11a
54
(K11a
54
)
1
Arc Sequences
5 1 11 2 10 9 3 4 6 7 8
Solving Sequence
1,5
2 3
4,8
9 7 6 11 10
c
1
c
2
c
4
c
8
c
7
c
6
c
11
c
10
c
3
, c
5
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
69
u
68
+ ··· + 7u + 1, 8.47341 × 10
67
u
68
9.26291 × 10
67
u
67
+ ··· + 2.58951 × 10
68
b 2.21273 × 10
68
,
4.24949 × 10
68
u
68
+ 2.84101 × 10
68
u
67
+ ··· + 2.58951 × 10
68
a + 5.34329 × 10
68
i
There are 1 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
= hu
69
u
68
+· · ·+7u+1, 8.47×10
67
u
68
9.26×10
67
u
67
+· · ·+2.59×10
68
b
2.21× 10
68
, 4.25× 10
68
u
68
+2.84 ×10
68
u
67
+· · · +2.59 ×10
68
a + 5.34× 10
68
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
4
=
u
u
3
+ u
a
8
=
1.64104u
68
1.09712u
67
+ ··· + 5.71086u 2.06344
0.327221u
68
+ 0.357709u
67
+ ··· + 6.38253u + 0.854498
a
9
=
0.463649u
68
0.296453u
67
+ ··· + 3.83790u 2.15954
0.877685u
68
0.782988u
67
+ ··· + 4.44104u + 0.573880
a
7
=
0.545471u
68
0.00203410u
67
+ ··· + 7.43942u 1.73880
0.399488u
68
0.413066u
67
+ ··· + 5.70183u + 0.809950
a
6
=
0.799209u
68
1.44703u
67
+ ··· + 10.4230u 0.157404
0.735587u
68
0.775293u
67
+ ··· 3.65851u 0.690440
a
11
=
0.538699u
68
+ 1.40351u
67
+ ··· 5.31473u 1.67566
0.864806u
68
+ 0.656660u
67
+ ··· 2.09524u 0.538699
a
10
=
0.356103u
68
+ 0.122437u
67
+ ··· + 7.81858u + 4.48517
0.390348u
68
+ 0.466506u
67
+ ··· + 1.79336u + 0.396660
a
10
=
0.356103u
68
+ 0.122437u
67
+ ··· + 7.81858u + 4.48517
0.390348u
68
+ 0.466506u
67
+ ··· + 1.79336u + 0.396660
(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 = 1.013215 0.613592I
a = 0.007078 + 0.705429I
b = 0.134513 0.744011I
0.32305 + 5.26485I 10.62493 7.08679I
u = 1.013215 + 0.613592I
a = 0.007078 0.705429I
b = 0.134513 + 0.744011I
0.32305 5.26485I 10.62493 + 7.08679I
u = 1.010783 0.331574I
a = 0.048907 + 0.618626I
b = 0.065612 0.755901I
0.61350 1.71624I 11.68058 + 0.71153I
u = 1.010783 + 0.331574I
a = 0.048907 0.618626I
b = 0.065612 + 0.755901I
0.61350 + 1.71624I 11.68058 0.71153I
u = 0.985003 0.485819I
a = 0.041263 0.675457I
b = 0.099375 + 0.743016I
4.38283 + 1.75150I 16.4419 3.6342I
u = 0.985003 + 0.485819I
a = 0.041263 + 0.675457I
b = 0.099375 0.743016I
4.38283 1.75150I 16.4419 + 3.6342I
u = 0.821651 1.021946I
a = 0.293989 0.744331I
b = 0.298168 + 0.672387I
0.91382 + 1.30908I 7.74666 4.37397I
u = 0.821651 + 1.021946I
a = 0.293989 + 0.744331I
b = 0.298168 0.672387I
0.91382 1.30908I 7.74666 + 4.37397I
u = 0.741295 1.123285I
a = 0.391287 + 0.664536I
