11a
283
(K11a
283
)
1
Arc Sequences
6 9 1 11 2 10 4 3 5 7 8
Solving Sequence
1,3 4,8
9 2 7 11 5 6 10
c
3
c
8
c
2
c
7
c
11
c
4
c
5
c
10
c
1
, c
6
, c
9
Representation Ideals
I =
3
\
i=1
I
u
i
I
u
1
= hu
7
2u
6
+ u
5
2u
4
+ 2u
3
+ u + 1, u
4
+ u
3
+ b + u, u
3
u
2
+ a 1i
I
u
2
= hu
20
3u
19
+ ··· + 2u + 1, 4.51619 × 10
16
u
19
1.54413 × 10
17
u
18
+ ··· + 8.87160 × 10
16
b + 2.44218 × 10
16
,
6.53718 × 10
16
u
19
2.20241 × 10
17
u
18
+ ··· + 8.87160 × 10
16
a 5.87784 × 10
16
i
I
u
3
= hu
86
+ 10u
85
+ ··· + 578u + 79,
9.59266 × 10
474
u
85
+ 9.00126 × 10
475
u
84
+ ··· + 1.62663 × 10
477
b 6.15787 × 10
476
,
2.75954 × 10
478
u
85
2.67363 × 10
479
u
84
+ ··· + 6.42520 × 10
479
a 3.92446 × 10
480
i
There are 3 irreducible components with 113 representations.
1
The knot diagram image is adapter from “C. Livingston and A. H. Moore, KnotInfo: Table of Knot
Invariants, http://www.indiana.edu/ knotinfo”
1
I. I
u
1
= hu
7
2u
6
+ u
5
2u
4
+ 2u
3
+ u + 1, u
4
+ u
3
+ b + u, u
3
u
2
+ a 1i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
8
=
u
3
+ u
2
+ 1
u
4
u
3
u
a
9
=
u
3
+ u
2
+ 1
u
5
u
3
u
2
u
a
2
=
1
u
2
a
7
=
u
6
2u
5
+ u
4
2u
3
+ 2u
2
+ 1
u
6
+ 2u
5
u
2
u
a
11
=
0
u
a
5
=
u
u
3
+ u
a
6
=
0
u
a
10
=
u
6
2u
5
+ u
4
2u
3
+ 2u
2
+ 1
u
6
+ 2u
5
u
2
a
10
=
u
6
2u
5
+ u
4
2u
3
+ 2u
2
+ 1
u
6
+ 2u
5
u
2
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.512372
a = 1.39704
b = 0.715802
1.64493 6.00000
u = 0.439591 0.951858I
a = 0.822700 + 0.526253I
b = 0.862570 0.551757I
1.64493 6.00000
u = 0.439591 + 0.951858I
a = 0.822700 0.526253I
b = 0.862570 + 0.551757I
1.64493 6.00000
u = 0.173654 0.849744I
a = 0.679021 0.831820I
b = 0.588920 + 0.721443I
1.64493 6.00000
u = 0.173654 + 0.849744I
a = 0.679021 + 0.831820I
b = 0.588920 0.721443I
1.64493 6.00000
u = 1.52212 0.20837I
a = 0.054839 + 0.804922I
b = 0.084251 1.236617I
1.64493 6.00000
u = 1.52212 + 0.20837I
a = 0.054839 0.804922I
b = 0.084251 + 1.236617I
1.64493 6.00000
3
II. I
u
2
=
hu
20
3u
19
+ · · · +2u + 1, 4.52 × 10
16
u
19
1.54 × 10
17
u
18
+ · · · + 8.87 × 10
16
b +
2.44 × 10
16
, 6.54 × 10
16
u
19
2.20 × 10
17
u
18
+ · · · + 8.87 × 10
16
a 5.88 × 10
16
i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
8
=
0.736865u
19
+ 2.48253u
18
+ ··· 3.49550u + 0.662545
0.509062u
19
+ 1.74053u
18
+ ··· 4.14605u 0.275281
a
9
=
0.736865u
19
+ 2.48253u
18
+ ··· 3.49550u + 0.662545
0.570131u
19
+ 1.92327u
18
+ ··· 4.33904u 0.00334204
a
2
=
0.144919u
19
+ 0.295174u
18
+ ··· 4.75070u 0.464302
0.483433u
19
1.71707u
18
+ ··· + 1.44365u 0.221180
a
7
=
0.781078u
19
+ 2.62798u
18
+ ··· 3.22014u + 0.177262
0.464850u
19
+ 1.59508u
18
+ ··· 4.42141u + 0.210003
a
11
=
0.0815984u
19
