12a
0033
(K12a
0033
)
A knot diagram
1
Linearized knot diagam
3 5 6 9 2 12 1 11 4 8 10 7
Solving Sequence
4,9
5
7,10,12
1 6 3 2 11 8
c
4
c
9
c
12
c
6
c
3
c
2
c
11
c
8
c
1
, c
5
, c
7
, c
10
Ideals for irreducible components
2
of X
par
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
u
1
= ⟨4.19179 × 10
162
u
76
− 8.99312 × 10
162
u
75
+ ··· + 5.13128 × 10
164
d + 1.74805 × 10
165
,
5.20225 × 10
162
u
76
− 1.09357 × 10
163
u
75
+ ··· + 5.13128 × 10
164
c + 2.30253 × 10
165
,
5.03182 × 10
182
u
76
− 1.22724 × 10
183
u
75
+ ··· + 1.08760 × 10
185
b + 3.35895 × 10
185
,
− 3.61857 × 10
182
u
76
+ 6.18392 × 10
182
u
75
+ ··· + 5.43799 × 10
184
a − 1.83798 × 10
184
,
u
77
− 2u
76
+ ··· − 2560u
2
− 512⟩
I
u
2
= ⟨−43u
3
a
2
− 6a
2
u
2
− 37u
3
a − 62a
2
u − 58u
2
a + 38u
3
+ 36a
2
− 55au + 2u
2
+ 71d − 78a − 74u − 12,
− 47u
3
a
2
+ 5a
2
u
2
− 52u
3
a − 43a
2
u − 70u
2
a − 8u
3
+ 41a
2
− 37au + 22u
2
+ 71c − 6a − 104u + 10,
− 24u
3
a
2
− 5a
2
u
2
− 19u
3
a − 28a
2
u − u
2
a + 8u
3
+ 30a
2
− 34au − 22u
2
+ 71b − 65a − 38u − 10,
− 2u
3
a
2
− u
3
a + a
3
− 2a
2
u − 5u
2
a − u
3
+ 2a
2
− au + u
2
− u, u
4
+ u
2
− u + 1⟩
I
u
3
= ⟨−75u
5
a
2
+ 125u
5
a + ··· − 31a + 44, −55u
5
a
2
+ 167u
5
a + ··· + 143a − 28,
− 58u
5
a
2
+ 59u
5
a + ··· − 30a + 28,
− 2u
5
a
2
− 2u
4
a
2
+ 2u
5
a − 4u
3
a
2
+ u
4
a + u
5
− 4a
2
u
2
+ 3u
3
a + a
3
− 4a
2
u − 2u
2
a − 4a
2
+ 2au + 2a,
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1⟩
I
v
1
= ⟨a, d − v + 1, c + a, b + v −1, v
2
− v + 1⟩
I
v
2
= ⟨a, d, c − v, b − v − 1, v
2
+ v + 1⟩
I
v
3
= ⟨a, d + 1, c + a − 1, b − 1, v − 1⟩
I
v
4
= ⟨a, −b
2
v −bv + d + 2b −v + 1, −b
2
av −bav + cb + 2ba −av + a − 1,
v
2
c − bav + v
2
b − cv −av + v
2
+ c + 2a − 2v, b
2
v
2
+ v
2
b − 2bv + v
2
− v + 1⟩
* 6 irreducible components of dim
C
= 0, with total 112 representations.
* 1 irreducible components of dim
C
= 1
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
2
I.
I
u
1
= ⟨4.19×10
162
u
76
−8.99×10
162
u
75
+· · ·+5.13×10
164
d+1.75×10
165
, 5.20×
10
162
u
76
−1.09×10
163
u
75
+· · · + 5.13×10
164
c+2.30×10
165
, 5.03×10
182
u
76
−
1.23 × 10
183
u
75
+ · · · + 1.09 × 10
185
b + 3.36 × 10
185
, −3.62 × 10
182
u
76
+ 6.18 ×
10
182
u
75
+ · · · + 5.44 × 10
184
a − 1.84 × 10
184
, u
77
− 2u
76
+ · · · − 2560u
2
− 512⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
7
=
0.00665423u
76
− 0.0113717u
75
+ ··· − 8.65830u + 0.337989
−0.00462654u
76
+ 0.0112840u
75
+ ··· + 6.23600u − 3.08841
a
10
=
u
u
a
12
=
−0.0101383u
76
+ 0.0213118u
75
+ ··· + 12.1450u − 4.48724
−0.00816908u
76
+ 0.0175261u
75
+ ··· + 11.0464u − 3.40665
a
1
=
−0.0125394u
76
+ 0.0245545u
75
+ ··· + 16.0108u − 3.02234
−0.00622485u
76
+ 0.0135037u
75
+ ··· + 7.88286u − 2.23172
a
6
=
0.0108390u
76
− 0.0188168u
75
+ ··· − 14.5481u + 0.522142
−0.00170046u
76
+ 0.00573767u
75
+ ··· + 1.46268u − 2.50020
a
3
=
−0.00903125u
76
+ 0.0210962u
75
+ ··· + 7.69784u − 4.39652
−0.00575546u
76
+ 0.0105565u
75
+ ··· + 7.63073u + 1.82138
a
2
=
−0.00761038u
76
+ 0.0196600u
75
+ ··· + 4.69111u − 7.77114
−0.00621954u
76
+ 0.0118805u
75
+ ··· + 6.90325u + 1.10173
a
11
=
−0.00891820u
76
+ 0.0191719u
75
+ ··· + 11.1367u − 4.56543
−0.00694897u
76
+ 0.0153862u
75
+ ··· + 10.0381u − 3.48484
a
8
=
0.00196923u
76
− 0.00378574u
75
+ ··· − 1.09859u + 1.08059
−0.00694897u
76
+ 0.0153862u
75
+ ··· + 10.0381u − 3.48484
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.0221138u
76
− 0.0478032u
75
+ ··· − 21.6023u − 0.388088
3
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
77
+ 36u
76
+ ··· + 216u − 16
c
2
, c
5
u
77
+ 2u
76
+ ··· + 27u
2
− 4
c
3
u
77
− 2u
76
+ ··· + 351912u − 66564
c
4
, c
9
u
77
− 2u
76
+ ··· − 2560u
2
− 512
c
6
, c
7
, c
12
u
77
− 8u
76
+ ··· − 72u − 16
