11a
295
(K11a
295
)
1
Arc Sequences
6 9 1 8 2 10 11 3 5 7 4
Solving Sequence
2,9 3,5
6 10 7 11 1 8 4
c
2
c
5
c
9
c
6
c
10
c
1
c
8
c
4
c
3
, c
7
, c
11
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu
12
u
11
+ 5u
10
u
9
+ 12u
8
+ 2u
7
+ 18u
6
+ 8u
5
+ 16u
4
+ 7u
3
+ 7u
2
+ 2u + 1,
2u
11
u
10
+ 7u
9
+ 5u
8
+ 14u
7
+ 17u
6
+ 19u
5
+ 29u
4
+ 15u
3
+ 16u
2
+ b + 4u + 3,
2u
11
+ 6u
10
16u
9
+ 24u
8
37u
7
+ 44u
6
46u
5
+ 47u
4
24u
3
+ 28u
2
+ a 3u + 8i
I
u
2
= hu
66
+ 2u
65
+ ··· + 337u + 121,
1.18562 × 10
134
u
65
1.81175 × 10
133
u
64
+ ··· + 9.47090 × 10
134
b 3.58348 × 10
136
,
3.35223 × 10
136
u
65
4.73290 × 10
136
u
64
+ ··· + 1.14598 × 10
137
a + 1.61305 × 10
138
i
There are 2 irreducible components with 78 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
12
u
11
+· · ·+2u+1, 2u
11
u
10
+· · ·+b+3, 2u
11
+6u
10
+· · ·+a+8i
(i) Arc colorings
a
2
=
1
0
a
9
=
2u
11
6u
10
+ ··· + 3u 8
2u
11
+ u
10
+ ··· 4u 3
a
3
=
4u
11
3u
10
+ ··· + 19u + 9
u
10
+ u
9
4u
8
8u
6
2u
5
10u
4
6u
3
6u
2
u
a
5
=
0
u
a
6
=
u
u
a
10
=
2u
11
6u
10
+ ··· + 3u 8
4u
11
+ 3u
10
+ ··· 10u 7
a
7
=
3u
11
+ 8u
10
+ ··· 8u + 7
2u
10
2u
9
+ 10u
8
3u
7
+ 25u
6
+ 36u
4
+ 9u
3
+ 29u
2
+ 7u + 8
a
11
=
7u
11
+ 10u
10
+ ··· 10u
2
20u
u
9
+ u
8
4u
7
8u
5
2u
4
10u
3
5u
2
6u
a
1
=
u
2
+ 1
u
2
a
8
=
4u
11
6u
10
+ ··· + 12u + 2
u
11
4u
10
+ ··· 6u 5
a
4
=
3u
11
2u
10
+ ··· + 13u + 7
u
10
+ u
9
4u
8
8u
6
2u
5
10u
4
6u
3
6u
2
a
4
=
3u
11
2u
10
+ ··· + 13u + 7
u
10
+ u
9
4u
8
8u
6
2u
5
10u
4
6u
3
6u
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 = 0.498736 1.049043I
a = 0.344571 + 0.179120I
b = 0.436264 0.375928I
1.64985 + 2.57365I 12.02620 3.39540I
u = 0.498736 + 1.049043I
a = 0.344571 0.179120I
b = 0.436264 + 0.375928I
1.64985 2.57365I 12.02620 + 3.39540I
u = 0.300410 0.503097I
a = 0.13606 3.54713I
b = 0.276860 0.753139I
7.64591 + 4.32752I 14.4982 5.1187I
u = 0.300410 + 0.503097I
a = 0.13606 + 3.54713I
b = 0.276860 + 0.753139I
7.64591 4.32752I 14.4982 + 5.1187I
u = 0.296152 0.699894I
a = 0.539662 + 1.130002I
b = 0.476182 + 0.586558I
0.99987 + 2.95882I 8.95384 10.28538I
u = 0.296152 + 0.699894I
a = 0.539662 1.130002I
b = 0.476182 0.586558I
0.99987 2.95882I 8.95384 + 10.28538I
u = 0.100055 0.813215I
a = 0.471575 + 1.069468I
b = 0.57539 1.56859I
5.02229 1.34240I 13.23433 + 1.17063I
u = 0.100055 + 0.813215I
a = 0.471575 1.069468I
b = 0.57539 + 1.56859I
5.02229 + 1.34240I 13.23433 1.17063I
u = 0.533873 1.256768I
a = 0.709720 0.222372I
b = 0.211327 + 1.361949I
4.35770 2.95981I 6.70212 1.32008I
u = 0.533873 + 1.256768I
a = 0.709720 + 0.222372I
b = 0.211327 1.361949I
