11a
253
(K11a
253
)
1
Arc Sequences
4 7 1 2 8 3 10 11 5 6 9
Solving Sequence
2,7 3,10
8 6 11 5 4 1 9
c
2
c
7
c
6
c
10
c
5
c
4
c
1
c
9
c
3
, c
8
, c
11
Representation Ideals
I = I
u
1
\
I
v
1
I
u
1
= hu
71
+ u
70
+ ··· + 160u + 32,
2.35300 × 10
152
u
70
7.10205 × 10
152
u
69
+ ··· + 1.62062 × 10
154
a 5.96150 × 10
153
,
2.17790 × 10
153
u
70
2.13015 × 10
153
u
69
+ ··· + 1.62062 × 10
154
b 2.97154 × 10
154
i
I
v
1
= hb
5
+ 4b
4
+ 4b
3
b
2
2b + 1, b
4
5b
3
8b
2
3b + v + 2, ai
There are 2 irreducible components with 76 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
71
+ u
70
+ · · · + 160u + 32, 2.35 × 10
152
u
70
7.10 × 10
152
u
69
+
· · · + 1.62 × 10
154
a 5.96 × 10
153
, 2.18 × 10
153
u
70
2.13 × 10
153
u
69
+ · · · +
1.62 × 10
154
b 2.97 × 10
154
i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
0.0145191u
70
+ 0.0438230u
69
+ ··· + 14.4284u + 0.367853
0.134387u
70
+ 0.131440u
69
+ ··· + 19.0881u + 1.83358
a
8
=
0.108461u
70
+ 0.0741811u
69
+ ··· 9.74812u 2.96766
0.0554443u
70
0.0200513u
69
+ ··· 16.1138u 4.29324
a
6
=
u
u
3
+ u
a
11
=
0.0797658u
70
+ 0.0887972u
69
+ ··· + 20.7537u + 0.696950
0.0824925u
70
+ 0.0884155u
69
+ ··· + 11.6070u + 0.855761
a
5
=
0.0854343u
70
+ 0.0782277u
69
+ ··· + 61.9408u + 15.3168
0.0229377u
70
+ 0.0553663u
69
+ ··· + 21.4631u + 4.87327
a
4
=
0.108372u
70
+ 0.133594u
69
+ ··· + 83.4039u + 20.1901
0.0229377u
70
+ 0.0553663u
69
+ ··· + 21.4631u + 4.87327
a
1
=
0.108372u
70
+ 0.133594u
69
+ ··· + 83.4039u + 20.1901
0.00716550u
70
+ 0.0115983u
69
+ ··· + 13.7836u + 2.86964
a
9
=
0.136527u
70
0.178173u
69
+ ··· 96.3610u 23.6700
0.0990125u
70
+ 0.0113981u
69
+ ··· 16.0189u 5.30772
a
9
=
0.136527u
70
0.178173u
69
+ ··· 96.3610u 23.6700
0.0990125u
70
+ 0.0113981u
69
+ ··· 16.0189u 5.30772
(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 = 1.204064 0.543396I
a = 1.034089 0.330399I
b = 0.70914 + 1.56799I
0.14862 9.86900I 0.17397 + 6.31432I
u = 1.204064 + 0.543396I
a = 1.034089 + 0.330399I
b = 0.70914 1.56799I
0.14862 + 9.86900I 0.17397 6.31432I
u = 1.049026 0.353850I
a = 1.245783 + 0.485692I
b = 1.24924 1.54414I
3.94869 4.27443I 3.00004 + 5.15320I
u = 1.049026 + 0.353850I
a = 1.245783 0.485692I
b = 1.24924 + 1.54414I
3.94869 + 4.27443I 3.00004 5.15320I
u = 0.967998 0.212799I
a = 0.192828 + 0.865113I
b = 0.428273 0.626339I
4.87893 + 2.71275I 9.31371 4.28774I
u = 0.967998 + 0.212799I
a = 0.192828 0.865113I
b = 0.428273 + 0.626339I
4.87893 2.71275I 9.31371 + 4.28774I
u = 0.78926 1.18254I
a = 0.080607 0.448362I
b = 0.615118 + 0.510422I
1.70771 + 3.92061I 2.90621 12.12775I
u = 0.78926 + 1.18254I
a = 0.080607 + 0.448362I
b = 0.615118 0.510422I
1.70771 3.92061I 2.90621 + 12.12775I
u = 0.782344 0.411126I
a = 0.20171 + 1.54915I
b = 0.57343 2.81840I
0.57965 2.48080I 4.91011 + 4.29716I
u = 0.782344 + 0.411126I
a = 0.20171 1.54915I
b = 0.57343 + 2.81840I
0.57965 + 2.48080I 4.91011 4.29716I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.77537 1.24885I
