0.904391I
a = 0.40485 − 2.13305I
b = −0.630839 + 0.827296I
c = 0.511473 + 0.076007I
d = 0.656946 − 0.846832I
−0.525136 − 0.811264I −5.97406 − 0.21615I
u = 0.365087 + 0.973537I
a = 0.740296 − 0.786236I
b = 0.321145 + 0.492436I
c = −0.16022 + 1.66799I
d = −0.929376 − 1.041310I
−0.19294 − 3.49535I −5.62111 + 3.75014I
u = 0.365087 + 0.973537I
a = 0.430751 + 0.032296I
b = −1.68235 + 0.45298I
c = 0.551911 − 0.122902I
d = 0.673544 + 0.926090I
−0.19294 − 3.49535I −5.62111 + 3.75014I
u = 0.365087 − 0.973537I
a = 0.740296 + 0.786236I
b = 0.321145 − 0.492436I
c = −0.16022 − 1.66799I
d = −0.929376 + 1.041310I
−0.19294 + 3.49535I −5.62111 − 3.75014I
u = 0.365087 − 0.973537I
a = 0.430751 − 0.032296I
b = −1.68235 − 0.45298I
c = 0.551911 + 0.122902I
d = 0.673544 − 0.926090I
−0.19294 + 3.49535I −5.62111 − 3.75014I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.655999 + 0.827108I
a = 0.439925 − 0.062584I
b = −1.40758 − 0.77847I
c = 1.336620 + 0.280068I
d = 2.26895 − 0.64367I
−7.12278 + 2.53588I −15.8469 − 3.8333I
u = −0.655999 + 0.827108I
a = −0.70483 − 2.22687I
b = −1.10847 + 0.92180I
c = 0.25079 + 1.50290I
d = 1.330420 − 0.248626I
−7.12278 + 2.53588I −15.8469 − 3.8333I
u = −0.655999 − 0.827108I
a = 0.439925 + 0.062584I
b = −1.40758 + 0.77847I
c = 1.336620 − 0.280068I
d = 2.26895 + 0.64367I
−7.12278 − 2.53588I −15.8469 + 3.8333I
u = −0.655999 − 0.827108I
a = −0.70483 + 2.22687I
b = −1.10847 − 0.92180I
c = 0.25079 − 1.50290I
d = 1.330420 + 0.248626I
−7.12278 − 2.53588I −15.8469 + 3.8333I
u = 0.705852 + 0.611410I
a = 0.700829 − 0.414305I
b = 0.387427 − 0.071708I
c = −0.37932 + 1.38368I
d = −0.960020 + 0.179730I
−3.90189 + 1.16771I −12.59463 − 0.48242I
u = 0.705852 + 0.611410I
a = 0.462699 + 0.073809I
b = −1.113740 + 0.744755I
c = 0.263314 − 0.329674I
d = 1.065300 + 0.322317I
−3.90189 + 1.16771I −12.59463 − 0.48242I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.705852 − 0.611410I
a = 0.700829 + 0.414305I
b = 0.387427 + 0.071708I
c = −0.37932 − 1.38368I
d = −0.960020 − 0.179730I
−3.90189 − 1.16771I −12.59463 + 0.48242I
u = 0.705852 − 0.611410I
a = 0.462699 − 0.073809I
b = −1.113740 − 0.744755I
c = 0.263314 + 0.329674I
d = 1.065300 − 0.322317I
−3.90189 − 1.16771I −12.59463 + 0.48242I
u = −1.045080 + 0.368116I
a = 0.564228 + 0.293694I
b = 0.371258 + 0.572713I
c = 0.195454 + 1.068160I
d = 0.561597 + 1.186680I
1.47991 − 0.62379I −5.11442 − 0.32782I
u = −1.045080 + 0.368116I
a = 0.475227 − 0.134196I
b = −0.597470 − 1.044360I
c = −0.144309 − 0.598841I
d = −1.296590 − 0.561094I
1.47991 − 0.62379I −5.11442 − 0.32782I
u = −1.045080 − 0.368116I
a = 0.564228 − 0.293694I
b = 0.371258 − 0.572713I
c = 0.195454 − 1.068160I
d = 0.561597 − 1.186680I
1.47991 + 0.62379I −5.11442 + 0.32782I
u = −1.045080 − 0.368116I
a = 0.475227 + 0.134196I
b = −0.597470 + 1.044360I
c = −0.144309 + 0.598841I
d = −1.296590 + 0.561094I
