11a
298
(K11a
298
)
1
Arc Sequences
4 8 1 9 2 11 10 5 3 6 7
Solving Sequence
5,8 3,9
10 2 6 11 4 1 7
c
8
c
9
c
2
c
5
c
10
c
4
c
1
c
7
c
3
, c
6
, c
11
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= h5u
2
5u + 1, b, a + 15u 10i
I
u
2
= h5u
67
26u
66
+ ··· + 534u 9,
3.39088 × 10
442
u
66
1.67941 × 10
443
u
65
+ ··· + 8.46140 × 10
441
b 1.07856 × 10
443
,
1.56641 × 10
444
u
66
+ 8.10698 × 10
444
u
65
+ ··· + 2.53842 × 10
442
a 2.95737 × 10
445
i
There are 2 irreducible components with 69 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
= h5u
2
5u + 1, b, a + 15u 10i
(i) Arc colorings
a
5
=
0
u
a
8
=
15u + 10
0
a
3
=
1
0
a
9
=
15u + 10
2u + 1
a
10
=
13u + 9
2u + 1
a
2
=
1
0
a
6
=
u
u
a
11
=
11u + 8
4u + 2
a
4
=
20u + 15
1
a
1
=
20u 14
1
a
7
=
17u 13
3u 2
a
7
=
17u 13
3u 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 = 0.276393
a = 5.85410
b = 0
10.5276 16.2997
u = 0.723607
a = 0.854102
b = 0
2.63189 15.8997
3
II. I
u
2
= h5u
67
26u
66
+ · · · + 534u 9, 3.39 × 10
442
u
66
1.68 × 10
443
u
65
+
· · · + 8.46 × 10
441
b 1.08 × 10
443
, 1.57 × 10
444
u
66
+ 8.11 × 10
444
u
65
+ · · · +
2.54 × 10
442
a 2.96 × 10
445
i
(i) Arc colorings
a
5
=
0
u
a
8
=
61.7081u
66
319.371u
65
+ ··· 61278.3u + 1165.04
4.00747u
66
+ 19.8479u
65
+ ··· 111.747u + 12.7469
a
3
=
1
0
a
9
=
61.7081u
66
319.371u
65
+ ··· 61278.3u + 1165.04
4.97154u
66
+ 24.5609u
65
+ ··· 162.049u + 15.4667
a
10
=
66.6797u
66
343.932u
65
+ ··· 61116.3u + 1149.58
4.97154u
66
+ 24.5609u
65
+ ··· 162.049u + 15.4667
a
2
=
106.901u
66
540.203u
65
+ ··· 72238.9u + 1391.72
4.66417u
66
23.5987u
65
+ ··· 3326.21u + 66.4706
a
6
=
62.0936u
66
314.719u
65
+ ··· 47674.3u + 955.482
3.30535u
66
16.5919u
65
+ ··· 1745.48u + 33.1374
a
11
=
106.436u
66
538.983u
65
+ ··· 64251.9u + 1155.93
5.64853u
66
29.1245u
65
+ ··· 6005.95u + 120.410
a
4
=
50.0388u
66
257.995u
65
+ ··· 54633.9u + 1141.76
16.0771u
66
+ 81.0152u
65
+ ··· + 9881.71u 188.450
a
1
=
106.122u
66
541.179u
65
+ ··· 91308.2u + 1841.46
15.2363u
66
+ 76.7013u
65
+ ··· + 8994.51u 169.502
a
7
=
141.235u
66
+ 718.589u
65
+ ··· + 113394.u 2224.11
12.5644u
66
63.0421u
65
+ ··· 6410.64u + 114.660
a
7
=
141.235u
66
+ 718.589u
65
+ ··· + 113394.u 2224.11
12.5644u
66
63.0421u
65
+ ··· 6410.64u + 114.660
(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 = 3.73117 4.29349I
a = 0.145985 0.107602I
b = 0.347997 + 0.068126I
2.87450 + 2.88828I 34.8061 + 9.5012I
u = 3.73117 + 4.29349I
a = 0.145985 + 0.107602I
b = 0.347997 0.068126I
2.87450 2.88828I 34.8061 9.5012I
u = 2.31287 0.86712I
a = 0.018189 0.508046I
b = 1.06953 + 1.54069I
0.68934 + 9.55585I 10.57407 7.64853I
u = 2.31287 + 0.86712I
a = 0.018189 + 0.508046I
b = 1.06953 1.54069I