a = 0.209500 + 1.105011I
b = 1.73251 1.58384I
2.4732 + 16.9235I 0.76013 9.20932I
u = 0.77537 + 1.24885I
a = 0.209500 1.105011I
b = 1.73251 + 1.58384I
2.4732 16.9235I 0.76013 + 9.20932I
u = 0.640749 1.227976I
a = 0.347825 1.306573I
b = 1.89432 + 1.28950I
6.73040 + 10.34398I 3.27718 8.29339I
u = 0.640749 + 1.227976I
a = 0.347825 + 1.306573I
b = 1.89432 1.28950I
6.73040 10.34398I 3.27718 + 8.29339I
u = 0.572860 1.122135I
a = 1.57921 + 0.15066I
b = 0.39463 + 1.61598I
1.60491 + 7.59190I 2.13528 7.96073I
u = 0.572860 + 1.122135I
a = 1.57921 0.15066I
b = 0.39463 1.61598I
1.60491 7.59190I 2.13528 + 7.96073I
u = 0.470368 1.055658I
a = 0.10526 + 1.70042I
b = 1.43677 0.36845I
0.67110 + 3.32518I 3.10242 2.55375I
u = 0.470368 + 1.055658I
a = 0.10526 1.70042I
b = 1.43677 + 0.36845I
0.67110 3.32518I 3.10242 + 2.55375I
u = 0.434959 1.171367I
a = 0.402407 + 0.984247I
b = 0.521206 1.277336I
0.83262 + 6.84654I 0.10721 5.00564I
u = 0.434959 + 1.171367I
a = 0.402407 0.984247I
b = 0.521206 + 1.277336I
0.83262 6.84654I 0.10721 + 5.00564I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.422840 0.530363I
a = 1.58018 + 0.37044I
b = 1.229749 0.663799I
1.050552 + 0.525213I 3.80566 5.40228I
u = 0.422840 + 0.530363I
a = 1.58018 0.37044I
b = 1.229749 + 0.663799I
1.050552 0.525213I 3.80566 + 5.40228I
u = 0.418183 0.830193I
a = 0.380920 0.222170I
b = 2.78057 + 1.17528I
1.53422 + 1.77853I 13.6461 + 18.0080I
u = 0.418183 + 0.830193I
a = 0.380920 + 0.222170I
b = 2.78057 1.17528I
1.53422 1.77853I 13.6461 18.0080I
u = 0.363096 0.475061I
a = 0.704381 0.763707I
b = 0.800547 0.085552I
0.638942 + 1.236306I 4.36186 4.95807I
u = 0.363096 + 0.475061I
a = 0.704381 + 0.763707I
b = 0.800547 + 0.085552I
0.638942 1.236306I 4.36186 + 4.95807I
u = 0.342943 0.988238I
a = 0.135827 + 0.432654I
b = 0.202926 1.048137I
0.62570 + 2.03170I 1.27918 2.72742I
u = 0.342943 + 0.988238I
a = 0.135827 0.432654I
b = 0.202926 + 1.048137I
0.62570 2.03170I 1.27918 + 2.72742I
u = 0.300612 1.059858I
a = 1.57884 + 0.21984I
b = 1.28821 1.15740I
3.63710 0.29930I 1.93002 + 2.27593I
u = 0.300612 + 1.059858I
a = 1.57884 0.21984I
b = 1.28821 + 1.15740I
3.63710 + 0.29930I 1.93002 2.27593I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.259845
a = 2.49022
b = 0.994070
2.31401 2.89562
u = 0.182154 0.954080I
a = 0.593804 1.160767I
b = 0.131187 + 1.133753I
2.76633 + 1.81907I 5.04908 2.94377I
u = 0.182154 + 0.954080I
a = 0.593804 + 1.160767I
b = 0.131187 1.133753I
2.76633 1.81907I 5.04908 + 2.94377I
u = 0.158109 0.674265I
a = 0.814539 0.084505I
b = 1.47452 0.89524I
0.733207 + 1.164173I 5.75824 3.22185I
u = 0.158109 + 0.674265I
a = 0.814539 + 0.084505I
b = 1.47452 + 0.89524I
0.733207 1.164173I 5.75824 + 3.22185I
u = 0.116001 1.363919I
a = 0.321544 0.992289I
b = 0.263487 0.334702I
10.36011 0.43943I 6.98123 + 0.61175I
u = 0.116001 + 1.363919I
a = 0.321544 + 0.992289I