+ 0.372640u
18
+ ··· + 6.58573u + 2.03093
0.0443048u
19
+ 0.165402u
18
+ ··· + 1.70655u + 0.880340
a
5
=
0.659142u
19
2.66504u
18
+ ··· 5.39296u 1.56492
0.0635505u
19
+ 0.0209443u
18
+ ··· 0.00750863u 1.84693
a
6
=
0.782962u
19
3.58708u
18
+ ··· 1.18862u 2.44788
0.205309u
19
+ 0.787547u
18
+ ··· 0.290611u 0.953486
a
10
=
0.950052u
19
+ 4.20746u
18
+ ··· + 1.22523u + 2.82209
0.381503u
19
+ 1.16132u
18
+ ··· 3.18636u + 0.778525
a
10
=
0.950052u
19
+ 4.20746u
18
+ ··· + 1.22523u + 2.82209
0.381503u
19
+ 1.16132u
18
+ ··· 3.18636u + 0.778525
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
4
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 2.05932 0.51289I
a = 0.022590 0.624437I
b = 0.428420 + 0.634387I
3.70849 7.77575I 1.98042 + 8.91503I
u = 2.05932 + 0.51289I
a = 0.022590 + 0.624437I
b = 0.428420 0.634387I
3.70849 + 7.77575I 1.98042 8.91503I
u = 0.564894 0.693008I
a = 0.77649 + 1.45312I
b = 1.22470 1.34250I
4.70501 3.26631I 10.94198 + 7.13391I
u = 0.564894 + 0.693008I
a = 0.77649 1.45312I
b = 1.22470 + 1.34250I
4.70501 + 3.26631I 10.94198 7.13391I
u = 0.460291 0.362148I
a = 2.40026 0.69294I
b = 0.569025 0.383444I
0.96215 2.51362I 0.64139 + 9.41977I
u = 0.460291 + 0.362148I
a = 2.40026 + 0.69294I
b = 0.569025 + 0.383444I
0.96215 + 2.51362I 0.64139 9.41977I
u = 0.398273 0.505596I
a = 1.87132 1.16017I
b = 1.008725 + 0.396393I
7.04665 + 2.30270I 1.55456 0.79605I
u = 0.398273 + 0.505596I
a = 1.87132 + 1.16017I
b = 1.008725 0.396393I
7.04665 2.30270I 1.55456 + 0.79605I
u = 0.041274 0.327366I
a = 2.12898 + 0.27491I
b = 0.370853 + 1.112918I
3.67242 + 1.15933I 9.29729 1.48128I
u = 0.041274 + 0.327366I
a = 2.12898 0.27491I
b = 0.370853 1.112918I
3.67242 1.15933I 9.29729 + 1.48128I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.345896 1.225691I
a = 0.210558 0.124153I
b = 0.788726 + 0.189203I
3.10647 + 2.21537I 10.72853 2.81043I
u = 0.345896 + 1.225691I
a = 0.210558 + 0.124153I
b = 0.788726 0.189203I
3.10647 2.21537I 10.72853 + 2.81043I
u = 0.892681 0.271514I
a = 1.090428 + 0.100284I
b = 0.448804 + 0.393731I
0.64266 + 3.90221I 3.24651 7.37049I
u = 0.892681 + 0.271514I
a = 1.090428 0.100284I
b = 0.448804 0.393731I
0.64266 3.90221I 3.24651 + 7.37049I
u = 0.897651 0.884576I
a = 0.063361 0.732937I
b = 0.976142 + 0.655162I
1.58446 + 3.70556I 0.94050 4.83089I
u = 0.897651 + 0.884576I
a = 0.063361 + 0.732937I
b = 0.976142 0.655162I
1.58446 3.70556I 0.94050 + 4.83089I
u = 1.28550 0.59311I
a = 0.356979 0.778562I
b = 0.385793 + 1.177103I
1.65051 1.14565I 6.04640 + 4.20488I
u = 1.28550 + 0.59311I
a = 0.356979 + 0.778562I
b = 0.385793 1.177103I
1.65051 + 1.14565I 6.04640 4.20488I
u = 1.60233 1.19450I
a = 0.151782 + 0.463541I