c
8
, c
10
u
77
+ 8u
76
+ ··· − 72u − 16
c
11
u
77
− 34u
76
+ ··· + 1568u − 256
4
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
77
+ 12y
76
+ ··· + 84256y −256
c
2
, c
5
y
77
+ 36y
76
+ ··· + 216y −16
c
3
y
77
− 12y
76
+ ··· + 120020616504y −4430766096
c
4
, c
9
y
77
+ 30y
76
+ ··· − 2621440y −262144
c
6
, c
7
, c
12
y
77
− 74y
76
+ ··· + 7712y −256
c
8
, c
10
y
77
− 34y
76
+ ··· + 1568y −256
c
11
y
77
+ 26y
76
+ ··· + 3416576y −65536
5
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.508886 + 0.845592I
a = 1.118510 + 0.861761I
b = 0.504405 − 0.239677I
c = −0.82230 − 2.15378I
d = −1.077350 − 0.552668I
2.40889 + 4.27390I 3.74115 − 6.44221I
u = 0.508886 − 0.845592I
a = 1.118510 − 0.861761I
b = 0.504405 + 0.239677I
c = −0.82230 + 2.15378I
d = −1.077350 + 0.552668I
2.40889 − 4.27390I 3.74115 + 6.44221I
u = −0.848496 + 0.585068I
a = −0.008580 + 0.439129I
b = 0.103075 − 0.222508I
c = 0.749137 − 0.747672I
d = 1.049330 + 0.534087I
3.78378 + 2.11500I 7.65464 − 1.99007I
u = −0.848496 − 0.585068I
a = −0.008580 − 0.439129I
b = 0.103075 + 0.222508I
c = 0.749137 + 0.747672I
d = 1.049330 − 0.534087I
3.78378 − 2.11500I 7.65464 + 1.99007I
u = −0.990280 + 0.319237I
a = −1.79246 + 0.10308I
b = −0.675932 − 1.005350I
c = −1.016130 + 0.043329I
d = −1.111790 − 0.533215I
−2.98745 + 0.86657I 0
u = −0.990280 − 0.319237I
a = −1.79246 − 0.10308I
b = −0.675932 + 1.005350I
c = −1.016130 − 0.043329I
d = −1.111790 + 0.533215I
−2.98745 − 0.86657I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.617221 + 0.733532I
a = −0.619707 + 0.764557I
b = −0.277695 − 0.242708I
c = 0.75499 − 1.66880I
d = 1.079400 − 0.162408I
4.09446 + 0.35704I 8.04104 + 0.70386I
u = −0.617221 − 0.733532I
a = −0.619707 − 0.764557I
b = −0.277695 + 0.242708I
c = 0.75499 + 1.66880I
d = 1.079400 + 0.162408I
4.09446 − 0.35704I 8.04104 − 0.70386I
u = 0.517431 + 0.792256I
a = −0.602670 + 0.058164I
b = −1.312620 + 0.060155I
c = −0.799858 − 0.461927I
d = −2.05780 − 0.08517I
2.57405 − 0.08416I 4.54592 − 2.74373I
u = 0.517431 − 0.792256I
a = −0.602670 − 0.058164I
b = −1.312620 − 0.060155I
c = −0.799858 + 0.461927I
d = −2.05780 + 0.08517I
2.57405 + 0.08416I 4.54592 + 2.74373I
u = −0.082487 + 0.936352I
a = −0.948613 + 0.464331I
b = −0.836303 + 0.719975I
c = 0.066226 + 0.663106I
d = −0.575224 + 0.771574I
−1.72016 + 1.41215I −1.65188 − 3.77223I
u = −0.082487 − 0.936352I
a = −0.948613 − 0.464331I
b = −0.836303 − 0.719975I
c = 0.066226 − 0.663106I
d = −0.575224 − 0.771574I
−1.72016 − 1.41215I −1.65188 + 3.77223I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.582500 + 0.889546I
a = 0.372525 + 0.042062I
b = 0.984114 − 0.079699I
c = 0.620752 − 0.807952I
d = 1.88365 − 0.53487I
3.62010 − 5.07823I 6.10660 + 7.37918I
u = −0.582500 − 0.889546I
a = 0.372525 − 0.042062I
b = 0.984114 + 0.079699I
c = 0.620752 + 0.807952I
d = 1.88365 + 0.53487I
3.62010 + 5.07823I 6.10660 − 7.37918I
u = 0.228301 + 1.040040I
a = −0.13810 − 1.60777I
b = −1.48108 − 2.66829I
c = −0.126234 + 0.944655I
d = 0.516753 + 0.893507I
−3.92825 − 1.69884I −4.65730 + 2.32962I
u = 0.228301 − 1.040040I
a = −0.13810 + 1.60777I
b = −1.48108 + 2.66829I
c = −0.126234 − 0.944655I
d = 0.516753 − 0.893507I
−3.92825 + 1.69884I −4.65730 − 2.32962I
u = 0.782003 + 0.468875I
a = −2.36435 − 2.24948I
b = −1.06894 + 1.62874I
c = −0.310023 − 0.749893I
d = −0.722438 + 0.469371I
0.65497 − 3.51390I 3.54011 + 4.44478I
u = 0.782003 − 0.468875I
a = −2.36435 + 2.24948I
b = −1.06894 − 1.62874I
c = −0.310023 + 0.749893I
d = −0.722438 − 0.469371I
0.65497 + 3.51390I 3.54011 − 4.44478I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.374962 + 1.039940I
a = 0.00241 − 1.81691I
b = 1.04564 − 2.79506I
c = −0.054535 + 1.153860I
d = −0.648190 + 1.006590I