4.35770 + 2.95981I 6.70212 + 1.32008I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.96137 1.43587I
a = 0.661001 0.084483I
b = 0.151135 1.234645I
1.09062 4.53454I 3.08537 + 5.69650I
u = 0.96137 + 1.43587I
a = 0.661001 + 0.084483I
b = 0.151135 + 1.234645I
1.09062 + 4.53454I 3.08537 5.69650I
4
II. I
u
2
= hu
66
+ 2u
65
+ · · · + 337u + 121, 1.19 × 10
134
u
65
1.81 × 10
133
u
64
+
· · · + 9.47 × 10
134
b 3.58 × 10
136
, 3.35 × 10
136
u
65
4.73 × 10
136
u
64
+ · · · +
1.15 × 10
137
a + 1.61 × 10
138
i
(i) Arc colorings
a
2
=
1
0
a
9
=
0.292521u
65
+ 0.413000u
64
+ ··· + 4.66027u 14.0757
0.125186u
65
+ 0.0191297u
64
+ ··· + 79.1053u + 37.8368
a
3
=
0.0851133u
65
+ 0.0788565u
64
+ ··· + 92.4004u + 42.2237
0.678774u
65
1.38228u
64
+ ··· 188.600u 44.8380
a
5
=
0
u
a
6
=
u
u
a
10
=
0.292521u
65
+ 0.413000u
64
+ ··· + 4.66027u 14.0757
0.144207u
65
+ 0.344911u
64
+ ··· + 56.5220u + 17.0196
a
7
=
0.265775u
65
+ 0.709300u
64
+ ··· + 177.381u + 47.1015
0.00974749u
65
+ 0.661588u
64
+ ··· + 233.587u + 92.0427
a
11
=
0.497188u
65
0.770818u
64
+ ··· 10.5479u + 13.3467
0.177945u
65
0.358838u
64
+ ··· 136.543u 85.8897
a
1
=
u
2
+ 1
u
2
a
8
=
0.239273u
65
0.560967u
64
+ ··· 84.5604u 19.8704
1.00693u
65
+ 0.956754u
64
+ ··· 102.931u 115.394
a
4
=
0.118077u
65
+ 0.0396210u
64
+ ··· + 96.8931u + 46.0532
0.695708u
65
1.45455u
64
+ ··· 208.600u 52.7154
a
4
=
0.118077u
65
+ 0.0396210u
64
+ ··· + 96.8931u + 46.0532
0.695708u
65
1.45455u
64
+ ··· 208.600u 52.7154
(ii) Obstruction class = 1
(iii) Cusp Shapes =unknown
5
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.354558 0.246255I
a = 0.369961 + 0.652290I
b = 0.418270 + 1.216759I
7.53925 8.57953I 10.36804 + 6.24736I
u = 1.354558 + 0.246255I
a = 0.369961 0.652290I
b = 0.418270 1.216759I
7.53925 + 8.57953I 10.36804 6.24736I
u = 1.116290 0.041930I
a = 0.408138 + 0.706863I
b = 0.420123 + 1.112897I
1.13230 + 5.61385I 7.73447 7.80820I
u = 1.116290 + 0.041930I
a = 0.408138 0.706863I
b = 0.420123 1.112897I
1.13230 5.61385I 7.73447 + 7.80820I
u = 0.85216 1.36098I
a = 0.692019 0.151226I
b = 0.115704 1.020082I
0.16047 + 3.95702I 8.80042 3.39843I
u = 0.85216 + 1.36098I
a = 0.692019 + 0.151226I
b = 0.115704 + 1.020082I
0.16047 3.95702I 8.80042 + 3.39843I
u = 0.845743
a = 1.38571
b = 0.638431
6.81634 14.5151
u = 0.66897 1.35203I
a = 1.208238 0.208542I
b = 0.55812 + 1.41815I
3.9251 + 15.5092I 8.61877 7.80735I
u = 0.66897 + 1.35203I
a = 1.208238 + 0.208542I
b = 0.55812 1.41815I
3.9251 15.5092I 8.61877 + 7.80735I
u = 0.634117 0.759014I
a = 0.47320 + 1.68936I
b = 0.200360 + 0.695523I
7.42737 + 2.83943I 11.81996 1.03899I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.634117 + 0.759014I