b = 1.007736 0.591502I
1.71598 + 6.19605I 8.61255 6.55788I
u = 1.60233 + 1.19450I
a = 0.151782 0.463541I
b = 1.007736 + 0.591502I
1.71598 6.19605I 8.61255 + 6.55788I
6
III. I
u
3
= hu
86
+ 10u
85
+ · · · + 578u + 79, 9.59 × 10
474
u
85
+ 9.00 ×
10
475
u
84
+ · · · + 1.63 × 10
477
b 6.16 × 10
476
, 2.76 × 10
478
u
85
2.67 ×
10
479
u
84
+ · · · + 6.43 × 10
479
a 3.92 × 10
480
i
(i) Arc colorings
a
1
=
1
0
a
3
=
0
u
a
4
=
u
u
a
8
=
0.0429487u
85
+ 0.416117u
84
+ ··· + 50.3426u + 6.10793
0.00589725u
85
0.0553367u
84
+ ··· 5.20215u + 0.378565
a
9
=
0.0429487u
85
+ 0.416117u
84
+ ··· + 50.3426u + 6.10793
0.00897296u
85
0.0853405u
84
+ ··· 9.53721u 0.677684
a
2
=
0.0426467u
85
0.422351u
84
+ ··· 56.6166u 20.1735
0.0149468u
85
+ 0.146409u
84
+ ··· + 13.5030u + 3.50014
a
7
=
0.0448924u
85
+ 0.435090u
84
+ ··· + 53.0421u + 6.87695
0.00784092u
85
0.0743096u
84
+ ··· 7.90161u 0.390458
a
11
=
0.0401899u
85
0.387516u
84
+ ··· 75.3380u 8.73656
0.00184411u
85
+ 0.0157898u
84
+ ··· + 9.72247u 0.564930
a
5
=
0.0261521u
85
+ 0.265885u
84
+ ··· + 56.9667u + 26.7454
0.0101131u
85
0.100488u
84
+ ··· 27.7922u 6.56219
a
6
=
0.0402227u
85
+ 0.395119u
84
+ ··· + 70.0078u + 14.5373
0.00338721u
85
0.0322823u
84
+ ··· 9.52461u 0.761642
a
10
=
0.0865597u
85
0.842662u
84
+ ··· 131.076u 18.0842
0.00797848u
85
+ 0.0750717u
84
+ ··· + 15.2370u + 0.172451
a
10
=
0.0865597u
85
0.842662u
84
+ ··· 131.076u 18.0842
0.00797848u
85
+ 0.0750717u
84
+ ··· + 15.2370u + 0.172451
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
7
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 2.20649 0.94736I
a = 0.266652 + 0.447978I
b = 0.604045 0.163616I
4.48521 + 6.86672I 1.90243 4.16210I
u = 2.20649 + 0.94736I
a = 0.266652 0.447978I
b = 0.604045 + 0.163616I
4.48521 6.86672I 1.90243 + 4.16210I
u = 1.79532 1.18311I
a = 0.219361 0.501685I
b = 0.996687 + 0.618711I
0.51451 6.45826I 1.76014 + 6.43944I
u = 1.79532 + 1.18311I
a = 0.219361 + 0.501685I
b = 0.996687 0.618711I
0.51451 + 6.45826I 1.76014 6.43944I
u = 1.61628 1.34034I
a = 0.329118 0.593932I
b = 0.467174 + 0.794714I
2.71748 7.52821I 8.84323 + 6.90477I
u = 1.61628 + 1.34034I
a = 0.329118 + 0.593932I
b = 0.467174 0.794714I
2.71748 + 7.52821I 8.84323 6.90477I
u = 1.58581 1.00036I
a = 0.277790 + 0.673136I
b = 0.793262 0.757007I
5.14196 5.75508I 0.53063 + 6.31940I
u = 1.58581 + 1.00036I
a = 0.277790 0.673136I
b = 0.793262 + 0.757007I
5.14196 + 5.75508I 0.53063 6.31940I
u = 1.37620 0.78896I
a = 0.388565 + 0.742403I
b = 1.12032 0.97919I
6.21226 5.37580I 0.06492 + 5.30246I
u = 1.37620 + 0.78896I
a = 0.388565 0.742403I
b = 1.12032 + 0.97919I
6.21226 + 5.37580I 0.06492 5.30246I
8