0.68934 9.55585I 10.57407 + 7.64853I
u = 2.23783 0.62569I
a = 0.018851 + 0.544138I
b = 0.87620 1.46714I
5.66368 + 5.86500I 5.37991 6.33692I
u = 2.23783 + 0.62569I
a = 0.018851 0.544138I
b = 0.87620 + 1.46714I
5.66368 5.86500I 5.37991 + 6.33692I
u = 2.04240 0.24739I
a = 0.096001 0.617685I
b = 0.557568 + 1.295298I
3.33579 + 2.19465I 7.86655 1.20153I
u = 2.04240 + 0.24739I
a = 0.096001 + 0.617685I
b = 0.557568 1.295298I
3.33579 2.19465I 7.86655 + 1.20153I
u = 1.68919 0.10893I
a = 0.120899 0.746930I
b = 0.409797 + 0.975823I
3.10200 + 2.24588I 7.87626 2.77695I
u = 1.68919 + 0.10893I
a = 0.120899 + 0.746930I
b = 0.409797 0.975823I
3.10200 2.24588I 7.87626 + 2.77695I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.52351 0.20917I
a = 0.210490 0.655884I
b = 0.623898 + 0.011951I
2.00089 2.82137I 12.55288 + 3.14931I
u = 1.52351 + 0.20917I
a = 0.210490 + 0.655884I
b = 0.623898 0.011951I
2.00089 + 2.82137I 12.55288 3.14931I
u = 1.51639 2.22961I
a = 0.336609 + 0.169455I
b = 0.498525 + 0.057019I
1.52367 0.14015I 14.2937 4.2199I
u = 1.51639 + 2.22961I
a = 0.336609 0.169455I
b = 0.498525 0.057019I
1.52367 + 0.14015I 14.2937 + 4.2199I
u = 1.47066 0.34672I
a = 0.384997 0.851896I
b = 0.046954 + 0.897792I
4.46866 + 1.41400I 4.95439 4.71232I
u = 1.47066 + 0.34672I
a = 0.384997 + 0.851896I
b = 0.046954 0.897792I
4.46866 1.41400I 4.95439 + 4.71232I
u = 1.210455 0.604607I
a = 0.699565 + 0.876598I
b = 0.278039 0.784173I
1.18945 + 5.01515I 9.96327 7.03774I
u = 1.210455 + 0.604607I
a = 0.699565 0.876598I
b = 0.278039 + 0.784173I
1.18945 5.01515I 9.96327 + 7.03774I
u = 1.081556 0.885123I
a = 0.309828 + 0.751909I
b = 1.255225 0.530443I
2.47273 + 2.48121I 12.98455 4.26320I
u = 1.081556 + 0.885123I
a = 0.309828 0.751909I
b = 1.255225 + 0.530443I
2.47273 2.48121I 12.98455 + 4.26320I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.096706 0.427933I
a = 0.25515 1.42081I
b = 0.869928 0.794145I
2.79764 + 5.70186I 13.9344 5.1674I
u = 0.096706 + 0.427933I
a = 0.25515 + 1.42081I
b = 0.869928 + 0.794145I
2.79764 5.70186I 13.9344 + 5.1674I
u = 0.064801 0.310092I
a = 0.06664 + 1.98905I
b = 0.607828 + 0.763446I
1.93198 + 2.14020I 7.90136 3.81097I
u = 0.064801 + 0.310092I
a = 0.06664 1.98905I
b = 0.607828 0.763446I
1.93198 2.14020I 7.90136 + 3.81097I
u = 0.032372 0.183662I
a = 0.94021 3.94300I
b = 0.188831 0.779818I
1.02190 1.39824I 10.01705 + 1.69482I
u = 0.032372 + 0.183662I
a = 0.94021 + 3.94300I
b = 0.188831 + 0.779818I
1.02190 + 1.39824I 10.01705 1.69482I
u = 0.0845999 0.1040022I
a = 4.12966 + 7.08001I
b = 0.714519 0.900643I
1.12210 + 6.34169I 11.92397 6.79037I
u = 0.0845999 + 0.1040022I
a = 4.12966 7.08001I
b = 0.714519 + 0.900643I
1.12210 6.34169I 11.92397 + 6.79037I
