11a
66
(K11a
66
)
1
Arc Sequences
5 1 10 2 9 4 11 3 6 7 8
Solving Sequence
1,5
2
3,8
9 4 11 7 6 10
c
1
c
2
c
8
c
4
c
11
c
7
c
6
c
10
c
3
, c
5
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
59
u
58
+ ··· + 14u + 1, 2.17261 × 10
60
u
58
+ 2.09783 × 10
59
u
57
+ ··· + 6.08228 × 10
60
b + 5.44455 × 10
60
,
3.95323 × 10
60
u
58
2.32669 × 10
60
u
57
+ ··· + 6.08228 × 10
60
a + 8.60598 × 10
61
i
There are 1 irreducible components with 59 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
59
u
58
+· · ·+14u+1, 2.17×10
60
u
58
+2.10×10
59
u
57
+· · ·+6.08×10
60
b+
5.44 × 10
60
, 3.95 × 10
60
u
58
2.33 × 10
60
u
57
+ · · · + 6.08 × 10
60
a + 8.61 × 10
61
i
(i) Arc colorings
a
1
=
1
0
a
5
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
8
=
0.649958u
58
+ 0.382537u
57
+ ··· + 0.741729u 14.1493
0.357203u
58
0.0344909u
57
+ ··· + 8.04524u 0.895150
a
9
=
0.383028u
58
+ 0.241588u
57
+ ··· + 5.51077u 15.3155
0.136065u
58
+ 0.548598u
57
+ ··· + 10.8401u 0.679348
a
4
=
u
u
3
+ u
a
11
=
0.686276u
58
0.176394u
57
+ ··· 14.9222u + 20.5447
0.0885939u
58
0.420144u
57
+ ··· 12.3359u + 1.20213
a
7
=
1.32955u
58
2.13655u
57
+ ··· 25.2960u + 15.3108
0.509375u
58
0.628741u
57
+ ··· 7.03251u + 1.03517
a
6
=
0.801503u
58
1.38943u
57
+ ··· 18.4220u + 15.9304
0.931862u
58
1.22997u
57
+ ··· 11.3675u + 0.634603
a
10
=
0.0980844u
58
+ 1.22423u
57
+ ··· + 3.04674u 3.16147
1.12615u
58
+ 0.545980u
57
+ ··· + 1.78829u 0.0980844
a
10
=
0.0980844u
58
+ 1.22423u
57
+ ··· + 3.04674u 3.16147
1.12615u
58
+ 0.545980u
57
+ ··· + 1.78829u 0.0980844
(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 = 1.064355 0.710563I
a = 1.97629 0.37437I
b = 1.49940 0.03329I
7.24513 + 3.41415I 10.58303 5.98914I
u = 1.064355 + 0.710563I
a = 1.97629 + 0.37437I
b = 1.49940 + 0.03329I
7.24513 3.41415I 10.58303 + 5.98914I
u = 1.010790 0.212758I
a = 1.82402 0.02120I
b = 1.50177 + 0.00830I
7.78177 + 0.18045I 11.96377 + 1.17208I
u = 1.010790 + 0.212758I
a = 1.82402 + 0.02120I
b = 1.50177 0.00830I
7.78177 0.18045I 11.96377 1.17208I
u = 0.790245 0.723149I
a = 0.396987 + 0.079977I
b = 0.490640 + 0.130399I
0.68155 + 2.84567I 8.20760 7.93876I
u = 0.790245 + 0.723149I
a = 0.396987 0.079977I
b = 0.490640 0.130399I
0.68155 2.84567I 8.20760 + 7.93876I
u = 0.784703 0.971609I
a = 2.03608 1.22107I
b = 1.47328 0.05201I
6.50993 + 3.19293I 9.34631 1.82839I
u = 0.784703 + 0.971609I
a = 2.03608 + 1.22107I
b = 1.47328 + 0.05201I
6.50993 3.19293I 9.34631 + 1.82839I
u = 0.74140 1.27765I
a = 1.23355 + 1.05672I
b = 1.47786 + 0.08730I
4.61526 + 6.26348I 6.34536 8.28457I
u = 0.74140 + 1.27765I
a = 1.23355 1.05672I
b = 1.47786 0.08730I
4.61526 6.26348I 6.34536 + 8.28457I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.593823 1.153395I
a = 0.253486 0.558942I
b = 0.402436 0.343152I
1.56344 + 4.78630I 2.02963 10.35215I
u = 0.593823 + 1.153395I
a = 0.253486 + 0.558942I
b = 0.402436 + 0.343152I
1.56344 4.78630I 2.02963 + 10.35215I
