11a
69
(K11a
69
)
1
Arc Sequences
5 1 11 2 10 9 4 3 6 7 8
Solving Sequence
1,5
2
3,8
9 4 7 6 11 10
c
1
c
2
c
8
c
4
c
7
c
6
c
11
c
10
c
3
, c
5
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
70
u
69
+ ··· 7u + 1, 6.82950 × 10
70
u
69
1.52385 × 10
70
u
68
+ ··· + 6.61166 × 10
70
a + 3.61726 × 10
71
,
1.32395 × 10
70
u
69
+ 4.90259 × 10
70
u
68
+ ··· + 6.61166 × 10
70
b + 4.90917 × 10
70
i
There are 1 irreducible components with 70 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
70
u
69
+· · ·7u+1, 6.83×10
70
u
69
1.52×10
70
u
68
+· · ·+6.61×10
70
a+
3.62 × 10
71
, 1.32× 10
70
u
69
+ 4.90 × 10
70
u
68
+ · · · + 6.61× 10
70
b + 4.91 × 10
70
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
=
1.03295u
69
+ 0.230480u
68
+ ··· + 12.8135u 5.47103
0.200245u
69
0.741507u
68
+ ··· + 7.88951u 0.742501
a
9
=
0.218838u
69
0.721185u
68
+ ··· + 16.3322u 5.53922
0.568243u
69
+ 0.396283u
68
+ ··· + 3.68684u 0.0730781
a
4
=
u
u
3
+ u
a
7
=
0.351653u
69
0.0562920u
68
+ ··· + 9.51195u 4.96448
0.652628u
69
+ 0.0138570u
68
+ ··· + 9.11067u 0.854526
a
6
=
0.561639u
69
1.06041u
68
+ ··· + 7.46541u 2.71413
0.475520u
69
+ 0.477952u
68
+ ··· 3.57338u + 0.825199
a
11
=
0.539784u
69
+ 0.407632u
68
+ ··· 21.4593u + 3.02626
0.132152u
69
+ 0.189434u
68
+ ··· + 0.752232u 0.539784
a
10
=
0.770820u
69
+ 0.798589u
68
+ ··· 13.0113u + 4.13938
0.412590u
69
0.332882u
68
+ ··· + 0.316261u 0.240663
a
10
=
0.770820u
69
+ 0.798589u
68
+ ··· 13.0113u + 4.13938
0.412590u
69
0.332882u
68
+ ··· + 0.316261u 0.240663
(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 = 1.003967 0.281861I
a = 0.603104 0.049560I
b = 0.756164 + 0.054992I
6.67319 1.90375I 10.82437 + 0.84693I
u = 1.003967 + 0.281861I
a = 0.603104 + 0.049560I
b = 0.756164 0.054992I
6.67319 + 1.90375I 10.82437 0.84693I
u = 1.001640 0.651261I
a = 0.718177 0.020199I
b = 0.739049 0.145003I
6.29345 + 5.42481I 9.42014 7.24239I
u = 1.001640 + 0.651261I
a = 0.718177 + 0.020199I
b = 0.739049 + 0.145003I
6.29345 5.42481I 9.42014 + 7.24239I
u = 0.838536 0.993294I
a = 0.758362 0.266685I
b = 0.676531 0.281724I
5.26003 + 1.16982I 7.23729 4.39808I
u = 0.838536 + 0.993294I
a = 0.758362 + 0.266685I
b = 0.676531 + 0.281724I
5.26003 1.16982I 7.23729 + 4.39808I
u = 0.833768 0.669179I
a = 0.825160 0.019096I
b = 0.684395 + 0.137169I
1.32084 + 2.75218I 4.00267 8.42337I
u = 0.833768 + 0.669179I
a = 0.825160 + 0.019096I
b = 0.684395 0.137169I
1.32084 2.75218I 4.00267 + 8.42337I
u = 0.728444 0.317658I
a = 0.577971 + 0.204619I
b = 0.704091 0.047297I
1.64058 + 0.33786I 6.07692 + 1.73353I
u = 0.728444 + 0.317658I
a = 0.577971 0.204619I
b = 0.704091 + 0.047297I
1.64058 0.33786I 6.07692 1.73353I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.693479 1.215560I
a = 0.567968 + 0.412304I
b = 0.668101 + 0.423676I
3.90043 + 8.04691I 3.82020 10.58986I
u = 0.693479 + 1.215560I
a = 0.567968 0.412304I
b = 0.668101 0.423676I