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.353187 0.385379I
a = 0.100586 + 1.071322I
b = 0.886329 0.336760I
5.61570 9.08985I 0.32107 + 8.28317I
u = 1.353187 + 0.385379I
a = 0.100586 1.071322I
b = 0.886329 + 0.336760I
5.61570 + 9.08985I 0.32107 8.28317I
u = 1.27008 1.27440I
a = 0.401734 + 0.784748I
b = 1.28157 0.90744I
3.4892 17.6295I 3.06884 + 9.10802I
u = 1.27008 + 1.27440I
a = 0.401734 0.784748I
b = 1.28157 + 0.90744I
3.4892 + 17.6295I 3.06884 9.10802I
u = 1.25108 1.27334I
a = 0.593678 0.447117I
b = 0.786372 + 0.097584I
8.25891 + 3.00812I 6.79941 2.91249I
u = 1.25108 + 1.27334I
a = 0.593678 + 0.447117I
b = 0.786372 0.097584I
8.25891 3.00812I 6.79941 + 2.91249I
u = 1.07442 1.07358I
a = 0.489062 0.943535I
b = 1.33874 + 0.92434I
8.42324 11.27470I 0.50654 + 7.93296I
u = 1.07442 + 1.07358I
a = 0.489062 + 0.943535I
b = 1.33874 0.92434I
8.42324 + 11.27470I 0.50654 7.93296I
u = 0.872563 0.427374I
a = 0.30827 1.72104I
b = 0.696897 + 0.215062I
7.86731 4.29450I 3.32355 + 4.55601I
u = 0.872563 + 0.427374I
a = 0.30827 + 1.72104I
b = 0.696897 0.215062I
7.86731 + 4.29450I 3.32355 4.55601I
9
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.816502 0.731762I
a = 0.797817 0.811692I
b = 1.58024 + 0.96432I
7.29903 + 0.31589I 0.11598 + 2.44941I
u = 0.816502 + 0.731762I
a = 0.797817 + 0.811692I
b = 1.58024 0.96432I
7.29903 0.31589I 0.11598 2.44941I
u = 0.781265 0.093712I
a = 0.15649 + 1.76213I
b = 0.982343 0.478243I
6.14811 + 0.65193I 0.47300 + 1.86196I
u = 0.781265 + 0.093712I
a = 0.15649 1.76213I
b = 0.982343 + 0.478243I
6.14811 0.65193I 0.47300 1.86196I
u = 0.780824 0.879312I
a = 0.288894 + 0.182447I
b = 0.020347 0.776368I
4.95207 + 1.65937I 17.2147 3.6067I
u = 0.780824 + 0.879312I
a = 0.288894 0.182447I
b = 0.020347 + 0.776368I
4.95207 1.65937I 17.2147 + 3.6067I
u = 0.742449 0.769656I
a = 0.464364 0.620052I
b = 0.908284 + 0.879263I
4.82477 6.81993I 10.08009 + 4.71115I
u = 0.742449 + 0.769656I
a = 0.464364 + 0.620052I
b = 0.908284 0.879263I
4.82477 + 6.81993I 10.08009 4.71115I
u = 0.525472 0.785193I
a = 0.93268 + 1.48381I
b = 1.48810 1.18066I
5.01653 3.29033I 14.7213 + 8.7999I
u = 0.525472 + 0.785193I
a = 0.93268 1.48381I
b = 1.48810 + 1.18066I
5.01653 + 3.29033I 14.7213 8.7999I
10
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.447264 0.472519I
a = 0.865893 + 0.639221I
b = 0.783105 0.781755I
0.06236 2.46466I 6.83396 + 3.77647I
u = 0.447264 + 0.472519I
a = 0.865893 0.639221I
b = 0.783105 + 0.781755I
0.06236 + 2.46466I 6.83396 3.77647I
u = 0.393183 0.598655I
a = 1.240330 + 0.528905I
b = 0.553669 0.538966I
1.71658 1.70443I 3.26271 + 0.57830I
u = 0.393183 + 0.598655I
a = 1.240330 0.528905I
b = 0.553669 + 0.538966I
1.71658 + 1.70443I 3.26271 0.57830I