a = 0.47320 1.68936I
b = 0.200360 0.695523I
7.42737 2.83943I 11.81996 + 1.03899I
u = 0.583417 0.964228I
a = 1.320965 + 0.483188I
b = 0.669641 + 0.580855I
6.78842 + 2.02734I 12.06412 3.13769I
u = 0.583417 + 0.964228I
a = 1.320965 0.483188I
b = 0.669641 0.580855I
6.78842 2.02734I 12.06412 + 3.13769I
u = 0.554991 0.832246I
a = 0.365924 0.583201I
b = 0.006605 0.382994I
0.63556 + 2.23216I 3.27314 + 0.28739I
u = 0.554991 + 0.832246I
a = 0.365924 + 0.583201I
b = 0.006605 + 0.382994I
0.63556 2.23216I 3.27314 0.28739I
u = 0.51147 1.33806I
a = 1.057054 + 0.307355I
b = 0.57803 1.42790I
3.18615 + 11.21571I 5.77248 8.25519I
u = 0.51147 + 1.33806I
a = 1.057054 0.307355I
b = 0.57803 + 1.42790I
3.18615 11.21571I 5.77248 + 8.25519I
u = 0.468529 0.501931I
a = 1.002967 0.967865I
b = 0.489851 0.829291I
1.02770 + 2.29601I 9.69444 1.14356I
u = 0.468529 + 0.501931I
a = 1.002967 + 0.967865I
b = 0.489851 + 0.829291I
1.02770 2.29601I 9.69444 + 1.14356I
u = 0.382935 1.209541I
a = 0.791307 + 0.504739I
b = 0.672686 + 0.122268I
2.99874 + 4.32150I 10.39713 4.09568I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.382935 + 1.209541I
a = 0.791307 0.504739I
b = 0.672686 0.122268I
2.99874 4.32150I 10.39713 + 4.09568I
u = 0.36799 1.45280I
a = 0.700985 0.240357I
b = 0.044674 + 1.054040I
3.85841 + 0.35943I 2.42133 + 0.09883I
u = 0.36799 + 1.45280I
a = 0.700985 + 0.240357I
b = 0.044674 1.054040I
3.85841 0.35943I 2.42133 0.09883I
u = 0.316427 1.238150I
a = 0.833635 0.467169I
b = 0.64639 + 1.48451I
3.39375 + 5.20124I 6.22642 6.09033I
u = 0.316427 + 1.238150I
a = 0.833635 + 0.467169I
b = 0.64639 1.48451I
3.39375 5.20124I 6.22642 + 6.09033I
u = 0.298966
a = 1.58840
b = 0.368557
0.660290 15.1129
u = 0.192173 0.876307I
a = 0.274596 + 0.060055I
b = 0.97672 1.47152I
4.71138 + 2.03235I 10.76063 8.45784I
u = 0.192173 + 0.876307I
a = 0.274596 0.060055I
b = 0.97672 + 1.47152I
4.71138 2.03235I 10.76063 + 8.45784I
u = 0.166328 0.889378I
a = 0.178912 + 1.257134I
b = 0.26921 1.73433I
4.74716 0.24143I 11.20357 1.33057I
u = 0.166328 + 0.889378I
a = 0.178912 1.257134I
b = 0.26921 + 1.73433I
4.74716 + 0.24143I 11.20357 + 1.33057I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.131125 1.039573I
a = 0.754120 0.339995I
b = 0.646631 + 0.152437I
2.00698 + 1.67505I 2.85750 4.67727I
u = 0.131125 + 1.039573I
a = 0.754120 + 0.339995I
b = 0.646631 0.152437I
2.00698 1.67505I 2.85750 + 4.67727I
u = 0.129596 0.501602I
a = 1.57343 1.02791I
b = 0.580495 0.820287I
1.05491 + 2.33150I 8.86448 + 1.77699I
u = 0.129596 + 0.501602I
a = 1.57343 + 1.02791I
b = 0.580495 + 0.820287I
1.05491 2.33150I 8.86448 1.77699I