b = 0.366792 0.656630I
2.46511 + 4.51237I 11.3986 8.8654I
u = 0.741295 + 1.123285I
a = 0.391287 0.664536I
b = 0.366792 + 0.656630I
2.46511 4.51237I 11.3986 + 8.8654I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.716579 1.203072I
a = 0.398029 0.586343I
b = 0.410131 + 0.672622I
1.97766 + 7.97069I 5.23827 10.57806I
u = 0.716579 + 1.203072I
a = 0.398029 + 0.586343I
b = 0.410131 0.672622I
1.97766 7.97069I 5.23827 + 10.57806I
u = 0.551106 0.795185I
a = 2.29984 + 0.68430I
b = 0.504210 0.078733I
2.50160 0.87317I 12.68469 1.79956I
u = 0.551106 + 0.795185I
a = 2.29984 0.68430I
b = 0.504210 + 0.078733I
2.50160 + 0.87317I 12.68469 + 1.79956I
u = 0.546073 0.910104I
a = 2.14797 + 1.30675I
b = 0.410472 0.259906I
2.86842 + 5.27183I 5.8136 + 15.1333I
u = 0.546073 + 0.910104I
a = 2.14797 1.30675I
b = 0.410472 + 0.259906I
2.86842 5.27183I 5.8136 15.1333I
u = 0.545287 0.961436I
a = 0.880471 0.968907I
b = 0.335838 + 0.444934I
0.07982 + 2.77352I 2.01744 1.22489I
u = 0.545287 + 0.961436I
a = 0.880471 + 0.968907I
b = 0.335838 0.444934I
0.07982 2.77352I 2.01744 + 1.22489I
u = 0.540656 0.860419I
a = 2.51739 1.05488I
b = 0.404462 + 0.147302I
1.37720 + 2.17002I 20.8441 + 10.9028I
u = 0.540656 + 0.860419I
a = 2.51739 + 1.05488I
b = 0.404462 0.147302I
1.37720 2.17002I 20.8441 10.9028I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.476152 0.761801I
a = 0.57435 + 1.55522I
b = 0.016463 0.537976I
0.64094 + 1.45108I 5.67805 6.58266I
u = 0.476152 + 0.761801I
a = 0.57435 1.55522I
b = 0.016463 + 0.537976I
0.64094 1.45108I 5.67805 + 6.58266I
u = 0.389681 1.187679I
a = 0.639196 + 0.271993I
b = 0.584779 0.548250I
4.28780 + 2.43362I 0.55603 5.51061I
u = 0.389681 + 1.187679I
a = 0.639196 0.271993I
b = 0.584779 + 0.548250I
4.28780 2.43362I 0.55603 + 5.51061I
u = 0.380257 0.909412I
a = 1.34638 1.53724I
b = 0.264971 + 0.536131I
3.74691 0.61271I 7.72112 + 2.11922I
u = 0.380257 + 0.909412I
a = 1.34638 + 1.53724I
b = 0.264971 0.536131I
3.74691 + 0.61271I 7.72112 2.11922I
u = 0.254514 0.249135I
a = 2.93336 1.32927I
b = 0.671325 + 0.054175I
2.37890 + 3.34092I 0.25060 3.93790I
u = 0.254514 + 0.249135I
a = 2.93336 + 1.32927I
b = 0.671325 0.054175I
2.37890 3.34092I 0.25060 + 3.93790I
u = 0.189635
a = 4.83453
b = 0.601558
1.60413 5.38982
u = 0.180375 0.359379I
a = 1.36960 + 0.46073I
b = 0.066463 0.708592I
0.572882 + 1.093977I 6.17226 6.06480I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.180375 + 0.359379I
a = 1.36960 0.46073I
b = 0.066463 + 0.708592I