−3.38837 − 3.78470I 0
u = −0.374962 − 1.039940I
a = 0.00241 + 1.81691I
b = 1.04564 + 2.79506I
c = −0.054535 − 1.153860I
d = −0.648190 − 1.006590I
−3.38837 + 3.78470I 0
u = 0.965284 + 0.548957I
a = −0.183189 + 0.297060I
b = −0.297598 − 0.221943I
c = −0.820096 − 0.337678I
d = −1.051710 + 0.877929I
1.81197 − 6.85619I 0
u = 0.965284 − 0.548957I
a = −0.183189 − 0.297060I
b = −0.297598 + 0.221943I
c = −0.820096 + 0.337678I
d = −1.051710 − 0.877929I
1.81197 + 6.85619I 0
u = 0.288832 + 1.092220I
a = 1.30645 + 0.68041I
b = 1.045540 + 0.686079I
c = −0.140070 + 1.099610I
d = 0.513316 + 0.990185I
−4.40655 + 2.61636I 0
u = 0.288832 − 1.092220I
a = 1.30645 − 0.68041I
b = 1.045540 − 0.686079I
c = −0.140070 − 1.099610I
d = 0.513316 − 0.990185I
−4.40655 − 2.61636I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.815552 + 0.276755I
a = −0.393181 + 0.675339I
b = −0.097483 + 0.217571I
c = 0.125990 − 0.372709I
d = −0.310498 + 0.604570I
−0.065597 − 0.205341I 1.21551 + 1.86968I
u = 0.815552 − 0.276755I
a = −0.393181 − 0.675339I
b = −0.097483 − 0.217571I
c = 0.125990 + 0.372709I
d = −0.310498 − 0.604570I
−0.065597 + 0.205341I 1.21551 − 1.86968I
u = −0.008067 + 1.164640I
a = 0.831879 + 0.802027I
b = 0.838657 + 0.822115I
c = −0.537680 + 0.563389I
d = 0.297322 + 0.581051I
−4.97078 − 4.99360I 0
u = −0.008067 − 1.164640I
a = 0.831879 − 0.802027I
b = 0.838657 − 0.822115I
c = −0.537680 − 0.563389I
d = 0.297322 − 0.581051I
−4.97078 + 4.99360I 0
u = 1.177360 + 0.140655I
a = 1.271130 − 0.073091I
b = 0.52624 − 1.59073I
c = 0.914208 − 0.465491I
d = 0.97456 − 1.22806I
−6.72367 + 2.38646I 0
u = 1.177360 − 0.140655I
a = 1.271130 + 0.073091I
b = 0.52624 + 1.59073I
c = 0.914208 + 0.465491I
d = 0.97456 + 1.22806I
−6.72367 − 2.38646I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.516220 + 1.088150I
a = −0.25335 + 1.54951I
b = −2.64287 + 2.22003I
c = −0.099851 − 0.875419I
d = 1.071770 − 0.719904I
−2.28765 − 3.11487I 0
u = −0.516220 − 1.088150I
a = −0.25335 − 1.54951I
b = −2.64287 − 2.22003I
c = −0.099851 + 0.875419I
d = 1.071770 + 0.719904I
−2.28765 + 3.11487I 0
u = 1.143240 + 0.423905I
a = 1.84398 − 0.15315I
b = 1.05407 − 1.18141I
c = 1.391370 − 0.013506I
d = 1.59551 − 0.65628I
−5.54743 − 5.38085I 0
u = 1.143240 − 0.423905I
a = 1.84398 + 0.15315I
b = 1.05407 + 1.18141I
c = 1.391370 + 0.013506I
d = 1.59551 + 0.65628I
−5.54743 + 5.38085I 0
u = 1.079500 + 0.575143I
a = −1.83354 − 0.15848I
b = −0.99311 + 2.16498I
c = −1.062600 − 0.002710I
d = −1.21557 + 1.20650I
−1.00971 − 5.65602I 0
u = 1.079500 − 0.575143I
a = −1.83354 + 0.15848I
b = −0.99311 − 2.16498I
c = −1.062600 + 0.002710I
d = −1.21557 − 1.20650I
−1.00971 + 5.65602I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.163010 + 0.411297I
a = 0.932646 − 0.077718I
b = 0.61556 + 2.18561I
c = 0.600063 + 0.450923I
d = 0.71184 + 1.55150I
−5.58247 + 2.79509I 0
u = −1.163010 − 0.411297I
a = 0.932646 + 0.077718I
b = 0.61556 − 2.18561I
c = 0.600063 − 0.450923I
d = 0.71184 − 1.55150I
−5.58247 − 2.79509I 0
u = 0.530613 + 1.137340I
a = −0.105063 + 0.441883I
b = −0.477698 + 0.273175I
c = 0.250279 − 0.980703I
d = −0.925423 − 0.856938I
−2.68982 + 5.10175I 0
u = 0.530613 − 1.137340I
a = −0.105063 − 0.441883I
b = −0.477698 − 0.273175I
c = 0.250279 + 0.980703I
d = −0.925423 + 0.856938I
−2.68982 − 5.10175I 0
u = 0.601554 + 1.104580I
a = −0.00922 + 1.88522I
b = 2.21114 + 2.74600I
c = 0.048393 − 1.187080I
d = −1.17229 − 1.05265I
−1.29562 + 8.75795I 0
u = 0.601554 − 1.104580I
a = −0.00922 − 1.88522I
b = 2.21114 − 2.74600I
c = 0.048393 + 1.187080I
d = −1.17229 + 1.05265I
−1.29562 − 8.75795I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.666542 + 1.084300I
a = −0.037947 + 0.186829I
b = 0.412925 − 0.063735I