u = 0.370149 0.378564I
a = 1.16621 2.22185I
b = 0.51756 + 1.53574I
1.10942 9.46579I 5.88505 + 7.75269I
u = 0.370149 + 0.378564I
a = 1.16621 + 2.22185I
b = 0.51756 1.53574I
1.10942 + 9.46579I 5.88505 7.75269I
u = 0.340450 0.211846I
a = 0.68348 + 3.04420I
b = 0.33975 1.62541I
4.58690 2.56469I 8.50204 1.29154I
u = 0.340450 + 0.211846I
a = 0.68348 3.04420I
b = 0.33975 + 1.62541I
4.58690 + 2.56469I 8.50204 + 1.29154I
u = 0.21108 1.59629I
a = 0.939679 0.018101I
b = 1.151205 + 0.056856I
3.17742 0.08844I 1.82214 0.21597I
u = 0.21108 + 1.59629I
a = 0.939679 + 0.018101I
b = 1.151205 0.056856I
3.17742 + 0.08844I 1.82214 + 0.21597I
11
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.191885 0.124177I
a = 3.96105 5.26029I
b = 1.157362 + 0.247059I
5.72875 + 3.11452I 2.35660 2.88543I
u = 0.191885 + 0.124177I
a = 3.96105 + 5.26029I
b = 1.157362 0.247059I
5.72875 3.11452I 2.35660 + 2.88543I
u = 0.186619 0.529078I
a = 0.948670 0.611240I
b = 0.262372 + 0.594253I
0.948430 + 0.603776I 9.01347 4.18465I
u = 0.186619 + 0.529078I
a = 0.948670 + 0.611240I
b = 0.262372 0.594253I
0.948430 0.603776I 9.01347 + 4.18465I
u = 0.106872 0.454744I
a = 2.66551 + 2.22451I
b = 0.458312 0.731943I
0.43071 3.88005I 8.57640 + 9.33204I
u = 0.106872 + 0.454744I
a = 2.66551 2.22451I
b = 0.458312 + 0.731943I
0.43071 + 3.88005I 8.57640 9.33204I
u = 0.113314 0.988562I
a = 0.220994 0.927982I
b = 0.937868 + 1.042349I
2.54751 + 4.69288I 8.01340 6.49441I
u = 0.113314 + 0.988562I
a = 0.220994 + 0.927982I
b = 0.937868 1.042349I
2.54751 4.69288I 8.01340 + 6.49441I
u = 0.208990 0.160847I
a = 2.14296 + 3.65421I
b = 0.59050 1.70373I
2.56807 + 2.29900I 6.18096 6.37760I
u = 0.208990 + 0.160847I
a = 2.14296 3.65421I
b = 0.59050 + 1.70373I
2.56807 2.29900I 6.18096 + 6.37760I
12
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.214147 0.808833I
a = 0.341089 + 0.606239I
b = 1.04113 0.97357I
4.56662 0.11637I 12.84009 2.25680I
u = 0.214147 + 0.808833I
a = 0.341089 0.606239I
b = 1.04113 + 0.97357I
4.56662 + 0.11637I 12.84009 + 2.25680I
u = 0.265781 0.181610I
a = 0.63664 4.70598I
b = 0.320711 0.381753I
1.18894 2.12493I 10.53913 4.74272I
u = 0.265781 + 0.181610I
a = 0.63664 + 4.70598I
b = 0.320711 + 0.381753I
1.18894 + 2.12493I 10.53913 + 4.74272I
u = 0.33118 1.65651I
a = 0.587665 0.200822I
b = 1.307116 + 0.135504I
1.54553 + 2.70454I 5.51874 3.86994I
u = 0.33118 + 1.65651I
a = 0.587665 + 0.200822I
b = 1.307116 0.135504I
1.54553 2.70454I 5.51874 + 3.86994I
u = 0.529003 0.826672I
a = 0.31067 1.51145I
b = 0.796678 + 1.008823I
2.09582 + 4.89045I 0.76502 11.52498I
u = 0.529003 + 0.826672I
a = 0.31067 + 1.51145I
b = 0.796678 1.008823I
2.09582 4.89045I 0.76502 + 11.52498I