u = 0.069243 1.205932I
a = 0.369347 + 1.150265I
b = 0.083413 1.085398I
1.28963 3.11000I 6.45685 + 4.52196I
u = 0.069243 + 1.205932I
a = 0.369347 1.150265I
b = 0.083413 + 1.085398I
1.28963 + 3.11000I 6.45685 4.52196I
u = 0.108265 0.901145I
a = 0.66170 2.91284I
b = 0.141222 + 1.012845I
6.59255 4.44136I 6.67316 + 4.43410I
u = 0.108265 + 0.901145I
a = 0.66170 + 2.91284I
b = 0.141222 1.012845I
6.59255 + 4.44136I 6.67316 4.43410I
u = 0.211446 0.973281I
a = 1.47266 + 0.60580I
b = 0.662180 + 0.862296I
6.10476 + 3.03885I 9.55611 2.46724I
u = 0.211446 + 0.973281I
a = 1.47266 0.60580I
b = 0.662180 0.862296I
6.10476 3.03885I 9.55611 + 2.46724I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.267187 1.100177I
a = 1.117029 0.381105I
b = 0.32459 + 1.44481I
5.36608 1.78436I 3.12908 1.84447I
u = 0.267187 + 1.100177I
a = 1.117029 + 0.381105I
b = 0.32459 1.44481I
5.36608 + 1.78436I 3.12908 + 1.84447I
u = 0.33589 1.60254I
a = 0.074889 + 0.284896I
b = 0.023131 1.237405I
1.08058 2.59004I 5.02423 + 1.90961I
u = 0.33589 + 1.60254I
a = 0.074889 0.284896I
b = 0.023131 + 1.237405I
1.08058 + 2.59004I 5.02423 1.90961I
u = 0.337298 0.972157I
a = 0.638983 0.271543I
b = 1.40483 + 0.19256I
1.69376 4.59816I 10.4204 + 9.7829I
u = 0.337298 + 0.972157I
a = 0.638983 + 0.271543I
b = 1.40483 0.19256I
1.69376 + 4.59816I 10.4204 9.7829I
u = 0.343310 0.961201I
a = 0.618118 + 0.380697I
b = 0.538056 0.549223I
1.13118 1.76995I 5.98304 2.62479I
u = 0.343310 + 0.961201I
a = 0.618118 0.380697I
b = 0.538056 + 0.549223I
1.13118 + 1.76995I 5.98304 + 2.62479I
u = 0.410191 1.244111I
a = 1.282277 + 0.327942I
b = 0.387740 1.305755I
6.38275 5.64915I 1.66768 + 6.17247I
u = 0.410191 + 1.244111I
a = 1.282277 0.327942I
b = 0.387740 + 1.305755I
6.38275 + 5.64915I 1.66768 6.17247I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.527410 1.279417I
a = 1.50944 0.32278I
b = 0.430569 + 1.221428I
0.32445 8.55031I 6.94019 + 6.62913I
u = 0.527410 + 1.279417I
a = 1.50944 + 0.32278I
b = 0.430569 1.221428I
0.32445 + 8.55031I 6.94019 6.62913I
u = 0.550607 0.350148I
a = 0.714393 + 0.999376I
b = 0.809871 0.432123I
3.37039 + 1.11848I 13.33885 1.54614I
u = 0.550607 + 0.350148I
a = 0.714393 0.999376I
b = 0.809871 + 0.432123I
3.37039 1.11848I 13.33885 + 1.54614I
u = 0.555703 1.115224I
a = 0.902903 + 0.292985I
b = 1.212907 0.088188I
8.62445 9.32694I 11.47318 + 6.49002I
u = 0.555703 + 1.115224I
a = 0.902903 0.292985I
b = 1.212907 + 0.088188I
8.62445 + 9.32694I 11.47318 6.49002I
u = 0.699120 0.048731I
a = 0.533265 + 1.119477I
b = 0.086918 + 1.120974I
2.54829 1.52445I 3.35567 + 4.49090I
u = 0.699120 + 0.048731I
a = 0.533265 1.119477I