c = 0.116654 − 1.386120I
d = 1.37592 − 1.25181I
2.21245 − 7.79054I 0
u = −0.666542 − 1.084300I
a = −0.037947 − 0.186829I
b = 0.412925 + 0.063735I
c = 0.116654 + 1.386120I
d = 1.37592 + 1.25181I
2.21245 + 7.79054I 0
u = −0.620529 + 0.325559I
a = 1.77807 − 5.56934I
b = 1.16767 + 1.32481I
c = −0.359051 − 0.919317I
d = 0.376140 + 0.228285I
−0.115678 − 1.341920I 2.41782 + 1.83708I
u = −0.620529 − 0.325559I
a = 1.77807 + 5.56934I
b = 1.16767 − 1.32481I
c = −0.359051 + 0.919317I
d = 0.376140 − 0.228285I
−0.115678 + 1.341920I 2.41782 − 1.83708I
u = −1.161000 + 0.625559I
a = 1.85681 + 0.28553I
b = 1.03264 + 2.35339I
c = 1.348640 + 0.218279I
d = 1.44939 + 1.44440I
−3.39852 + 10.69180I 0
u = −1.161000 − 0.625559I
a = 1.85681 − 0.28553I
b = 1.03264 − 2.35339I
c = 1.348640 − 0.218279I
d = 1.44939 − 1.44440I
−3.39852 − 10.69180I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.423653 + 0.527399I
a = −1.74593 − 0.28445I
b = −0.556628 + 0.090443I
c = −0.424220 + 0.542119I
d = −0.623453 + 0.419471I
−1.92120 + 0.81846I −4.58107 + 0.87681I
u = −0.423653 − 0.527399I
a = −1.74593 + 0.28445I
b = −0.556628 − 0.090443I
c = −0.424220 − 0.542119I
d = −0.623453 − 0.419471I
−1.92120 − 0.81846I −4.58107 − 0.87681I
u = −0.662834 + 0.003253I
a = 0.226784 + 0.451173I
b = −0.577746 + 0.442113I
c = −0.680090 − 0.132286I
d = −0.197422 + 0.184363I
−0.58945 + 2.77011I 1.22579 − 6.61866I
u = −0.662834 − 0.003253I
a = 0.226784 − 0.451173I
b = −0.577746 − 0.442113I
c = −0.680090 + 0.132286I
d = −0.197422 − 0.184363I
−0.58945 − 2.77011I 1.22579 + 6.61866I
u = 0.703559 + 1.143570I
a = 0.181516 + 0.233850I
b = −0.233401 − 0.053613I
c = 0.04116 − 1.61209I
d = −1.22614 − 1.51356I
−0.07596 + 12.98220I 0
u = 0.703559 − 1.143570I
a = 0.181516 − 0.233850I
b = −0.233401 + 0.053613I
c = 0.04116 + 1.61209I
d = −1.22614 + 1.51356I
−0.07596 − 12.98220I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.624723 + 1.201920I
a = −0.19734 − 2.12904I
b = 0.63726 − 2.75540I
c = −0.33021 + 1.80553I
d = −0.96291 + 1.48151I
−5.70918 − 6.67323I 0
u = −0.624723 − 1.201920I
a = −0.19734 + 2.12904I
b = 0.63726 + 2.75540I
c = −0.33021 − 1.80553I
d = −0.96291 − 1.48151I
−5.70918 + 6.67323I 0
u = 0.127875 + 0.624992I
a = 0.97951 + 3.07905I
b = 0.341044 + 0.403757I
c = 0.03373 − 2.60509I
d = −0.194927 − 0.524028I
0.93270 − 1.56780I −1.99036 − 0.81001I
u = 0.127875 − 0.624992I
a = 0.97951 − 3.07905I
b = 0.341044 − 0.403757I
c = 0.03373 + 2.60509I
d = −0.194927 + 0.524028I
0.93270 + 1.56780I −1.99036 + 0.81001I
u = −0.115044 + 1.357830I
a = 0.565753 − 0.402137I
b = −1.143390 − 0.603699I
c = −1.139500 + 0.344978I
d = −0.179723 + 0.294069I
−9.14335 − 2.92995I 0
u = −0.115044 − 1.357830I
a = 0.565753 + 0.402137I
b = −1.143390 + 0.603699I
c = −1.139500 − 0.344978I
d = −0.179723 − 0.294069I
−9.14335 + 2.92995I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.518606 + 1.307430I
a = 0.40096 − 2.01546I
b = −0.57151 − 2.58245I
c = −0.09494 + 1.89349I
d = 0.61008 + 1.60156I
−10.68990 + 3.50430I 0
u = 0.518606 − 1.307430I
a = 0.40096 + 2.01546I
b = −0.57151 + 2.58245I
c = −0.09494 − 1.89349I
d = 0.61008 − 1.60156I
−10.68990 − 3.50430I 0
u = 0.758435 + 1.184640I
a = −0.64579 + 2.27951I
b = 1.18564 + 3.27514I
c = 0.10967 − 1.88745I
d = −1.17616 − 1.81573I
−2.97939 + 12.30500I 0
u = 0.758435 − 1.184640I
a = −0.64579 − 2.27951I
b = 1.18564 − 3.27514I
c = 0.10967 + 1.88745I
d = −1.17616 + 1.81573I
−2.97939 − 12.30500I 0
u = 0.69467 + 1.24791I
a = 0.21709 − 2.24890I
b = −0.58292 − 2.80554I
c = 0.45261 + 2.01847I
d = 1.09745 + 1.65272I
−8.2281 + 11.9338I 0
u = 0.69467 − 1.24791I
a = 0.21709 + 2.24890I
b = −0.58292 + 2.80554I
c = 0.45261 − 2.01847I
d = 1.09745 − 1.65272I