u = 0.593231 0.887882I
a = 0.772276 + 0.440343I
b = 0.344914 + 0.168527I
0.46273 + 2.38122I 3.10427 1.63624I
u = 0.593231 + 0.887882I
a = 0.772276 0.440343I
b = 0.344914 0.168527I
0.46273 2.38122I 3.10427 + 1.63624I
u = 0.584520 0.180468I
a = 0.038478 + 0.173054I
b = 0.526798 0.021630I
1.131639 + 0.063901I 10.49402 + 0.56940I
u = 0.584520 + 0.180468I
a = 0.038478 0.173054I
b = 0.526798 + 0.021630I
1.131639 0.063901I 10.49402 0.56940I
u = 0.507209 0.868992I
a = 9.8119 + 13.0662I
b = 1.42247 + 0.01167I
3.30587 + 2.05347I 89.717 + 117.950I
u = 0.507209 + 0.868992I
a = 9.8119 13.0662I
b = 1.42247 0.01167I
3.30587 2.05347I 89.717 117.950I
u = 0.501934 0.957791I
a = 0.93817 + 1.38499I
b = 0.253207 + 0.285102I
1.85782 + 2.60565I 2.86490 + 11.40100I
u = 0.501934 + 0.957791I
a = 0.93817 1.38499I
b = 0.253207 0.285102I
1.85782 2.60565I 2.86490 11.40100I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.433780 0.723088I
a = 0.35427 1.55677I
b = 0.023287 0.400883I
1.06640 + 1.39300I 4.87303 6.40557I
u = 0.433780 + 0.723088I
a = 0.35427 + 1.55677I
b = 0.023287 + 0.400883I
1.06640 1.39300I 4.87303 + 6.40557I
u = 0.206110 1.093181I
a = 0.305183 + 0.654125I
b = 1.384972 + 0.131008I
3.26189 + 3.67751I 6.15406 4.60503I
u = 0.206110 + 1.093181I
a = 0.305183 0.654125I
b = 1.384972 0.131008I
3.26189 3.67751I 6.15406 + 4.60503I
u = 0.0685067
a = 14.5941
b = 1.45449
3.37740 1.89727
u = 0.063726 1.379460I
a = 0.434563 0.370125I
b = 1.43879 0.18099I
0.67928 + 6.89950I 1.35104 6.34651I
u = 0.063726 + 1.379460I
a = 0.434563 + 0.370125I
b = 1.43879 + 0.18099I
0.67928 6.89950I 1.35104 + 6.34651I
u = 0.043408 0.621532I
a = 0.885935 1.059150I
b = 0.009641 0.561258I
1.27830 + 1.37033I 1.75929 4.49534I
u = 0.043408 + 0.621532I
a = 0.885935 + 1.059150I
b = 0.009641 + 0.561258I
1.27830 1.37033I 1.75929 + 4.49534I
u = 0.028294 0.707313I
a = 0.48950 + 1.33869I
b = 1.179588 0.072832I
1.93352 0.03829I 3.14711 0.23207I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.028294 + 0.707313I
a = 0.48950 1.33869I
b = 1.179588 + 0.072832I
1.93352 + 0.03829I 3.14711 + 0.23207I
u = 0.048802 1.218231I
a = 0.227155 + 0.474700I
b = 0.331322 + 0.631890I
6.37379 + 4.04787I 3.93072 5.51814I
u = 0.048802 + 1.218231I
a = 0.227155 0.474700I
b = 0.331322 0.631890I
6.37379 4.04787I 3.93072 + 5.51814I
u = 0.192917 1.026281I
a = 0.94151 1.12510I
b = 0.738862 0.507440I
5.18481 + 0.07298I 2.77397 + 1.06751I
u = 0.192917 + 1.026281I
a = 0.94151 + 1.12510I
b = 0.738862 + 0.507440I
5.18481 0.07298I 2.77397 1.06751I
u = 0.533797 0.505845I
a = 1.196272 0.262387I
b = 0.298346 0.756487I
1.35810 + 1.65554I 2.46202 2.77708I
u = 0.533797 + 0.505845I
a = 1.196272 + 0.262387I
b = 0.298346 + 0.756487I
1.35810 1.65554I 2.46202 + 2.77708I
u = 0.577196 1.015582I
a = 0.251793 0.158582I
b = 0.513328 + 0.905605I
2.77146 6.25200I 0.81747 + 7.69148I
u = 0.577196 + 1.015582I
a = 0.251793 + 0.158582I