0.572882 1.093977I 6.17226 + 6.06480I
u = 0.083389 1.231878I
a = 0.405180 + 0.109590I
b = 0.813096 + 0.571885I
1.87888 + 4.75178I 3.16509 7.67915I
u = 0.083389 + 1.231878I
a = 0.405180 0.109590I
b = 0.813096 0.571885I
1.87888 4.75178I 3.16509 + 7.67915I
u = 0.036581 1.312135I
a = 0.293353 0.067755I
b = 0.832233 0.635120I
6.94265 + 8.21032I 1.29488 7.80737I
u = 0.036581 + 1.312135I
a = 0.293353 + 0.067755I
b = 0.832233 + 0.635120I
6.94265 8.21032I 1.29488 + 7.80737I
u = 0.017291 1.055815I
a = 0.444427 0.458584I
b = 0.930858 0.441550I
3.31539 + 1.42653I 1.46022 0.90595I
u = 0.017291 + 1.055815I
a = 0.444427 + 0.458584I
b = 0.930858 + 0.441550I
3.31539 1.42653I 1.46022 + 0.90595I
u = 0.155367 0.798808I
a = 1.42581 1.31408I
b = 0.141687 + 1.116931I
4.90709 + 3.41016I 0.82557 4.30817I
u = 0.155367 + 0.798808I
a = 1.42581 + 1.31408I
b = 0.141687 1.116931I
4.90709 3.41016I 0.82557 + 4.30817I
u = 0.194887 1.153274I
a = 0.055963 + 0.399744I
b = 1.057873 + 0.601922I
9.60907 + 0.11401I 4.74802 0.58295I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.194887 + 1.153274I
a = 0.055963 0.399744I
b = 1.057873 0.601922I
9.60907 0.11401I 4.74802 + 0.58295I
u = 0.557159 1.062343I
a = 0.93811 + 1.72516I
b = 1.00842 1.29021I
7.30954 7.36946I 1.30694 + 7.82981I
u = 0.557159 + 1.062343I
a = 0.93811 1.72516I
b = 1.00842 + 1.29021I
7.30954 + 7.36946I 1.30694 7.82981I
u = 0.568825 0.669802I
a = 0.14098 1.97291I
b = 1.38682 + 0.66400I
1.50104 + 3.50534I 6.45504 5.38433I
u = 0.568825 + 0.669802I
a = 0.14098 + 1.97291I
b = 1.38682 0.66400I
1.50104 3.50534I 6.45504 + 5.38433I
u = 0.591164 0.961287I
a = 1.139865 0.076863I
b = 1.34433 1.22274I
2.38282 8.18392I 4.19379 + 11.22593I
u = 0.591164 + 0.961287I
a = 1.139865 + 0.076863I
b = 1.34433 + 1.22274I
2.38282 + 8.18392I 4.19379 11.22593I
u = 0.597458 0.808717I
a = 0.32211 + 2.12154I
b = 1.56343 0.98545I
3.31253 1.10291I 16.0867 0.2611I
u = 0.597458 + 0.808717I
a = 0.32211 2.12154I
b = 1.56343 + 0.98545I
3.31253 + 1.10291I 16.0867 + 0.2611I
u = 0.604946 0.875247I
a = 1.45074 0.25214I
b = 1.21317 + 1.46983I
3.10224 3.65612I 14.6967 + 8.0899I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.604946 + 0.875247I
a = 1.45074 + 0.25214I
b = 1.21317 1.46983I
3.10224 + 3.65612I 14.6967 8.0899I
u = 0.607578 0.720494I
a = 1.40160 + 0.87809I
b = 0.78542 1.42958I
1.57123 + 1.30415I 10.11030 4.92987I
u = 0.607578 + 0.720494I
a = 1.40160 0.87809I
b = 0.78542 + 1.42958I
1.57123 1.30415I 10.11030 + 4.92987I