−8.2281 − 11.9338I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.043030 + 0.567805I
a = −0.248115 + 0.756603I
b = −0.40870 + 1.85697I
c = −0.182345 + 1.003610I
d = −0.42920 + 2.02878I
0.91327 + 2.30980I −2.35018 − 5.72620I
u = 0.043030 − 0.567805I
a = −0.248115 − 0.756603I
b = −0.40870 − 1.85697I
c = −0.182345 − 1.003610I
d = −0.42920 − 2.02878I
0.91327 − 2.30980I −2.35018 + 5.72620I
u = −0.68480 + 1.26233I
a = 0.77022 + 1.88079I
b = −1.05613 + 2.67355I
c = −0.52883 − 1.71234I
d = 0.71570 − 1.66643I
−8.38263 − 9.37788I 0
u = −0.68480 − 1.26233I
a = 0.77022 − 1.88079I
b = −1.05613 − 2.67355I
c = −0.52883 + 1.71234I
d = 0.71570 + 1.66643I
−8.38263 + 9.37788I 0
u = −0.80648 + 1.20827I
a = 0.81681 + 2.38600I
b = −0.91530 + 3.40016I
c = −0.12117 − 2.11842I
d = 1.18116 − 2.06331I
−5.3240 − 17.7550I 0
u = −0.80648 − 1.20827I
a = 0.81681 − 2.38600I
b = −0.91530 − 3.40016I
c = −0.12117 + 2.11842I
d = 1.18116 + 2.06331I
−5.3240 + 17.7550I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.00564 + 1.45291I
a = −0.851063 − 0.822170I
b = 0.636678 − 1.070480I
c = 1.36039 + 0.81823I
d = 0.427830 + 0.688849I
−13.06970 − 1.34685I 0
u = −0.00564 − 1.45291I
a = −0.851063 + 0.822170I
b = 0.636678 + 1.070480I
c = 1.36039 − 0.81823I
d = 0.427830 − 0.688849I
−13.06970 + 1.34685I 0
u = 0.22004 + 1.44810I
a = −0.929164 − 0.066704I
b = 0.729786 − 0.060469I
c = 1.50177 + 0.01187I
d = 0.470629 − 0.058111I
−12.6554 + 7.5654I 0
u = 0.22004 − 1.44810I
a = −0.929164 + 0.066704I
b = 0.729786 + 0.060469I
c = 1.50177 − 0.01187I
d = 0.470629 + 0.058111I
−12.6554 − 7.5654I 0
u = 0.499413
a = −1.13138
b = 0.269950
c = 1.32737
d = −0.0790890
1.20722 9.11790
18
II. I
u
2
=
⟨−43a
2
u
3
−37au
3
+· · ·−78a−12, −47a
2
u
3
−52au
3
+· · ·−6a+10, −24a
2
u
3
−
19au
3
+ · · · − 65a − 10, −2u
3
a
2
− u
3
a + · · · + a
3
+ 2a
2
, u
4
+ u
2
− u + 1⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
7
=
a
0.338028a
2
u
3
+ 0.267606au
3
+ ··· + 0.915493a + 0.140845
a
10
=
u
u
a
12
=
0.661972a
2
u
3
+ 0.732394au
3
+ ··· + 0.0845070a − 0.140845
0.605634a
2
u
3
+ 0.521127au
3
+ ··· + 1.09859a + 0.169014
a
1
=
u
u
a
6
=
u
3
u
3
+ u
a
3
=
−u
3
+ u
2
+ 1
−u
3
+ u
2
− u + 1
a
2
=
−u
3
+ u
2
− u + 1
u
2
− u + 1
a
11
=
0.338028a
2
u
3
+ 0.267606au
3
+ ··· − 0.0845070a + 0.140845
0.281690a
2
u
3
+ 0.0563380au
3
+ ··· + 0.929577a + 0.450704
a
8
=
−0.0563380a
2
u
3
− 0.211268au
3
+ ··· + 1.01408a + 0.309859
0.281690a
2
u
3
+ 0.0563380au
3
+ ··· + 0.929577a + 0.450704
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u
2
+ 2
19
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
c
2
, c
4
, c
5
c
9
(u
4
+ u
2
− u + 1)
3
c
3
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
c
6
, c
7
, c
8
c
10
, c
12
u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1
c
11
u
12
− 8u
11
+ ··· + 5u + 1
20
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
c
2
, c
4
, c
5
c
9
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
c
3
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
c
6
, c
7
, c
8
c
10
, c
12
y
12
− 8y
11
+ ··· + 5y + 1
c
11
y
12
− 8y
11
+ ··· − 31y + 1
21
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −1.89198 − 0.26082I
b = −3.05256 + 0.49971I
c = −1.42862 − 0.19451I
d = −2.88321 + 0.32177I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 + 0.585652I
a = −0.0684280 + 0.0496997I
b = 0.375309 + 0.506052I
c = 0.571089 + 0.621740I
d = 0.814495 + 0.406682I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 + 0.585652I
a = 0.25679 + 2.03371I
b = 0.973637 + 0.816821I
c = −0.23731 − 1.59853I
d = −0.729744 − 0.077176I
0.98010 + 1.39709I 3.77019 − 3.86736I
u = 0.547424 − 0.585652I
a = −1.89198 + 0.26082I
b = −3.05256 − 0.49971I
c = −1.42862 + 0.19451I