3.90043 8.04691I 3.82020 + 10.58986I
u = 0.616639 1.172648I
a = 0.565812 0.505437I
b = 0.617845 0.438744I
0.93135 + 4.88535I 2.28013 10.40687I
u = 0.616639 + 1.172648I
a = 0.565812 + 0.505437I
b = 0.617845 + 0.438744I
0.93135 4.88535I 2.28013 + 10.40687I
u = 0.612892 0.951335I
a = 1.008808 + 0.587650I
b = 0.515214 + 0.290990I
0.54295 + 2.64582I 2.44579 0.83594I
u = 0.612892 + 0.951335I
a = 1.008808 0.587650I
b = 0.515214 0.290990I
0.54295 2.64582I 2.44579 + 0.83594I
u = 0.541955 0.776960I
a = 0.63182 + 2.26229I
b = 0.059607 + 0.520507I
3.56607 0.95896I 11.21360 3.18554I
u = 0.541955 + 0.776960I
a = 0.63182 2.26229I
b = 0.059607 0.520507I
3.56607 + 0.95896I 11.21360 + 3.18554I
u = 0.536274 0.919865I
a = 1.37304 2.08210I
b = 0.284130 0.399162I
3.11019 + 5.29914I 3.0401 + 15.5285I
u = 0.536274 + 0.919865I
a = 1.37304 + 2.08210I
b = 0.284130 + 0.399162I
3.11019 5.29914I 3.0401 15.5285I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.485312 0.908136I
a = 1.78720 + 1.87066I
b = 0.341793 + 0.291449I
1.29895 + 2.30609I 11.5630 + 16.8929I
u = 0.485312 + 0.908136I
a = 1.78720 1.87066I
b = 0.341793 0.291449I
1.29895 2.30609I 11.5630 16.8929I
u = 0.437497 0.816872I
a = 0.14154 2.07415I
b = 0.101470 0.501644I
0.93813 + 1.54075I 3.94589 11.49495I
u = 0.437497 + 0.816872I
a = 0.14154 + 2.07415I
b = 0.101470 + 0.501644I
0.93813 1.54075I 3.94589 + 11.49495I
u = 0.416221 1.189184I
a = 0.313235 + 0.632253I
b = 0.555488 + 0.566144I
1.99705 + 2.44523I 0.42203 5.58212I
u = 0.416221 + 1.189184I
a = 0.313235 0.632253I
b = 0.555488 0.566144I
1.99705 2.44523I 0.42203 + 5.58212I
u = 0.401964 0.917807I
a = 1.57399 1.40654I
b = 0.505018 0.276523I
2.39518 0.54119I 8.37251 + 3.42089I
u = 0.401964 + 0.917807I
a = 1.57399 + 1.40654I
b = 0.505018 + 0.276523I
2.39518 + 0.54119I 8.37251 3.42089I
u = 0.250675 0.338013I
a = 1.35492 + 2.51441I
b = 0.051209 + 0.692143I
3.63488 + 3.48634I 1.23972 4.18650I
u = 0.250675 + 0.338013I
a = 1.35492 2.51441I
b = 0.051209 0.692143I
3.63488 3.48634I 1.23972 + 4.18650I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.006202 1.312425I
a = 0.087110 0.263404I
b = 0.641500 0.851768I
1.19896 + 8.13596I 2.64385 7.58232I
u = 0.006202 + 1.312425I
a = 0.087110 + 0.263404I
b = 0.641500 + 0.851768I
1.19896 8.13596I 2.64385 + 7.58232I
u = 0.050089 1.257285I
a = 0.182007 + 0.232896I
b = 0.619110 + 0.903635I
5.92974 + 4.34707I 7.96325 5.56332I
u = 0.050089 + 1.257285I
a = 0.182007 0.232896I
b = 0.619110 0.903635I
5.92974 4.34707I 7.96325 + 5.56332I
u = 0.140513 1.175145I
a = 0.344278 0.143372I
b = 0.591502 1.001911I
3.16104 + 0.50300I 5.18092 0.50402I
u = 0.140513 + 1.175145I
a = 0.344278 + 0.143372I
b = 0.591502 + 1.001911I
3.16104 0.50300I 5.18092 + 0.50402I
u = 0.224664 0.169997I
a = 3.33119 + 0.02340I
b = 0.423967 0.698653I
1.37636 + 0.69918I 5.13733 2.33652I
u = 0.224664 + 0.169997I
a = 3.33119 0.02340I
b = 0.423967 + 0.698653I