u = 0.618942 0.924861I
a = 0.68112 1.99323I
b = 1.31556 + 1.26267I
0.96001 6.16584I 8.49904 + 10.58231I
u = 0.618942 + 0.924861I
a = 0.68112 + 1.99323I
b = 1.31556 1.26267I
0.96001 + 6.16584I 8.49904 10.58231I
u = 0.634036 0.280540I
a = 1.00364 1.53962I
b = 0.705502 + 0.967920I
5.27570 + 2.79528I 1.29544 3.38630I
u = 0.634036 + 0.280540I
a = 1.00364 + 1.53962I
b = 0.705502 0.967920I
5.27570 2.79528I 1.29544 + 3.38630I
u = 0.674946 1.055982I
a = 0.73983 1.69867I
b = 1.10412 + 1.17365I
1.05725 7.83679I 4.74980 + 5.14827I
u = 0.674946 + 1.055982I
a = 0.73983 + 1.69867I
b = 1.10412 1.17365I
1.05725 + 7.83679I 4.74980 5.14827I
u = 0.691729 1.130530I
a = 0.75449 1.59791I
b = 1.05392 + 1.13373I
1.9859 16.7029I 2.60168 + 9.74352I
8
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.691729 + 1.130530I
a = 0.75449 + 1.59791I
b = 1.05392 1.13373I
1.9859 + 16.7029I 2.60168 9.74352I
u = 0.692620 1.100095I
a = 0.74086 + 1.63279I
b = 1.07393 1.14446I
3.23009 12.46901I 6.85262 + 8.75626I
u = 0.692620 + 1.100095I
a = 0.74086 1.63279I
b = 1.07393 + 1.14446I
3.23009 + 12.46901I 6.85262 8.75626I
u = 0.821583 0.588202I
a = 0.936920 + 1.002539I
b = 0.84955 1.15608I
2.48274 + 2.22918I 7.13721 0.56666I
u = 0.821583 + 0.588202I
a = 0.936920 1.002539I
b = 0.84955 + 1.15608I
2.48274 2.22918I 7.13721 + 0.56666I
u = 0.899108 0.540063I
a = 0.820043 1.041524I
b = 0.868426 + 1.112588I
4.94303 + 6.60072I 9.45233 4.66175I
u = 0.899108 + 0.540063I
a = 0.820043 + 1.041524I
b = 0.868426 1.112588I
4.94303 6.60072I 9.45233 + 4.66175I
u = 0.939775 0.500176I
a = 0.759370 + 1.074750I
b = 0.875883 1.090006I
0.04985 + 10.73452I 4.96208 6.09806I
u = 0.939775 + 0.500176I
a = 0.759370 1.074750I
b = 0.875883 + 1.090006I
0.04985 10.73452I 4.96208 + 6.09806I
9
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
(u
69
+ u
68
+ ··· + 7u 1)
c
2
(u
69
+ 27u
68
+ ··· + 7u 1)
c
3
(u
69
+ 7u
68
+ ··· + u + 1)
c
5
, c
9
(u
69
+ u
68
+ ··· + 5u 1)
c
6
(u
69
+ u
68
+ ··· + 5u 1)
c
7
(u
69
+ u
68
+ ··· 375u + 103)
c
8
(u
69
+ u
68
+ ··· + 137u 119)
c
10
(u
69
+ u
68
+ ··· + 12027u + 1217)
c
11
(u
69
+ 5u
68
+ ··· u 1)
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
69
+ 27y
68
+ ··· + 7y 1)
c
2
(y
69
+ 31y
68
+ ··· + 611y 1)
c
3
(y
69
5y
68
+ ··· + 7y 1)
c
5
(y
69
+ 59y
68
+ ··· 5y 1)
c
6
, c
9
(y
69
+ 59y
68
+ ··· 5y 1)
c
7
(y
69
+ 83y
68
+ ··· 603653y 10609)
c
8
(y
69
+ 59y
68
+ ··· 207093y 14161)
c
10
(y
69
25y
68
+ ··· 20237733y 1481089)
c
11
(y
69
+ 7y
68
+ ··· 5y 1)
11