d = −2.88321 − 0.32177I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.547424 − 0.585652I
a = −0.0684280 − 0.0496997I
b = 0.375309 − 0.506052I
c = 0.571089 − 0.621740I
d = 0.814495 − 0.406682I
0.98010 − 1.39709I 3.77019 + 3.86736I
u = 0.547424 − 0.585652I
a = 0.25679 − 2.03371I
b = 0.973637 − 0.816821I
c = −0.23731 + 1.59853I
d = −0.729744 + 0.077176I
0.98010 − 1.39709I 3.77019 + 3.86736I
22
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.547424 + 1.120870I
a = 0.522652 − 0.149285I
b = 0.017395 + 0.374071I
c = −0.25807 + 1.52032I
d = −0.86105 + 1.25168I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.547424 + 1.120870I
a = 1.11333 − 1.38898I
b = 1.91343 − 0.82551I
c = −0.173830 − 1.019770I
d = 1.013450 − 0.887820I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.547424 + 1.120870I
a = −0.93237 + 2.97895I
b = −1.22720 + 1.89212I
c = 1.52675 − 2.74230I
d = 1.64606 − 1.16492I
−2.62503 − 7.64338I −1.77019 + 6.51087I
u = −0.547424 − 1.120870I
a = 0.522652 + 0.149285I
b = 0.017395 − 0.374071I
c = −0.25807 − 1.52032I
d = −0.86105 − 1.25168I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = 1.11333 + 1.38898I
b = 1.91343 + 0.82551I
c = −0.173830 + 1.019770I
d = 1.013450 + 0.887820I
−2.62503 + 7.64338I −1.77019 − 6.51087I
u = −0.547424 − 1.120870I
a = −0.93237 − 2.97895I
b = −1.22720 − 1.89212I
c = 1.52675 + 2.74230I
d = 1.64606 + 1.16492I
−2.62503 + 7.64338I −1.77019 − 6.51087I
23
III. I
u
3
= ⟨−75a
2
u
5
+ 125au
5
+ · · · − 31a + 44, −55a
2
u
5
+ 167au
5
+ · · · +
143a − 28, −58a
2
u
5
+ 59au
5
+ · · · − 30a + 28, −2u
5
a
2
+ 2u
5
a + · · · − 4a
2
+
2a, u
6
+ u
5
+ · · · + 2u + 1⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
0
u
a
5
=
1
−u
2
a
7
=
a
0.513274a
2
u
5
− 0.522124au
5
+ ··· + 0.265487a − 0.247788
a
10
=
u
u
a
12
=
0.486726a
2
u
5
− 1.47788au
5
+ ··· − 1.26549a + 0.247788
0.663717a
2
u
5
− 1.10619au
5
+ ··· + 0.274336a − 0.389381
a
1
=
u
u
a
6
=
u
3
u
3
+ u
a
3
=
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 2
u
5
+ 2u
3
+ u
2
+ 2u + 1
a
2
=
u
4
+ u
2
+ u + 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
a
11
=
0.513274a
2
u
5
− 0.522124au
5
+ ··· − 0.734513a − 0.247788
0.690265a
2
u
5
− 0.150442au
5
+ ··· + 0.805310a − 0.884956
a
8
=
0.176991a
2
u
5
+ 0.371681au
5
+ ··· + 1.53982a − 0.637168
0.690265a
2
u
5
− 0.150442au
5
+ ··· + 0.805310a − 0.884956
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
3
− 4u − 2
24
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
c
2
, c
4
, c
5
c
9
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
c
3
(u
3
+ u
2
− 1)
6
c
6
, c
7
, c
8
c
10
, c
12
u
18
− 6u
16
+ ··· + 2u
3
+ 1
c
11
u
18
− 12u
17
+ ··· + 8u
2
+ 1
25
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
c
2
, c
4
, c
5
c
9
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
c
3
(y
3
− y
2
+ 2y −1)
6
c
6
, c
7
, c
8
c
10
, c
12
y
18
− 12y
17
+ ··· + 8y
2
+ 1
c
11
y
18
− 12y
17
+ ··· + 16y + 1
26
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = −1.17148 − 1.07480I
b = −1.99587 − 0.45347I
c = −0.157661 − 0.713279I
d = −1.32986 − 0.49621I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.498832 + 1.001300I
a = −0.358089 − 0.128198I
b = 0.131651 + 0.402262I
c = 0.299325 + 1.234880I
d = 0.840299 + 1.017300I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.498832 + 1.001300I
a = 0.73236 + 2.80324I
b = 1.06700 + 1.65145I
c = −1.13933 − 2.52421I
d = −1.30532 − 0.92346I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = 0.498832 − 1.001300I
a = −1.17148 + 1.07480I
b = −1.99587 + 0.45347I
c = −0.157661 + 0.713279I
d = −1.32986 + 0.49621I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.498832 − 1.001300I
a = −0.358089 + 0.128198I
b = 0.131651 − 0.402262I
c = 0.299325 − 1.234880I