1.47991 + 0.62379I −5.11442 + 0.32782I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713294 + 0.504864I
a = 0.476506 − 0.077725I
b = −0.979215 − 0.696369I
c = 1.60039 + 0.36375I
d = 3.52020 − 0.13811I
−3.98776 − 3.19845I −13.06265 + 3.08489I
u = −0.713294 + 0.504864I
a = −2.05407 − 2.74671I
b = −1.32519 + 0.54852I
c = 0.454246 + 1.297780I
d = 0.749391 + 0.298357I
−3.98776 − 3.19845I −13.06265 + 3.08489I
u = −0.713294 − 0.504864I
a = 0.476506 + 0.077725I
b = −0.979215 + 0.696369I
c = 1.60039 − 0.36375I
d = 3.52020 + 0.13811I
−3.98776 + 3.19845I −13.06265 − 3.08489I
u = −0.713294 − 0.504864I
a = −2.05407 + 2.74671I
b = −1.32519 − 0.54852I
c = 0.454246 − 1.297780I
d = 0.749391 − 0.298357I
−3.98776 + 3.19845I −13.06265 − 3.08489I
u = −0.413724 + 1.080130I
a = 0.635679 + 0.786411I
b = 0.448358 − 0.581931I
c = 1.102290 + 0.168328I
d = 0.919931 − 0.368351I
1.87781 + 3.59908I −3.00767 − 3.96847I
u = −0.413724 + 1.080130I
a = 0.05598 − 1.74978I
b = −0.637860 + 1.120970I
c = −0.608484 − 0.182028I
d = −0.669357 + 1.086300I
1.87781 + 3.59908I −3.00767 − 3.96847I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.413724 − 1.080130I
a = 0.635679 − 0.786411I
b = 0.448358 + 0.581931I
c = 1.102290 − 0.168328I
d = 0.919931 + 0.368351I
1.87781 − 3.59908I −3.00767 + 3.96847I
u = −0.413724 − 1.080130I
a = 0.05598 + 1.74978I
b = −0.637860 − 1.120970I
c = −0.608484 + 0.182028I
d = −0.669357 − 1.086300I
1.87781 − 3.59908I −3.00767 + 3.96847I
u = 0.511698 + 1.037850I
a = 0.422963 + 0.044547I
b = −1.73049 + 0.65920I
c = −1.175210 + 0.189303I
d = −1.233950 − 0.610623I
−1.31903 − 2.68874I −7.41111 + 2.89622I
u = 0.511698 + 1.037850I
a = −0.14705 + 1.84591I
b = −0.797818 − 1.122820I
c = −0.15037 + 1.59324I
d = −1.39944 − 0.99690I
−1.31903 − 2.68874I −7.41111 + 2.89622I
u = 0.511698 − 1.037850I
a = 0.422963 − 0.044547I
b = −1.73049 − 0.65920I
c = −1.175210 − 0.189303I
d = −1.233950 + 0.610623I
−1.31903 + 2.68874I −7.41111 − 2.89622I
u = 0.511698 − 1.037850I
a = −0.14705 − 1.84591I
b = −0.797818 + 1.122820I
c = −0.15037 − 1.59324I
d = −1.39944 + 0.99690I
−1.31903 + 2.68874I −7.41111 − 2.89622I
21
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.060110 + 0.482223I
a = 0.558487 − 0.331278I
b = 0.511960 − 0.509925I
c = −0.177857 + 1.152110I
d = −0.91001 + 1.19977I
0.71766 + 6.15318I −6.72324 − 5.00692I
u = 1.060110 + 0.482223I
a = 0.459428 + 0.125654I
b = −0.744123 + 1.135600I
c = 0.218845 − 0.580562I
d = 1.54044 − 0.37557I
0.71766 + 6.15318I −6.72324 − 5.00692I
u = 1.060110 − 0.482223I
a = 0.558487 + 0.331278I
b = 0.511960 + 0.509925I
c = −0.177857 − 1.152110I
d = −0.91001 − 1.19977I
0.71766 − 6.15318I −6.72324 + 5.00692I
u = 1.060110 − 0.482223I
a = 0.459428 − 0.125654I
b = −0.744123 − 1.135600I
c = 0.218845 + 0.580562I
d = 1.54044 + 0.37557I
0.71766 − 6.15318I −6.72324 + 5.00692I
u = 0.600323 + 1.020000I
a = 0.612638 − 0.649478I
b = 0.610249 + 0.377168I
c = −1.235580 + 0.183942I
d = −1.47241 − 0.87989I
