11a
152
(K11a
152
)
1
Arc Sequences
6 1 11 10 2 9 5 3 7 4 8
Solving Sequence
1,6
2
3,9
7 10 5 4 8 11
c
1
c
2
c
6
c
9
c
5
c
4
c
8
c
11
c
3
, c
7
, c
10
Representation Ideals
I =
2
\
i=1
I
u
i
I
u
1
= hu + 1, a 1, 3b + 1i
I
u
2
= hu
59
+ 2u
58
+ ··· + 2u + 1, 6.26201 × 10
46
u
58
2.20250 × 10
46
u
57
+ ··· + 1.46597 × 10
47
b 4.15403 × 10
46
,
1.24691 × 10
47
u
58
2.95521 × 10
47
u
57
+ ··· + 1.95463 × 10
47
a 2.41334 × 10
47
i
There are 2 irreducible components with 60 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 + 1, a 1, 3b + 1i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
1
a
2
=
1
1
a
3
=
2
1
a
9
=
1
1
3
a
7
=
1
4
3
a
10
=
0
1
a
5
=
1
2
a
4
=
1
1
a
8
=
1
3
0
a
11
=
1
0
a
11
=
1
0
(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 = 1.00000
a = 1.00000
b = 0.333333
0 7.11111
3
II. I
u
2
=
hu
59
+2u
58
+· · ·+2u+1, 6.26×10
46
u
58
2.20×10
46
u
57
+· · ·+1.47×10
47
b
4.15× 10
46
, 1.25 × 10
47
u
58
2.96 ×10
47
u
57
+· · · +1.95 ×10
47
a 2.41× 10
47
i
(i) Arc colorings
a
1
=
1
0
a
6
=
0
u
a
2
=
1
u
2
a
3
=
u
2
+ 1
u
2
a
9
=
0.637930u
58
+ 1.51190u
57
+ ··· + 2.39473u + 1.23468
0.427158u
58
+ 0.150242u
57
+ ··· + 2.42536u + 0.283364
a
7
=
0.430739u
58
+ 1.19057u
57
+ ··· + 0.228063u + 0.805821
0.606150u
58
+ 0.450809u
57
+ ··· + 3.53454u + 0.634736
a
10
=
0.716693u
58
+ 1.10334u
57
+ ··· + 4.46995u + 1.45001
0.477190u
58
0.773083u
57
+ ··· 1.18568u 0.968726
a
5
=
u
u
3
+ u
a
4
=
1.29085u
58
2.20647u
57
+ ··· 0.324259u 2.41081
0.375240u
58
+ 1.02106u
57
+ ··· + 0.170898u + 1.29085
a
8
=
0.539708u
58
+ 0.734598u
57
+ ··· + 0.368500u + 0.439466
0.167631u
58
+ 0.255872u
57
+ ··· + 2.15526u + 0.327184
a
11
=
0.968726u
58
+ 1.46026u
57
+ ··· 0.180023u + 0.751771
0.330049u
58
0.528342u
57
+ ··· + 0.0166251u 0.716693
a
11
=
0.968726u
58
+ 1.46026u
57
+ ··· 0.180023u + 0.751771
0.330049u
58
0.528342u
57
+ ··· + 0.0166251u 0.716693
(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 = 1.082860 0.338807I
a = 0.906512 + 0.162772I
b = 0.410355 + 0.292248I
0.196305 0.379080I 0.28717 + 12.84558I
u = 1.082860 + 0.338807I
a = 0.906512 0.162772I
b = 0.410355 0.292248I
0.196305 + 0.379080I 0.28717 12.84558I
u = 0.916030 0.448271I
a = 1.44781 + 0.14196I
b = 0.604847 + 1.129777I
8.11873 9.85959I 0.63253 + 4.74202I
u = 0.916030 + 0.448271I
a = 1.44781 0.14196I
b = 0.604847 1.129777I
8.11873 + 9.85959I 0.63253 4.74202I
u = 0.726401 0.692652I
a = 0.017304 + 0.588654I
b = 0.408232 0.720581I
1.67726 + 2.08783I 6.30981 5.41216I
u = 0.726401 + 0.692652I
a = 0.017304 0.588654I
b = 0.408232 + 0.720581I
1.67726 2.08783I 6.30981 + 5.41216I
u = 0.681416 0.490122I
a = 0.829686 + 1.110163I
b = 0.32573 1.58972I
3.60110 3.99693I 1.95911 + 2.96828I
u = 0.681416 + 0.490122I
a = 0.829686 1.110163I
b = 0.32573 + 1.58972I
3.60110 + 3.99693I 1.95911 2.96828I
u = 0.660290 1.139698I
a = 0.180974 + 1.181926I
b = 1.98520 1.61428I
10.2296 + 15.6414I 2.78860 8.37827I
u = 0.660290 + 1.139698I
a = 0.180974 1.181926I
b = 1.98520 + 1.61428I
10.2296 15.6414I 2.78860 + 8.37827I
5
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.651495 1.183980I
a = 0.228656 + 0.883493I