d = 0.840299 − 1.017300I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = 0.498832 − 1.001300I
a = 0.73236 − 2.80324I
b = 1.06700 − 1.65145I
c = −1.13933 + 2.52421I
d = −1.30532 + 0.92346I
−0.26574 − 2.82812I 1.50976 + 2.97945I
27
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.284920 + 1.115140I
a = 0.589677 − 1.038010I
b = 1.292560 − 0.412855I
c = −0.384455 − 0.173537I
d = 0.624963 − 0.038245I
−4.40332 −5.01951 + 0.I
u = −0.284920 + 1.115140I
a = 0.295266 − 0.439795I
b = −0.225579 + 0.124250I
c = 0.183101 + 1.122730I
d = −0.485466 + 1.007580I
−4.40332 −5.01951 + 0.I
u = −0.284920 + 1.115140I
a = −0.45478 + 3.16140I
b = −0.63682 + 1.97219I
c = 0.77119 − 3.17947I
d = 0.86050 − 1.51603I
−4.40332 −5.01951 + 0.I
u = −0.284920 − 1.115140I
a = 0.589677 + 1.038010I
b = 1.292560 + 0.412855I
c = −0.384455 + 0.173537I
d = 0.624963 + 0.038245I
−4.40332 −5.01951 + 0.I
u = −0.284920 − 1.115140I
a = 0.295266 + 0.439795I
b = −0.225579 − 0.124250I
c = 0.183101 − 1.122730I
d = −0.485466 − 1.007580I
−4.40332 −5.01951 + 0.I
u = −0.284920 − 1.115140I
a = −0.45478 − 3.16140I
b = −0.63682 − 1.97219I
c = 0.77119 + 3.17947I
d = 0.86050 + 1.51603I
−4.40332 −5.01951 + 0.I
28
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −0.713912 + 0.305839I
a = −0.161975 + 1.103030I
b = −1.085250 + 0.272261I
c = −0.223253 − 0.651146I
d = 0.361764 + 0.394419I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.713912 + 0.305839I
a = −0.0828484 + 0.0502791I
b = −0.632432 + 0.441144I
c = −0.713791 + 0.255078I
d = −0.738624 − 0.097289I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.713912 + 0.305839I
a = 2.61188 − 0.13927I
b = 4.08474 + 0.30064I
c = 2.36487 − 0.21561I
d = 4.17174 + 0.10523I
−0.26574 + 2.82812I 1.50976 − 2.97945I
u = −0.713912 − 0.305839I
a = −0.161975 − 1.103030I
b = −1.085250 − 0.272261I
c = −0.223253 + 0.651146I
d = 0.361764 − 0.394419I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.713912 − 0.305839I
a = −0.0828484 − 0.0502791I
b = −0.632432 − 0.441144I
c = −0.713791 − 0.255078I
d = −0.738624 + 0.097289I
−0.26574 − 2.82812I 1.50976 + 2.97945I
u = −0.713912 − 0.305839I
a = 2.61188 + 0.13927I
b = 4.08474 − 0.30064I
c = 2.36487 + 0.21561I
d = 4.17174 − 0.10523I
−0.26574 − 2.82812I 1.50976 + 2.97945I
29
IV. I
v
1
= ⟨a, d − v + 1, c + a, b + v − 1, v
2
− v + 1⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
7
=
0
−v + 1
a
10
=
v
0
a
12
=
0
v −1
a
1
=
0
v −1
a
6
=
0
−v + 1
a
3
=
1
v
a
2
=
−v + 1
v
a
11
=
v
v −1
a
8
=
0
−v + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4v + 11
30
(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
7
c
9
, c
12
u
2
c
8
(u + 1)
2
c
10
, c
11
(u − 1)
2
31
(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
7
c
9
, c
12
y
2
c
8
, c
10
, c
11
(y −1)
2
32
(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 = 0
d = −0.500000 + 0.866025I
1.64493 + 2.02988I 9.00000 − 3.46410I
v = 0.500000 − 0.866025I
a = 0
b = 0.500000 + 0.866025I
c = 0
d = −0.500000 − 0.866025I
1.64493 − 2.02988I 9.00000 + 3.46410I
33
V. I
v
2
= ⟨a, d, c − v, b − v − 1, v
2
+ v + 1⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
7
=
0
v + 1
a
10
=
v
0
a
12
=
v
0
a
1
=
v
−v −1
a
6
=
−v
v + 1
a
3
=
0
−v
a
2
=
v
−v
a
11
=
v
0
a
8
=
v
0
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4v −1
34
(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
8
, c
9
c
10
, c
11
u
2
c
6
, c
7
(u − 1)
2
c
12
(u + 1)
2
35
(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
8
, c
9
c
10
, c
11
y
2
c
6
, c
7
, c
12
(y −1)
2
36
(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 = −0.500000 + 0.866025I
d = 0
−1.64493 − 2.02988I −3.00000 + 3.46410I
v = −0.500000 − 0.866025I
a = 0
b = 0.500000 − 0.866025I
c = −0.500000 − 0.866025I