−2.63440 − 6.20108I −10.04876 + 5.89177I
u = 0.600323 + 1.020000I
a = −0.34236 + 1.84493I
b = −0.92937 − 1.14986I
c = 0.536169 − 0.282721I
d = 1.01188 + 1.08387I
−2.63440 − 6.20108I −10.04876 + 5.89177I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.600323 − 1.020000I
a = 0.612638 + 0.649478I
b = 0.610249 − 0.377168I
c = −1.235580 − 0.183942I
d = −1.47241 + 0.87989I
−2.63440 + 6.20108I −10.04876 − 5.89177I
u = 0.600323 − 1.020000I
a = −0.34236 − 1.84493I
b = −0.92937 + 1.14986I
c = 0.536169 + 0.282721I
d = 1.01188 − 1.08387I
−2.63440 + 6.20108I −10.04876 − 5.89177I
u = −0.597289 + 1.062760I
a = 0.419111 − 0.051606I
b = −1.73974 − 0.78162I
c = 1.225120 + 0.159128I
d = 1.31473 − 0.95581I
−2.31683 + 8.24742I −9.43055 − 7.59916I
u = −0.597289 + 1.062760I
a = −0.31098 − 1.76298I
b = −0.90087 + 1.20697I
c = 0.14026 + 1.55817I
d = 1.67431 − 0.90584I
−2.31683 + 8.24742I −9.43055 − 7.59916I
u = −0.597289 − 1.062760I
a = 0.419111 + 0.051606I
b = −1.73974 + 0.78162I
c = 1.225120 − 0.159128I
d = 1.31473 + 0.95581I
−2.31683 − 8.24742I −9.43055 + 7.59916I
u = −0.597289 − 1.062760I
a = −0.31098 + 1.76298I
b = −0.90087 − 1.20697I
c = 0.14026 − 1.55817I
d = 1.67431 + 0.90584I
−2.31683 − 8.24742I −9.43055 + 7.59916I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.329730 + 0.664757I
a = 0.460522 + 0.030841I
b = −1.328710 + 0.336382I
c = −1.115640 + 0.653338I
d = −1.93080 + 0.91172I
−3.05354 − 1.15463I −8.48725 + 5.51426I
u = 0.329730 + 0.664757I
a = 0.74666 + 3.40319I
b = −0.802172 − 0.526207I
c = −0.38956 + 1.80556I
d = −0.530382 − 0.456050I
−3.05354 − 1.15463I −8.48725 + 5.51426I
u = 0.329730 − 0.664757I
a = 0.460522 − 0.030841I
b = −1.328710 − 0.336382I
c = −1.115640 − 0.653338I
d = −1.93080 − 0.91172I
−3.05354 + 1.15463I −8.48725 − 5.51426I
u = 0.329730 − 0.664757I
a = 0.74666 − 3.40319I
b = −0.802172 + 0.526207I
c = −0.38956 − 1.80556I
d = −0.530382 + 0.456050I
−3.05354 + 1.15463I −8.48725 − 5.51426I
u = −0.047497 + 1.362920I
a = 0.362035 + 1.073040I
b = 0.184947 − 1.201000I
c = 0.928348 − 0.073039I
d = −0.187009 + 0.492551I
8.17684 + 3.01120I −1.89563 − 2.75790I
u = −0.047497 + 1.362920I
a = 0.310277 − 1.144270I
b = 0.055453 + 1.268740I
c = −0.884845 − 0.104862I
d = 0.148418 + 0.751573I
8.17684 + 3.01120I −1.89563 − 2.75790I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.047497 − 1.362920I
a = 0.362035 − 1.073040I
b = 0.184947 + 1.201000I
c = 0.928348 + 0.073039I
d = −0.187009 − 0.492551I
8.17684 − 3.01120I −1.89563 + 2.75790I
u = −0.047497 − 1.362920I
a = 0.310277 + 1.144270I
b = 0.055453 − 1.268740I
c = −0.884845 + 0.104862I
d = 0.148418 − 0.751573I
8.17684 − 3.01120I −1.89563 + 2.75790I
u = −0.642257 + 1.206250I
a = 0.508332 + 0.676520I
b = 0.808390 − 0.548182I
c = 1.229650 + 0.076088I
d = 0.86410 − 1.39481I
4.15268 + 6.65019I −3.95665 − 3.46663I
u = −0.642257 + 1.206250I
a = −0.31655 − 1.51284I
b = −0.88153 + 1.43440I