u = 0.0918053 0.0424607I
a = 8.94677 6.85163I
b = 0.517342 + 0.735395I
2.70603 + 1.76569I 13.31586 3.73920I
u = 0.0918053 + 0.0424607I
a = 8.94677 + 6.85163I
b = 0.517342 0.735395I
2.70603 1.76569I 13.31586 + 3.73920I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.107252 0.140710I
a = 3.13531 5.35578I
b = 0.878585 + 0.936939I
6.62942 + 10.38302I 16.2511 7.0025I
u = 0.107252 + 0.140710I
a = 3.13531 + 5.35578I
b = 0.878585 0.936939I
6.62942 10.38302I 16.2511 + 7.0025I
u = 0.152397 0.012670I
a = 9.22875 + 1.84584I
b = 0.489027 0.188184I
10.71131 + 0.03287I 28.8992 9.5421I
u = 0.152397 + 0.012670I
a = 9.22875 1.84584I
b = 0.489027 + 0.188184I
10.71131 0.03287I 28.8992 + 9.5421I
u = 0.172680
a = 1.92607
b = 0.446292
0.581693 17.2428
u = 0.379154 0.936170I
a = 1.002764 + 0.032807I
b = 1.50133 0.43518I
0.06257 + 4.19245I 10.29586 9.03236I
u = 0.379154 + 0.936170I
a = 1.002764 0.032807I
b = 1.50133 + 0.43518I
0.06257 4.19245I 10.29586 + 9.03236I
u = 0.522501 0.622361I
a = 0.221833 + 0.540376I
b = 1.039114 0.108043I
5.00722 0.73302I 18.4484 + 0.5736I
u = 0.522501 + 0.622361I
a = 0.221833 0.540376I
b = 1.039114 + 0.108043I
5.00722 + 0.73302I 18.4484 0.5736I
u = 0.580142 0.565029I
a = 1.41683 + 0.35569I
b = 0.017649 0.777456I
0.49228 1.74583I 8.26446 1.66020I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.580142 + 0.565029I
a = 1.41683 0.35569I
b = 0.017649 + 0.777456I
0.49228 + 1.74583I 8.26446 + 1.66020I
u = 0.66762 1.29216I
a = 0.694351 0.059894I
b = 1.75777 + 0.62199I
5.00444 + 7.26595I 15.7529 8.7828I
u = 0.66762 + 1.29216I
a = 0.694351 + 0.059894I
b = 1.75777 0.62199I
5.00444 7.26595I 15.7529 + 8.7828I
u = 0.798619 0.007050I
a = 0.346573 1.112496I
b = 0.919385 + 0.635252I
1.03011 + 1.52508I 14.1900 0.3808I
u = 0.798619 + 0.007050I
a = 0.346573 + 1.112496I
b = 0.919385 0.635252I
1.03011 1.52508I 14.1900 + 0.3808I
u = 1.031232 0.374220I
a = 0.903112 0.771748I
b = 0.205934 + 0.898863I
4.07626 + 2.45751I 5.53723 4.39874I
u = 1.031232 + 0.374220I
a = 0.903112 + 0.771748I
b = 0.205934 0.898863I
4.07626 2.45751I 5.53723 + 4.39874I
u = 1.169761 0.510774I
a = 0.116221 0.319509I
b = 0.625972 + 0.729951I
1.45952 + 1.07936I 12.77452 1.30331I
u = 1.169761 + 0.510774I
a = 0.116221 + 0.319509I
b = 0.625972 0.729951I
1.45952 1.07936I 12.77452 + 1.30331I
u = 1.38161 0.78538I
a = 0.086114 + 0.337379I
b = 0.817959 1.112328I
6.38128 + 3.82220I 18.3457 1.9018I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.38161 + 0.78538I
a = 0.086114 0.337379I
b = 0.817959 + 1.112328I
6.38128 3.82220I 18.3457 + 1.9018I
u = 1.44300 0.07814I
a = 0.480392 + 0.817409I
b = 0.435757 1.009455I
1.33655 + 6.86297I 10.02668 7.94684I
u = 1.44300 + 0.07814I