b = 0.263487 + 0.334702I
10.36011 + 0.43943I 6.98123 0.61175I
u = 0.040910 0.635562I
a = 2.16615 + 0.56759I
b = 0.787624 + 0.283010I
3.76322 4.31820I 6.94666 + 1.76779I
u = 0.040910 + 0.635562I
a = 2.16615 0.56759I
b = 0.787624 0.283010I
3.76322 + 4.31820I 6.94666 1.76779I
u = 0.091987 1.395921I
a = 0.219595 + 0.366680I
b = 0.177799 0.120735I
0.50220 + 3.12016I 4.96274 11.92067I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.091987 + 1.395921I
a = 0.219595 0.366680I
b = 0.177799 + 0.120735I
0.50220 3.12016I 4.96274 + 11.92067I
u = 0.15556 1.52316I
a = 0.183715 + 0.730215I
b = 0.219110 0.018664I
8.97886 5.87062I 4.82008 + 5.91834I
u = 0.15556 + 1.52316I
a = 0.183715 0.730215I
b = 0.219110 + 0.018664I
8.97886 + 5.87062I 4.82008 5.91834I
u = 0.371326 1.151650I
a = 0.587732 0.269918I
b = 2.04457 + 0.45672I
4.63878 3.29846I 3.31669 + 7.32300I
u = 0.371326 + 1.151650I
a = 0.587732 + 0.269918I
b = 2.04457 0.45672I
4.63878 + 3.29846I 3.31669 7.32300I
u = 0.384908 0.642002I
a = 0.623596 0.380641I
b = 1.213242 0.130396I
2.06670 + 0.96031I 7.01026 + 0.44637I
u = 0.384908 + 0.642002I
a = 0.623596 + 0.380641I
b = 1.213242 + 0.130396I
2.06670 0.96031I 7.01026 0.44637I
u = 0.497375 1.156288I
a = 0.445390 0.296093I
b = 1.91967 + 0.54999I
3.73969 4.87336I 11.68238 4.88288I
u = 0.497375 + 1.156288I
a = 0.445390 + 0.296093I
b = 1.91967 0.54999I
3.73969 + 4.87336I 11.68238 + 4.88288I
u = 0.504028 1.050933I
a = 0.438287 1.311128I
b = 1.04554 + 1.56317I
1.17091 6.36314I 0.22757 + 8.33937I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.504028 + 1.050933I
a = 0.438287 + 1.311128I
b = 1.04554 1.56317I
1.17091 + 6.36314I 0.22757 8.33937I
u = 0.542577 0.884808I
a = 1.58430 + 0.17959I
b = 0.339960 + 0.879599I
3.42139 4.04641I 7.51093 + 7.61012I
u = 0.542577 + 0.884808I
a = 1.58430 0.17959I
b = 0.339960 0.879599I
3.42139 + 4.04641I 7.51093 7.61012I
u = 0.550290 0.713216I
a = 0.21085 + 1.69031I
b = 0.94593 1.45349I
3.94019 0.36090I 9.78961 + 0.85223I
u = 0.550290 + 0.713216I
a = 0.21085 1.69031I
b = 0.94593 + 1.45349I
3.94019 + 0.36090I 9.78961 0.85223I
u = 0.555330 0.426705I
a = 1.63897 + 0.66555I
b = 0.205728 1.067467I
0.63691 + 2.06340I 4.30464 4.04645I
u = 0.555330 + 0.426705I
a = 1.63897 0.66555I
b = 0.205728 + 1.067467I
0.63691 2.06340I 4.30464 + 4.04645I
u = 0.563000 1.270970I
a = 0.140634 + 0.553694I
b = 0.886130 1.038442I
6.53398 5.54394I 4.50504 + 1.63762I
u = 0.563000 + 1.270970I
a = 0.140634 0.553694I
b = 0.886130 + 1.038442I
6.53398 + 5.54394I 4.50504 1.63762I
u = 0.639775 1.172904I
a = 0.297392 + 1.094183I
b = 1.16427 1.61530I
3.01535 12.24188I 2.49289 + 8.41937I
8
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.639775 + 1.172904I
a = 0.297392 1.094183I
b = 1.16427 + 1.61530I
3.01535 + 12.24188I 2.49289 8.41937I
u = 0.753769 0.149844I
a = 0.098702 0.450913I
b = 0.39424 + 4.23052I
0.821815 + 0.287086I 15.6399 + 24.5037I