c = −0.632084 − 0.333620I
d = −1.00048 + 1.50587I
4.15268 + 6.65019I −3.95665 − 3.46663I
u = −0.642257 − 1.206250I
a = 0.508332 − 0.676520I
b = 0.808390 + 0.548182I
c = 1.229650 − 0.076088I
d = 0.86410 + 1.39481I
4.15268 − 6.65019I −3.95665 + 3.46663I
u = −0.642257 − 1.206250I
a = −0.31655 + 1.51284I
b = −0.88153 − 1.43440I
c = −0.632084 + 0.333620I
d = −1.00048 − 1.50587I
4.15268 − 6.65019I −3.95665 + 3.46663I
25
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.626561
a = 0.632339 + 0.026645I
b = −0.330383 + 0.076980I
c = 0.527297 + 0.122861I
d = −0.189194 + 0.064927I
−1.07873 −7.97520
u = −0.626561
a = 0.632339 − 0.026645I
b = −0.330383 − 0.076980I
c = 0.527297 − 0.122861I
d = −0.189194 − 0.064927I
−1.07873 −7.97520
u = 0.532829 + 0.309500I
a = 0.506148 + 0.049944I
b = −0.877913 + 0.369405I
c = −1.91148 + 0.59223I
d = −4.11672 + 0.79704I
−3.17896 − 1.46996I −12.94917 + 3.34118I
u = 0.532829 + 0.309500I
a = −3.92552 + 4.75017I
b = −1.201790 − 0.276044I
c = −0.93087 + 1.23399I
d = −0.327876 + 0.108379I
−3.17896 − 1.46996I −12.94917 + 3.34118I
u = 0.532829 − 0.309500I
a = 0.506148 − 0.049944I
b = −0.877913 − 0.369405I
c = −1.91148 − 0.59223I
d = −4.11672 − 0.79704I
−3.17896 + 1.46996I −12.94917 − 3.34118I
u = 0.532829 − 0.309500I
a = −3.92552 − 4.75017I
b = −1.201790 + 0.276044I
c = −0.93087 − 1.23399I
d = −0.327876 − 0.108379I
−3.17896 + 1.46996I −12.94917 − 3.34118I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704423 + 1.193170I
a = 0.502880 − 0.645463I
b = 0.867511 + 0.479891I
c = −1.260670 + 0.075283I
d = −1.03264 − 1.61588I
2.99525 − 12.51090I −5.90812 + 8.16035I
u = 0.704423 + 1.193170I
a = −0.40526 + 1.50005I
b = −0.97787 − 1.45117I
c = 0.616545 − 0.363068I
d = 1.16289 + 1.51848I
2.99525 − 12.51090I −5.90812 + 8.16035I
u = 0.704423 − 1.193170I
a = 0.502880 + 0.645463I
b = 0.867511 − 0.479891I
c = −1.260670 − 0.075283I
d = −1.03264 + 1.61588I
2.99525 + 12.51090I −5.90812 − 8.16035I
u = 0.704423 − 1.193170I
a = −0.40526 − 1.50005I
b = −0.97787 + 1.45117I
c = 0.616545 + 0.363068I
d = 1.16289 − 1.51848I
2.99525 + 12.51090I −5.90812 − 8.16035I
27
III. I
v
1
= ha, d, c − v, b + 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
2
=
0
−1
a
4
=
1
0
a
5
=
1
1
a
10
=
v
0
a
9
=
v
0
a
1
=
−1
−1
a
11
=
2v
v
a
7
=
v
0
a
6
=
v
0
a
12
=
2v + 1
v
(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
(u − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
u
2
c
4
(u + 1)
2
c
5
, c
12
u
2
+ u + 1
c
10
, c
11
u
2
− u + 1
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
(y − 1)
2
c
3
, c
6
, c
7
c
8
, c
9
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
1
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 0
b = −1.00000
c = −0.500000 + 0.866025I
d = 0
−1.64493 + 2.02988I −9.00000 − 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = −1.00000
c = −0.500000 − 0.866025I
d = 0
−1.64493 − 2.02988I −9.00000 + 3.46410I
31
IV. I
v
2