a = 0.480392 0.817409I
b = 0.435757 + 1.009455I
1.33655 6.86297I 10.02668 + 7.94684I
u = 1.47905 0.82478I
a = 0.051038 + 0.862312I
b = 0.893626 0.834525I
7.03449 6.70275I 16.2956 + 5.6811I
u = 1.47905 + 0.82478I
a = 0.051038 0.862312I
b = 0.893626 + 0.834525I
7.03449 + 6.70275I 16.2956 5.6811I
u = 1.51262 0.49949I
a = 0.374306 + 0.422148I
b = 1.11526 1.22891I
6.14223 0.20744I 18.0429 2.0449I
u = 1.51262 + 0.49949I
a = 0.374306 0.422148I
b = 1.11526 + 1.22891I
6.14223 + 0.20744I 18.0429 + 2.0449I
u = 1.70548 0.23609I
a = 0.069919 + 0.388090I
b = 0.131167 1.093020I
1.70121 1.12219I 12.55043 + 5.69637I
u = 1.70548 + 0.23609I
a = 0.069919 0.388090I
b = 0.131167 + 1.093020I
1.70121 + 1.12219I 12.55043 5.69637I
u = 1.88727 0.36334I
a = 0.113959 0.343244I
b = 0.01503 + 1.52850I
6.71014 3.51832I 18.4535 + 5.0158I
10
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 1.88727 + 0.36334I
a = 0.113959 + 0.343244I
b = 0.01503 1.52850I
6.71014 + 3.51832I 18.4535 5.0158I
u = 1.94400 0.43476I
a = 0.154014 0.693947I
b = 0.783881 + 1.145119I
0.61572 7.81558I 11.29229 + 4.31786I
u = 1.94400 + 0.43476I
a = 0.154014 + 0.693947I
b = 0.783881 1.145119I
0.61572 + 7.81558I 11.29229 4.31786I
u = 2.23210 0.58722I
a = 0.102144 + 0.606915I
b = 0.90969 1.26003I
2.41609 12.25376I 8.96204 + 8.44386I
u = 2.23210 + 0.58722I
a = 0.102144 0.606915I
b = 0.90969 + 1.26003I
2.41609 + 12.25376I 8.96204 8.44386I
u = 2.35334 0.76098I
a = 0.060507 0.573901I
b = 1.01562 + 1.29138I
2.9681 16.2798I 13.1314 + 9.0944I
u = 2.35334 + 0.76098I
a = 0.060507 + 0.573901I
b = 1.01562 1.29138I
2.9681 + 16.2798I 13.1314 9.0944I
11
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u 1)
2
(u
67
+ 3u
66
+ ··· 11u 25)
c
2
u
2
(u
67
+ u
66
+ ··· + 980u + 100)
c
3
(u + 1)
2
(u
67
+ 3u
66
+ ··· 11u 25)
c
4
(u
2
+ u 1)(u
67
+ 2u
66
+ ··· + 4u + 1)
c
5
(5u
2
+ 5u + 1)(5u
67
+ 44u
66
+ ··· + 396u 27)
c
6
(u
2
+ u 1)(u
67
+ 2u
66
+ ··· + 2u + 1)
c
7
(u
2
3u + 1)(u
67
+ 6u
66
+ ··· 618u 117)
c
8
(u
2
u 1)(u
67
+ 2u
66
+ ··· + 4u + 1)
c
9
(5u
2
1)(5u
67
+ 27u
66
+ ··· + 819u + 81)
c
10
(u
2
u 1)(u
67
+ 2u
66
+ ··· + 2u + 1)
c
11
(u
2
u 1)(u
67
+ 2u
66
+ ··· + 2u + 1)
12
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
(y 1)
2
(y
67
39y
66
+ ··· + 25671y 625)
c
2
y
2
(y
67
+ 15y
66
+ ··· + 203000y 10000)
c
3
(y 1)
2
(y
67
39y
66
+ ··· + 25671y 625)
c
4
, c
8
(y
2
3y + 1)(y
67
+ 36y
66
+ ··· + 4y 1)
c
5
(25y
2
15y + 1)(25y
67
+ 624y
66
+ ··· + 130896y 729)
c
6
(y
2
3y + 1)(y
67
60y
66
+ ··· + 4y 1)
c
7
(y
2
7y + 1)(y
67
+ 4y
66
+ ··· + 137160y 13689)
c
9
(5y 1)
2
(25y
67
79y
66
+ ··· 46413y 6561)
c
10
(y
2
3y + 1)(y
67
60y
66
+ ··· + 4y 1)
c
11
(y
2
3y + 1)(y
67
60y
66
+ ··· + 4y 1)
13