b = 1.29907 1.22571I
2.42227 + 6.38133I 0.90046 6.42822I
u = 0.651495 + 1.183980I
a = 0.228656 0.883493I
b = 1.29907 + 1.22571I
2.42227 6.38133I 0.90046 + 6.42822I
u = 0.621334 0.967374I
a = 0.444058 0.164780I
b = 0.469674 + 0.492578I
0.82881 + 3.06030I 4.18689 0.59937I
u = 0.621334 + 0.967374I
a = 0.444058 + 0.164780I
b = 0.469674 0.492578I
0.82881 3.06030I 4.18689 + 0.59937I
u = 0.589725 1.049109I
a = 0.974147 0.647305I
b = 0.65027 + 1.78415I
5.23405 + 8.92854I 1.43763 7.89156I
u = 0.589725 + 1.049109I
a = 0.974147 + 0.647305I
b = 0.65027 1.78415I
5.23405 8.92854I 1.43763 + 7.89156I
u = 0.508309
a = 0.519601
b = 0.347878
0.892681 11.5980
u = 0.478198 1.043560I
a = 0.13176 1.56616I
b = 1.88671 + 1.47624I
10.18439 + 5.57197I 6.62529 6.49533I
u = 0.478198 + 1.043560I
a = 0.13176 + 1.56616I
b = 1.88671 1.47624I
10.18439 5.57197I 6.62529 + 6.49533I
u = 0.477142 0.939669I
a = 0.337722 0.975082I
b = 1.72819 + 2.62260I
2.01075 + 2.52108I 10.02369 + 7.46616I
6
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.477142 + 0.939669I
a = 0.337722 + 0.975082I
b = 1.72819 2.62260I
2.01075 2.52108I 10.02369 7.46616I
u = 0.475233 0.194305I
a = 2.80927 + 0.02365I
b = 1.034361 0.874193I
8.07186 1.71448I 1.95195 + 1.33766I
u = 0.475233 + 0.194305I
a = 2.80927 0.02365I
b = 1.034361 + 0.874193I
8.07186 + 1.71448I 1.95195 1.33766I
u = 0.388284 0.766748I
a = 0.593509 0.729702I
b = 0.676086 1.196484I
1.34852 + 1.21434I 0.61490 9.36280I
u = 0.388284 + 0.766748I
a = 0.593509 + 0.729702I
b = 0.676086 + 1.196484I
1.34852 1.21434I 0.61490 + 9.36280I
u = 0.355783 1.016215I
a = 0.88013 1.46882I
b = 1.187677 + 0.225533I
10.99429 + 0.93911I 8.32737 1.66782I
u = 0.355783 + 1.016215I
a = 0.88013 + 1.46882I
b = 1.187677 0.225533I
10.99429 0.93911I 8.32737 + 1.66782I
u = 0.140005 0.951679I
a = 1.145599 0.505541I
b = 0.173571 0.842681I
7.99699 2.70852I 5.70787 + 2.68790I
u = 0.140005 + 0.951679I
a = 1.145599 + 0.505541I
b = 0.173571 + 0.842681I
7.99699 + 2.70852I 5.70787 2.68790I
u = 0.037114 1.274150I
a = 0.291840 + 1.134420I
b = 0.036185 0.899498I
14.4364 7.1649I 6.56375 + 4.09710I
7
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.037114 + 1.274150I
a = 0.291840 1.134420I
b = 0.036185 + 0.899498I
14.4364 + 7.1649I 6.56375 4.09710I
u = 0.040795 1.321705I
a = 0.138951 + 0.966975I
b = 0.003188 0.903134I
7.08101 + 2.98588I 6.30890 4.69732I
u = 0.040795 + 1.321705I
a = 0.138951 0.966975I
b = 0.003188 + 0.903134I
7.08101 2.98588I 6.30890 + 4.69732I
u = 0.151816 0.796485I
a = 0.805238 0.598449I
b = 0.041011 0.762641I
1.79094 + 1.03849I 2.00439 5.37844I
u = 0.151816 + 0.796485I
a = 0.805238 + 0.598449I
b = 0.041011 + 0.762641I
1.79094 1.03849I 2.00439 + 5.37844I
u = 0.290588 0.280288I
a = 2.24336 1.08501I
b = 0.429081 0.681749I
1.71907 + 0.84714I 1.58416 2.44825I
u = 0.290588 + 0.280288I
a = 2.24336 + 1.08501I
b = 0.429081 + 0.681749I
1.71907 0.84714I 1.58416 + 2.44825I
u = 0.377745 0.961338I
a = 0.689591 1.203527I
b = 0.581606 + 0.701387I
4.10264 1.33087I 6.62416 + 1.43922I
u = 0.377745 + 0.961338I
a = 0.689591 + 1.203527I
b = 0.581606 0.701387I
4.10264 + 1.33087I 6.62416 1.43922I