b = 0.513328 0.905605I
2.77146 + 6.25200I 0.81747 7.69148I
u = 0.579626 0.802771I
a = 1.68169 + 1.07389I
b = 1.70668 0.24332I
4.61241 1.25946I 15.0205 1.0987I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.579626 + 0.802771I
a = 1.68169 1.07389I
b = 1.70668 + 0.24332I
4.61241 + 1.25946I 15.0205 + 1.0987I
u = 0.593918 0.887645I
a = 1.77990 + 1.63401I
b = 1.61782 + 0.39605I
4.33658 3.40939I 12.6596 + 8.8101I
u = 0.593918 + 0.887645I
a = 1.77990 1.63401I
b = 1.61782 0.39605I
4.33658 + 3.40939I 12.6596 8.8101I
u = 0.594537 0.692099I
a = 0.235606 + 0.614018I
b = 0.780237 0.719781I
2.44555 + 0.67895I 9.33553 4.12644I
u = 0.594537 + 0.692099I
a = 0.235606 0.614018I
b = 0.780237 + 0.719781I
2.44555 0.67895I 9.33553 + 4.12644I
u = 0.606484 0.944340I
a = 1.202324 + 0.592165I
b = 0.610635 + 0.920920I
1.69330 5.46743I 7.02970 + 10.41189I
u = 0.606484 + 0.944340I
a = 1.202324 0.592165I
b = 0.610635 0.920920I
1.69330 + 5.46743I 7.02970 10.41189I
u = 0.642705 1.100128I
a = 1.033073 0.685018I
b = 0.602290 0.803555I
2.44624 11.82369I 1.37981 + 9.37680I
u = 0.642705 + 1.100128I
a = 1.033073 + 0.685018I
b = 0.602290 + 0.803555I
2.44624 + 11.82369I 1.37981 9.37680I
u = 0.700621 1.040867I
a = 1.63941 1.62857I
b = 1.57430 0.29595I
8.82124 9.84696I 7.90659 + 6.83623I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.700621 + 1.040867I
a = 1.63941 + 1.62857I
b = 1.57430 + 0.29595I
8.82124 + 9.84696I 7.90659 6.83623I
u = 0.707004 1.141365I
a = 1.56458 + 1.64473I
b = 1.56490 + 0.27474I
4.6425 15.8011I 4.42908 + 8.58260I
u = 0.707004 + 1.141365I
a = 1.56458 1.64473I
b = 1.56490 0.27474I
4.6425 + 15.8011I 4.42908 8.58260I
u = 0.831157 0.456494I
a = 0.518276 0.336586I
b = 0.610415 + 0.675553I
0.53563 + 6.33799I 3.85891 5.79197I
u = 0.831157 + 0.456494I
a = 0.518276 + 0.336586I
b = 0.610415 0.675553I
0.53563 6.33799I 3.85891 + 5.79197I
u = 0.840862 0.624993I
a = 2.01436 0.29583I
b = 1.57947 + 0.22255I
10.09090 + 4.09953I 10.00866 1.65050I
u = 0.840862 + 0.624993I
a = 2.01436 + 0.29583I
b = 1.57947 0.22255I
10.09090 4.09953I 10.00866 + 1.65050I
u = 0.975566 0.506822I
a = 2.06004 0.00741I
b = 1.55701 0.22591I
6.60505 + 9.68161I 6.60636 4.88328I
u = 0.975566 + 0.506822I
a = 2.06004 + 0.00741I
b = 1.55701 + 0.22591I
6.60505 9.68161I 6.60636 + 4.88328I
8
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
(u
59
+ u
58
+ ··· + 14u 1)
c
2
(u
59
+ 23u
58
+ ··· + 198u 1)
c
3
(u
59
+ 3u
58
+ ··· 4u 1)
c
5
, c
9
(u
59
+ u
58
+ ··· + 5u
2
1)
c
6
(u
59
+ 11u
58
+ ··· + 286u
2
+ 8)
c
7
, c
10
, c
11
(u
59
+ 5u
58
+ ··· 5u
2
+ 1)
c
8
(u
59
+ 15u
58
+ ··· 256u + 256)
9
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
59
+ 23y
58
+ ··· + 198y 1)
c
2
(y
59
+ 27y
58
+ ··· + 45406y 1)
c
3
(y
59
5y
58
+ ··· 18y 1)
c
5
, c
9
(y
59
37y
58
+ ··· + 10y 1)
c
6
(y
59
+ 279y
58
+ ··· 4576y 64)
c
7
, c
10
, c
11
(y
59
61y
58
+ ··· + 10y 1)
c
8
(y
59
+ 287y
58
+ ··· + 1015808y 65536)
10