b = 0.086918 1.120974I
2.54829 + 1.52445I 3.35567 4.49090I
u = 0.72595 1.30723I
a = 0.689031 0.055544I
b = 0.142627 + 1.332549I
4.54149 3.48085I 1.46862 + 11.56926I
u = 0.72595 + 1.30723I
a = 0.689031 + 0.055544I
b = 0.142627 1.332549I
4.54149 + 3.48085I 1.46862 11.56926I
11
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.861840 0.432177I
a = 0.944922 0.929606I
b = 0.805170 + 0.171054I
10.80041 + 4.11654I 14.8793 1.1556I
u = 0.861840 + 0.432177I
a = 0.944922 + 0.929606I
b = 0.805170 0.171054I
10.80041 4.11654I 14.8793 + 1.1556I
u = 0.945865 0.014510I
a = 0.942500 + 0.675101I
b = 0.271741 + 1.131805I
3.45574 + 3.28085I 8.60109 3.29735I
u = 0.945865 + 0.014510I
a = 0.942500 0.675101I
b = 0.271741 1.131805I
3.45574 3.28085I 8.60109 + 3.29735I
u = 1.05411 1.29516I
a = 0.701414 0.260601I
b = 0.156972 1.390425I
0.60146 4.40690I 8.84170 + 3.71176I
u = 1.05411 + 1.29516I
a = 0.701414 + 0.260601I
b = 0.156972 + 1.390425I
0.60146 + 4.40690I 8.84170 3.71176I
12
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u
12
u
11
+ ··· + 2u + 1)(u
66
+ 2u
65
+ ··· + 337u + 121)
c
2
(u
12
+ 6u
10
+ ··· 3u + 1)(u
66
+ u
65
+ ··· + 262u 97)
c
3
(u
12
+ 2u
11
+ ··· u + 1)(u
66
+ 3u
65
+ ··· 110u + 13)
c
4
(u
12
+ 2u
10
3u
9
+ 7u
8
6u
6
+ 8u
5
+ 7u
4
2u
3
+ u
2
+ 3u + 1)
(u
66
+ 5u
65
+ ··· 3840u 1447)
c
5
(u
12
+ u
11
+ ··· 2u + 1)(u
66
+ 2u
65
+ ··· + 337u + 121)
c
6
(u
12
8u
10
+ 24u
8
32u
6
u
5
+ 18u
4
+ u
3
3u
2
+ 1)
(u
66
+ 5u
65
+ ··· + 3u 1)
c
7
(u
12
8u
10
+ 24u
8
32u
6
u
5
+ 18u
4
+ u
3
3u
2
+ 1)
(u
66
+ 5u
65
+ ··· + 3u 1)
c
8
(u
12
+ 6u
10
+ ··· + 3u + 1)(u
66
+ u
65
+ ··· + 262u 97)
c
9
(u
12
+ u
11
u
10
+ 7u
8
8u
7
+ 7u
6
5u
5
+ 10u
4
10u
3
+ 7u
2
2u + 1)
(u
66
+ 5u
64
+ ··· + 2311u 389)
c
10
(u
12
8u
10
+ 24u
8
32u
6
+ u
5
+ 18u
4
u
3
3u
2
+ 1)
(u
66
+ 5u
65
+ ··· + 3u 1)
c
11
(u
12
2u
11
+ ··· + u + 1)(u
66
+ 3u
65
+ ··· 110u + 13)
13
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y
12
+ 9y
11
+ ··· + 10y + 1)(y
66
+ 42y
65
+ ··· + 122865y + 14641)
c
2
(y
12
+ 12y
11
+ ··· + 5y + 1)(y
66
+ 49y
65
+ ··· + 143204y + 9409)
c
3
(y
12
+ 10y
11
+ ··· + 9y + 1)(y
66
+ 47y
65
+ ··· 3000y + 169)
c
4
(y
12
+ 4y
11
+ ··· 7y + 1)
(y
66
19y
65
+ ··· 13709505y + 2093803)
c
6
(y
12
16y
11
+ ··· 6y + 1)(y
66
71y
65
+ ··· + 29y + 1)
c
7
(y
12
16y
11
+ ··· 6y + 1)(y
66
71y
65
+ ··· + 29y + 1)
c
8
(y
12
+ 12y
11
+ ··· + 5y + 1)(y
66
+ 49y
65
+ ··· + 143204y + 9409)
c
9
(y
12
3y
11
+ ··· + 10y + 1)(y
66
+ 10y
65
+ ··· + 4949885y + 151321)
c
10
(y
12
16y
11
+ ··· 6y + 1)(y
66
71y
65
+ ··· + 29y + 1)
c
11
(y
12
+ 10y
11
+ ··· + 9y + 1)(y
66
+ 47y
65
+ ··· 3000y + 169)
14