u = 0.753769 + 0.149844I
a = 0.098702 + 0.450913I
b = 0.39424 4.23052I
0.821815 0.287086I 15.6399 24.5037I
u = 0.82605 1.20952I
a = 0.117999 0.662388I
b = 1.105743 + 0.810313I
3.47932 8.87997I 0.32272 + 8.36236I
u = 0.82605 + 1.20952I
a = 0.117999 + 0.662388I
b = 1.105743 0.810313I
3.47932 + 8.87997I 0.32272 8.36236I
u = 0.919240 0.397727I
a = 1.138687 0.621518I
b = 0.284089 + 1.138636I
5.39522 + 6.50016I 6.35949 5.27624I
u = 0.919240 + 0.397727I
a = 1.138687 + 0.621518I
b = 0.284089 1.138636I
5.39522 6.50016I 6.35949 + 5.27624I
u = 1.00143
a = 0.393379
b = 0.0190921
2.81001 3.04703
u = 1.078048 0.845687I
a = 0.370141 0.148810I
b = 0.640624 0.374257I
1.94802 + 1.61598I 10.03099 8.04874I
u = 1.078048 + 0.845687I
a = 0.370141 + 0.148810I
b = 0.640624 + 0.374257I
1.94802 1.61598I 10.03099 + 8.04874I
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.45559
a = 0.350555
b = 0.559462
2.44443 13.2678
9
II. I
v
1
= hb
5
+ 4b
4
+ 4b
3
b
2
2b + 1, b
4
5b
3
8b
2
3b + v + 2, ai
(i) Arc colorings
a
2
=
1
0
a
7
=
b
4
+ 5b
3
+ 8b
2
+ 3b 2
0
a
3
=
1
0
a
10
=
0
b
a
8
=
b
4
+ 5b
3
+ 8b
2
+ 3b 2
b
2
+ b 1
a
6
=
b
4
+ 5b
3
+ 8b
2
+ 3b 2
0
a
11
=
b
2
+ 3b + 2
b
a
5
=
b
4
4b
3
4b
2
+ b + 3
1
a
4
=
b
4
4b
3
4b
2
+ b + 4
1
a
1
=
b
4
+ 4b
3
+ 4b
2
b 3
1
a
9
=
b
4
+ 4b
3
+ 4b
2
2b 4
1
a
9
=
b
4
+ 4b
3
+ 4b
2
2b 4
1
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
10
(iv) Complex Volumes and Cusp Shapes
Solution to I
v
1
1(vol +
1CS) Cusp shape
v = 0.345770
a = 0
b = 2.21774
0.756147 9.00265
v = 0.003977 + 0.626138I
a = 0
b = 1.30992 0.54991I
1.31583 + 1.53058I 1.45754 4.40323I
v = 0.003977 0.626138I
a = 0
b = 1.30992 + 0.54991I
1.31583 1.53058I 1.45754 + 4.40323I
v = 0.32314 2.69669I
a = 0
b = 0.418784 0.219165I
4.22763 4.40083I 10.04378 + 5.20937I
v = 0.32314 + 2.69669I
a = 0
b = 0.418784 + 0.219165I
4.22763 + 4.40083I 10.04378 5.20937I
11
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
5
(u
71
+ 6u
70
+ ··· + 8u + 1)
c
2
, c
6
u
5
(u
71
+ u
70
+ ··· + 160u + 32)
c
3
, c
4
(u + 1)
5
(u
71
+ 6u
70
+ ··· + 8u + 1)
c
5
(u
5
+ 3u
4
+ ··· u 1)(u
71
+ 6u
70
+ ··· + 2u + 1)
c
7
(u
5
+ u
4
+ ··· + u + 1)(u
71
+ 12u
70
+ ··· + 2u + 1)
c
8
(u
5
u
4
+ ··· + u + 1)(u
71
+ 2u
70
+ ··· 10u 1)
c
9
(u
5
+ u
4
+ ··· + u 1)(u
71
+ 2u
70
+ ··· + 1044u 216)
c
10
(u
5
u
4
+ ··· + u 1)(u
71
+ 2u
70
+ ··· 26u 71)
c
11
(u
5
+ u
4
+ ··· + u 1)(u
71
+ 2u
70
+ ··· 10u 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y 1)
5
(y
71
64y
70
+ ··· + 192y 1)
c
2
, c
6
y
5
(y
71
+ 33y
70
+ ··· 4608y 1024)
c
3
, c
4
(y 1)
5
(y
71
64y
70
+ ··· + 192y 1)
c
5
(y
5
y
4
+ ··· + 3y 1)(y
71
12y
70
+ ··· + 6y 1)
c
7
(y
5
+ 3y
4
+ ··· y 1)(y
71
+ 60y
69
+ ··· + 10y 1)
c
8
(y
5
5y
4
+ ··· y 1)(y
71
48y
70
+ ··· + 10y 1)
c
9
(y
5
5y
4
+ ··· y 1)(y
71
+ 48y
70
+ ··· + 5221584y 46656)
c
10
(y
5
+ 3y
4
+ ··· y 1)(y
71
+ 72y
70
+ ··· 272958y 5041)
c
11
(y
5
5y
4
+ ··· y 1)(y
71
48y
70
+ ··· + 10y 1)
13