u = 0.59084 1.38375I
a = 0.007010 0.481523I
b = 0.455370 + 0.640337I
2.64706 + 4.13307I 10.06650 7.67107I
u = 0.59084 + 1.38375I
a = 0.007010 + 0.481523I
b = 0.455370 0.640337I
2.64706 4.13307I 10.06650 + 7.67107I
13
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.710124 1.063139I
a = 0.298844 + 0.932510I
b = 0.975904 0.898638I
2.30617 + 11.65448I 5.71441 9.09907I
u = 0.710124 + 1.063139I
a = 0.298844 0.932510I
b = 0.975904 + 0.898638I
2.30617 11.65448I 5.71441 + 9.09907I
u = 0.758858 0.316144I
a = 1.191836 + 0.514142I
b = 0.565760 + 0.049963I
1.17731 + 3.15707I 1.95153 2.62504I
u = 0.758858 + 0.316144I
a = 1.191836 0.514142I
b = 0.565760 0.049963I
1.17731 3.15707I 1.95153 + 2.62504I
u = 0.849759 0.240272I
a = 0.424992 0.002820I
b = 0.907520 0.549937I
3.81257 0.89485I 2.25949 + 1.18834I
u = 0.849759 + 0.240272I
a = 0.424992 + 0.002820I
b = 0.907520 + 0.549937I
3.81257 + 0.89485I 2.25949 1.18834I
u = 0.877618 0.715990I
a = 0.427831 + 0.308325I
b = 0.633218 0.298276I
0.80790 + 2.80909I 5.98332 + 0.21201I
u = 0.877618 + 0.715990I
a = 0.427831 0.308325I
b = 0.633218 + 0.298276I
0.80790 2.80909I 5.98332 0.21201I
u = 0.882379 1.029063I
a = 0.560491 + 0.769666I
b = 1.43905 0.82459I
3.52274 + 6.07547I 1.55536 5.92381I
u = 0.882379 + 1.029063I
a = 0.560491 0.769666I
b = 1.43905 + 0.82459I
3.52274 6.07547I 1.55536 + 5.92381I
14
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 0.883652 0.950390I
a = 0.307223 0.811697I
b = 1.007473 + 0.744538I
0.75390 + 3.34791I 8.33721 1.05489I
u = 0.883652 + 0.950390I
a = 0.307223 + 0.811697I
b = 1.007473 0.744538I
0.75390 3.34791I 8.33721 + 1.05489I
u = 0.942729 0.702573I
a = 0.497003 + 0.989629I
b = 0.733721 0.111808I
4.40326 + 0.41121I 0.491158 + 0.871285I
u = 0.942729 + 0.702573I
a = 0.497003 0.989629I
b = 0.733721 + 0.111808I
4.40326 0.41121I 0.491158 0.871285I
u = 0.96988 1.17660I
a = 0.623775 0.598550I
b = 0.406763 0.030358I
0.50203 2.48920I 6.55080 + 4.53304I
u = 0.96988 + 1.17660I
a = 0.623775 + 0.598550I
b = 0.406763 + 0.030358I
0.50203 + 2.48920I 6.55080 4.53304I
u = 0.992238 0.794552I
a = 0.589589 + 0.091732I
b = 0.815814 + 0.353442I
2.45089 + 3.89737I 6.40177 6.57898I
u = 0.992238 + 0.794552I
a = 0.589589 0.091732I
b = 0.815814 0.353442I
2.45089 3.89737I 6.40177 + 6.57898I
u = 1.060493 0.536610I
a = 0.203449 1.085227I
b = 0.951281 + 0.344539I
2.11426 + 4.00334I 3.09554 4.75495I
u = 1.060493 + 0.536610I
a = 0.203449 + 1.085227I
b = 0.951281 0.344539I
2.11426 4.00334I 3.09554 + 4.75495I
15
Solution to I
u
3
1(vol +
1CS) Cusp shape
u = 1.16986 1.10198I
a = 0.412530 0.764289I
b = 1.30457 + 0.96288I
0.23737 + 11.07658I 4.89931 7.25180I
u = 1.16986 + 1.10198I