d = 0
−1.64493 + 2.02988I −3.00000 − 3.46410I
37
VI. I
v
3
= ⟨a, d + 1, c + a − 1, b − 1, v − 1⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
1
0
a
5
=
1
0
a
7
=
0
1
a
10
=
1
0
a
12
=
1
−1
a
1
=
1
0
a
6
=
1
0
a
3
=
1
0
a
2
=
1
0
a
11
=
2
−1
a
8
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 0
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
u
c
6
, c
7
, c
8
u + 1
c
10
, c
11
, c
12
u − 1
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
3
c
4
, c
5
, c
9
y
c
6
, c
7
, c
8
c
10
, c
11
, c
12
y −1
40
(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
0 0
41
VII. I
v
4
= ⟨a, −b
2
v − bv + · · · + 2b + 1, −b
2
av − bav + · · · + a − 1, v
2
c +
v
2
b + · · · + c + 2a, b
2
v
2
+ v
2
b + · · · − v + 1⟩
(i) Arc colorings
a
4
=
1
0
a
9
=
v
0
a
5
=
1
0
a
7
=
0
b
a
10
=
v
0
a
12
=
c
b
2
v + bv − 2b + v − 1
a
1
=
c
b
2
v + bv − b + v − 1
a
6
=
c
b
2
v + bv − b + v − 1
a
3
=
−cv −bv + c − v + 2
b
2
v + bv − b + v
a
2
=
−b
2
v −cv − 2bv + c + b − 2v + 2
b
2
v + bv − b + v
a
11
=
c + v
b
2
v + bv − 2b + v − 1
a
8
=
−c
−b
2
v −bv + 2b − v + 1
(ii) Obstruction class = −1
(iii) Cusp Shapes = 2b
3
v −b
2
v −3b
2
− bv −v
2
+ b − 3v + 4
(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.
42
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
4
√
−1(vol +
√
−1CS) Cusp shape
v = ···
a = ···
b = ···
c = ···
d = ···
− 2.02988I 1.64184 − 3.78338I
43
VIII. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
u(u
2
− u + 1)
2
(u
4
+ 2u
3
+ 3u
2
+ u + 1)
3
(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
3
· (u
77
+ 36u
76
+ ··· + 216u − 16)
c
2
u(u
2
+ u + 1)
2
(u
4
+ u
2
− u + 1)
3
· ((u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
)(u
77
+ 2u
76
+ ··· + 27u
2
− 4)
c
3
u(u
2
− u + 1)
2
(u
3
+ u
2
− 1)
6
(u
4
− 3u
3
+ 4u
2
− 3u + 2)
3
· (u
77
− 2u
76
+ ··· + 351912u − 66564)
c
4
, c
9
u
5
(u
4
+ u
2
− u + 1)
3
(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
· (u
77
− 2u
76
+ ··· − 2560u
2
− 512)
c
5
u(u
2
− u + 1)
2
(u
4
+ u
2
− u + 1)
3
· ((u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
3
)(u
77
+ 2u
76
+ ··· + 27u
2
− 4)
c
6
, c
7
u
2
(u − 1)
2
(u + 1)
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
− 8u
76
+ ··· − 72u − 16)
c
8
u
2
(u + 1)
3
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
+ 8u
76
+ ··· − 72u − 16)
c
10
u
2
(u − 1)
3
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
+ 8u
76
+ ··· − 72u − 16)
c
11
u
2
(u − 1)
3
(u
12
− 8u
11
+ ··· + 5u + 1)(u
18
− 12u
17
+ ··· + 8u
2
+ 1)
· (u
77
− 34u
76
+ ··· + 1568u − 256)
c
12
u
2
(u − 1)(u + 1)
2
· (u
12
− 4u
10
− 2u
9
+ 6u
8
+ 6u
7
− u
6
− 6u
5
− 5u
4
+ u
3
+ 3u
2
+ u + 1)
· (u
18
− 6u
16
+ ··· + 2u
3
+ 1)(u
77
− 8u
76
+ ··· − 72u − 16)
44
IX. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
y(y
2
+ y + 1)
2
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)
3
· ((y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
3
)(y
77
+ 12y
76
+ ··· + 84256y −256)
c
2
, c
5
y(y
2
+ y + 1)
2
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
77
+ 36y
76
+ ··· + 216y −16)
c
3
y(y
2
+ y + 1)
2
(y
3
− y
2
+ 2y −1)
6
(y
4
− y
3
+ 2y
2
+ 7y + 4)
3
· (y
77
− 12y
76
+ ··· + 120020616504y −4430766096)
c
4
, c
9
y
5
(y
4
+ 2y
3
+ 3y
2
+ y + 1)
3
(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
3
· (y
77
+ 30y
76
+ ··· − 2621440y −262144)
c
6
, c
7
, c
12
y
2
(y −1)
3
(y
12
− 8y
11
+ ··· + 5y + 1)(y
18
− 12y
17
+ ··· + 8y
2
+ 1)
· (y
77
− 74y
76
+ ··· + 7712y −256)
c
8
, c
10
y
2
(y −1)
3
(y
12
− 8y
11
+ ··· + 5y + 1)(y
18
− 12y
17
+ ··· + 8y
2
+ 1)
· (y
77
− 34y
76
+ ··· + 1568y −256)
c
11
y
2
(y −1)
3
(y
12
− 8y
11
+ ··· − 31y + 1)(y
18
− 12y
17
+ ··· + 16y + 1)
· (y
77
+ 26y
76
+ ··· + 3416576y −65536)
45