= hc, d + v + 1, b, a − 1, v
2
+ v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
2
=
1
0
a
4
=
1
0
a
5
=
1
0
a
10
=
0
−v − 1
a
9
=
v
−v − 1
a
1
=
1
0
a
11
=
v + 1
−v − 1
a
7
=
v
0
a
6
=
0
v + 1
a
12
=
v + 1
−v
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v − 7
32
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
u
2
c
5
, c
10
u
2
− u + 1
c
6
, c
8
(u − 1)
2
c
9
(u + 1)
2
c
11
, c
12
u
2
+ u + 1
33
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
7
y
2
c
5
, c
10
, c
11
c
12
y
2
+ y + 1
c
6
, c
8
, c
9
(y − 1)
2
34
(vi) Complex Volumes and Cusp Shapes
Solutions to I
v
2
√
−1(vol +
√
−1CS) Cusp shape
v = −0.500000 + 0.866025I
a = 1.00000
b = 0
c = 0
d = −0.500000 − 0.866025I
−1.64493 − 2.02988I −9.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 1.00000
b = 0
c = 0
d = −0.500000 + 0.866025I
−1.64493 + 2.02988I −9.00000 − 3.46410I
35
V. I
v
3
= ha, d + 1, c − a + 1, b + 1, v + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
−1
0
a
2
=
0
−1
a
4
=
1
0
a
5
=
1
1
a
10
=
−1
−1
a
9
=
−2
−1
a
1
=
−1
−1
a
11
=
−1
−1
a
7
=
−1
0
a
6
=
1
1
a
12
=
−1
−1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −12
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
6
c
8
u − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
u
c
4
, c
9
u + 1
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
y − 1
c
3
, c
5
, c
7
c
10
, c
11
, c
12
y
38
(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 = −1.00000
d = −1.00000
−3.28987 −12.0000
39
VI. I
v
4
= ha, c
2
v + cv + · · · + a − 1, dv − 1, c
2
v
2
+ v
2
c + · · · − 2a + 1, b + 1i
(i) Arc colorings
a
3
=
1
0
a
8
=
v
0
a
2
=
0
−1
a
4
=
1
0
a
5
=
1
1
a
10
=
c
−c
2
v − cv + 2c − v + 1
a
9
=
c + v
−c
2
v − cv + 2c − v + 1
a
1
=
−1
−1
a
11
=
c
2
v + cv + v − 1
c
a
7
=
v
0
a
6
=
−c
c
2
v + cv − 2c + v − 1
a
12
=
−c
3
v + c
2
+ v − 1
−c
3
v − c
2
v + c
2
− cv + c − 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = −2c
3
v − 7c
2
v + 3c
2
− 7cv + v
2
+ 7c − 5v − 12
(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.
40
(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 −12.47435 + 3.07723I
41
VII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
8
u
2
(u − 1)
3
(u
43
+ 19u
42
+ ··· + 11u + 1)
c
2
, c
6
u
2
(u − 1)
3
(u
43
− 5u
42
+ ··· − 5u + 1)
c
3
, c
7
u
5
(u
43
+ 3u
42
+ ··· + 64u + 32)
c
4
, c
9
u
2
(u + 1)
3
(u
43
− 5u
42
+ ··· − 5u + 1)
c
5
, c
11
u(u
2
− u + 1)(u
2
+ u + 1)(u
43
+ u
42
+ ··· + 8u + 4)
c
10
u(u
2
− u + 1)
2
(u
43
+ 15u
42
+ ··· + 88u − 16)
c
12
u(u
2
+ u + 1)
2
(u
43
+ 15u
42
+ ··· + 88u − 16)
42
VIII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
8
y
2
(y − 1)
3
(y
43
+ 21y
42
+ ··· − 117y − 1)
c
2
, c
4
, c
6
c
9
y
2
(y − 1)
3
(y
43
− 19y
42
+ ··· + 11y − 1)
c
3
, c
7
y
5
(y
43
+ 15y
42
+ ··· − 1024y − 1024)
c
5
, c
11
y(y
2
+ y + 1)
2
(y
43
+ 15y
42
+ ··· + 88y − 16)
c
10
, c
12
y(y
2
+ y + 1)
2
(y
43
+ 27y
42
+ ··· + 18208y − 256)
43