a = 0.412530 + 0.764289I
b = 1.30457 0.96288I
0.23737 11.07658I 4.89931 + 7.25180I
u = 1.32260 1.26903I
a = 0.118829 + 0.594580I
b = 1.013537 0.674443I
0.43505 + 5.35734I 3.49660 4.38372I
u = 1.32260 + 1.26903I
a = 0.118829 0.594580I
b = 1.013537 + 0.674443I
0.43505 5.35734I 3.49660 + 4.38372I
u = 1.62199 0.09003I
a = 0.115912 + 0.123935I
b = 0.702069 0.520997I
1.21164 + 5.29604I 2.45054 8.48280I
u = 1.62199 + 0.09003I
a = 0.115912 0.123935I
b = 0.702069 + 0.520997I
1.21164 5.29604I 2.45054 + 8.48280I
16
IV. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
7
2u
6
+ ··· + u + 1)(u
20
u
19
+ ··· + 3u + 1)
(u
86
+ 2u
85
+ ··· 4061u + 367)
c
2
(u
7
+ u
5
+ u 1)(u
20
+ 8u
18
+ ··· 3u + 1)
(u
86
+ u
85
+ ··· + 4313u + 839)
c
3
(u
7
2u
6
+ ··· + u + 1)(u
20
+ 3u
19
+ ··· 2u + 1)
(u
86
+ 10u
85
+ ··· + 578u + 79)
c
4
(u
7
2u
6
+ ··· + u 1)(u
20
7u
18
+ ··· 4u + 1)
(u
86
+ 5u
85
+ ··· 16u + 1)
c
5
(u
7
2u
6
+ ··· + u + 1)(u
20
+ u
19
+ ··· 3u + 1)
(u
86
+ 2u
85
+ ··· 4061u + 367)
c
6
(u + 1)
7
(u
20
8u
18
+ ··· + 2u + 3)(u
86
6u
85
+ ··· + 2700u + 200)
c
7
(u
7
+ 3u
5
+ ··· + 3u 2)(u
20
u
19
+ ··· 3u + 1)
(u
86
+ 4u
85
+ ··· + 379u + 169)
c
8
(u
7
+ u
5
+ u 1)(u
20
+ 8u
18
+ ··· + 3u + 1)
(u
86
+ u
85
+ ··· + 4313u + 839)
c
9
(u
7
+ 3u
5
+ ··· + 3u 2)(u
20
3u
18
+ ··· 6u + 1)
(u
86
+ u
85
+ ··· + 760186u + 130319)
c
10
(u + 1)
7
(u
20
8u
18
+ ··· 2u + 3)(u
86
6u
85
+ ··· + 2700u + 200)
c
11
(u
7
+ u
5
+ u 1)(u
20
4u
17
+ ··· 2u
2
+ 1)
(u
86
+ 5u
85
+ ··· + 690u + 179)
17
V. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y
7
2y
6
+ ··· + y 1)(y
20
+ 9y
19
+ ··· + 15y + 1)
(y
86
+ 58y
85
+ ··· 1366917y + 134689)
c
2
(y
7
+ 2y
6
+ ··· + y 1)(y
20
+ 16y
19
+ ··· + 27y + 1)
(y
86
+ 73y
85
+ ··· 7899685y + 703921)
c
3
(y
7
2y
6
3y
5
+ 2y
4
+ 10y
3
+ 8y
2
+ y 1)
(y
20
11y
19
+ ··· + 16y + 1)(y
86
14y
85
+ ··· 153964y + 6241)
c
4
(y
7
10y
6
+ 37y
5
30y
4
+ 58y
3
40y
2
+ 17y 1)
(y
20
14y
19
+ ··· 4y + 1)(y
86
5y
85
+ ··· + 200y + 1)
c
5
(y
7
2y
6
+ ··· + y 1)(y
20
+ 9y
19
+ ··· + 15y + 1)
(y
86
+ 58y
85
+ ··· 1366917y + 134689)
c
6
(y 1)
7
(y
20
16y
19
+ ··· + 62y + 9)
(y
86
58y
85
+ ··· 4211599y + 40000)
c
7
(y
7
+ 6y
6
+ 17y
5
+ 14y
4
14y
3
28y
2
15y 4)
(y
20
+ 5y
19
+ ··· + 5y + 1)(y
86
+ 14y
85
+ ··· + 1122168y + 28561)
c
8
(y
7
+ 2y
6
+ ··· + y 1)(y
20
+ 16y
19
+ ··· + 27y + 1)
(y
86
+ 73y
85
+ ··· 7899685y + 703921)
c
9
(y
7
+ 6y
6
+ 17y
5
+ 14y
4
14y
3
28y
2
15y 4)
(y
20
6y
19
+ ··· 26y + 1)
(y
86
+ 15y
85
+ ··· + 56388593440y + 16983563025)
c
10
(y 1)
7
(y
20
16y
19
+ ··· + 62y + 9)
(y
86
58y
85
+ ··· 4211599y + 40000)
c
11
(y
7
+ 2y
6
+ ··· + y 1)(y
20
+ 12y
18
+ ··· 4y + 1)
(y
86
19y
85
+ ··· 1161312y + 32041)
18