u = 0.487336 1.005408I
a = 0.004403 1.224492I
b = 1.72407 + 1.50482I
3.33182 4.55345I 4.30626 + 8.52736I
8
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.487336 + 1.005408I
a = 0.004403 + 1.224492I
b = 1.72407 1.50482I
3.33182 + 4.55345I 4.30626 8.52736I
u = 0.514327 0.820334I
a = 0.503213 0.897141I
b = 0.32237 7.16447I
6.55441 2.12552I 3.0626 37.0838I
u = 0.514327 + 0.820334I
a = 0.503213 + 0.897141I
b = 0.32237 + 7.16447I
6.55441 + 2.12552I 3.0626 + 37.0838I
u = 0.535245 0.944857I
a = 0.149141 0.084466I
b = 1.22863 1.06063I
5.12435 1.84537I 0.81905 + 3.28443I
u = 0.535245 + 0.944857I
a = 0.149141 + 0.084466I
b = 1.22863 + 1.06063I
5.12435 + 1.84537I 0.81905 3.28443I
u = 0.547708 0.428908I
a = 0.511741 0.559115I
b = 0.911747 0.087367I
3.80970 2.30389I 3.16410 + 2.52287I
u = 0.547708 + 0.428908I
a = 0.511741 + 0.559115I
b = 0.911747 + 0.087367I
3.80970 + 2.30389I 3.16410 2.52287I
u = 0.604291 1.022451I
a = 0.761616 0.425218I
b = 0.527627 + 1.286857I
1.09865 6.46666I 3.55713 + 8.78536I
u = 0.604291 + 1.022451I
a = 0.761616 + 0.425218I
b = 0.527627 1.286857I
1.09865 + 6.46666I 3.55713 8.78536I
u = 0.652394 1.151720I
a = 0.171724 + 1.049555I
b = 1.65616 1.52205I
2.98475 11.82366I 0.27767 + 9.15160I
9
Solution to I
u
2
1(vol +
1CS) Cusp shape
u = 0.652394 + 1.151720I
a = 0.171724 1.049555I
b = 1.65616 + 1.52205I
2.98475 + 11.82366I 0.27767 9.15160I
u = 0.686392 0.567950I
a = 0.444098 + 0.856911I
b = 0.409774 1.220146I
2.45484 + 1.46486I 7.14865 3.00711I
u = 0.686392 + 0.567950I
a = 0.444098 0.856911I
b = 0.409774 + 1.220146I
2.45484 1.46486I 7.14865 + 3.00711I
u = 0.731272 1.183572I
a = 0.471808 + 0.751737I
b = 1.257678 0.503242I
9.14972 1.51752I 8.98073 + 1.05717I
u = 0.731272 + 1.183572I
a = 0.471808 0.751737I
b = 1.257678 + 0.503242I
9.14972 + 1.51752I 8.98073 1.05717I
u = 0.929365 0.411469I
a = 1.249047 + 0.094882I
b = 0.418963 + 0.848799I
0.73398 + 6.05254I 2.05891 6.25817I
u = 0.929365 + 0.411469I
a = 1.249047 0.094882I
b = 0.418963 0.848799I
0.73398 6.05254I 2.05891 + 6.25817I
u = 0.986191 0.582632I
a = 0.812298 + 0.680937I
b = 0.980334 + 0.009595I
7.26563 4.89851I 3.75396 + 7.31193I
u = 0.986191 + 0.582632I
a = 0.812298 0.680937I
b = 0.980334 0.009595I
7.26563 + 4.89851I 3.75396 7.31193I
10
III. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
(u + 1)(u
59
+ 2u
58
+ ··· + 2u + 1)
c
2
(u 1)(u
59
+ 24u
58
+ ··· 4u 1)
c
3
, c
4
(u 1)(u
59
+ 2u
58
+ ··· 2u 1)
c
5
(u 1)(u
59
+ 2u
58
+ ··· + 2u + 1)
c
6
(u 1)(u
59
+ 2u
58
+ ··· 32u + 9)
c
7
(3u + 2)(3u
59
+ 29u
58
+ ··· + 96336u 7216)
c
8
(3u + 1)(3u
59
+ 44u
58
+ ··· 96u + 64)
c
9
(u + 1)(u
59
+ 2u
58
+ ··· 32u + 9)
c
10
(u + 1)(u
59
+ 2u
58
+ ··· 2u 1)
c
11
(u)(u
59
+ 5u
58
+ ··· + 108u + 18)
11
IV. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
5
(y 1)(y
59
+ 24y
58
+ ··· 4y 1)
c
2
(y 1)(y
59
+ 16y
58
+ ··· 76y 1)
c
3
, c
4
, c
10
(y 1)(y
59
+ 60y
58
+ ··· 4y 1)
c
6
, c
9
(y 1)(y
59
44y
58
+ ··· + 3472y 81)
c
7
(9y 4)(9y
59
787y
58
+ ··· + 4.57874 × 10
9
y 5.20707 × 10
7
)
c
8
(9y 1)(9y
59
424y
58
+ ··· 148480y 4096)
c
11
(y)(y
59
+ 9y
58
+ ··· 6300y 324)
12