1.37636 0.69918I 5.13733 + 2.33652I
u = 0.254902 0.847557I
a = 1.39483 + 1.45213I
b = 1.293790 + 0.202808I
0.95320 + 3.02207I 3.51437 4.78633I
u = 0.254902 + 0.847557I
a = 1.39483 1.45213I
b = 1.293790 0.202808I
0.95320 3.02207I 3.51437 + 4.78633I
6
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.297139 0.882531I
a = 1.170542 + 0.067964I
b = 0.282271 1.384166I
1.94107 + 0.75277I 7.49106 4.95501I
u = 0.297139 + 0.882531I
a = 1.170542 0.067964I
b = 0.282271 + 1.384166I
1.94107 0.75277I 7.49106 + 4.95501I
u = 0.406148 0.936613I
a = 1.69854 1.42899I
b = 1.62427 0.57750I
3.33093 1.52607I 13.07472 + 1.31899I
u = 0.406148 + 0.936613I
a = 1.69854 + 1.42899I
b = 1.62427 + 0.57750I
3.33093 + 1.52607I 13.07472 1.31899I
u = 0.469428 0.973496I
a = 0.697160 0.881105I
b = 0.87580 + 1.58062I
2.85780 3.99529I 10.44720 + 9.33363I
u = 0.469428 + 0.973496I
a = 0.697160 + 0.881105I
b = 0.87580 1.58062I
2.85780 + 3.99529I 10.44720 9.33363I
u = 0.489406 0.250651I
a = 1.71867 + 1.21428I
b = 0.900665 0.606704I
1.23691 + 2.50489I 0.44486 4.33475I
u = 0.489406 + 0.250651I
a = 1.71867 1.21428I
b = 0.900665 + 0.606704I
1.23691 2.50489I 0.44486 + 4.33475I
u = 0.507327 1.004447I
a = 1.83109 + 1.07834I
b = 1.45077 + 0.97835I
0.50648 6.46270I 4.51731 + 10.80382I
u = 0.507327 + 1.004447I
a = 1.83109 1.07834I
b = 1.45077 0.97835I
0.50648 + 6.46270I 4.51731 10.80382I
7
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.519294 0.588568I
a = 1.96772 + 0.12778I
b = 0.555679 + 1.264555I
4.08495 + 3.81337I 3.16539 5.10767I
u = 0.519294 + 0.588568I
a = 1.96772 0.12778I
b = 0.555679 1.264555I
4.08495 3.81337I 3.16539 + 5.10767I
u = 0.558838 0.987517I
a = 0.236110 + 1.031567I
b = 1.12142 1.39774I
2.91206 8.27553I 0.02494 + 11.22505I
u = 0.558838 + 0.987517I
a = 0.236110 1.031567I
b = 1.12142 + 1.39774I
2.91206 + 8.27553I 0.02494 11.22505I
u = 0.620167 1.091347I
a = 1.67136 + 0.83458I
b = 1.20512 + 1.04362I
0.05172 8.00134I 0.93933 + 5.30903I
u = 0.620167 + 1.091347I
a = 1.67136 0.83458I
b = 1.20512 1.04362I
0.05172 + 8.00134I 0.93933 5.30903I
u = 0.652177 1.126721I
a = 1.61508 0.80014I
b = 1.15985 1.03785I
1.87843 12.59620I 3.11036 + 9.02697I
u = 0.652177 + 1.126721I
a = 1.61508 + 0.80014I
b = 1.15985 + 1.03785I
1.87843 + 12.59620I 3.11036 9.02697I
u = 0.667838 0.997816I
a = 1.78911 0.70363I
b = 1.19304 1.16811I
8.13804 7.06461I 4.91208 + 7.07377I
u = 0.667838 + 0.997816I
a = 1.78911 + 0.70363I
b = 1.19304 + 1.16811I
8.13804 + 7.06461I 4.91208 7.07377I
8
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.680160 1.138337I
a = 1.59303 + 0.77025I
b = 1.13723 + 1.04455I
3.4715 16.7403I 1.05963 + 9.75592I
u = 0.680160 + 1.138337I
a = 1.59303 0.77025I
b = 1.13723 1.04455I
3.4715 + 16.7403I 1.05963 9.75592I
u = 0.768228 0.457281I
a = 1.20536 + 0.95025I
b = 1.095519 0.786479I
1.92693 + 2.73519I 2.12851 1.17713I
u = 0.768228 + 0.457281I
a = 1.20536 0.95025I
b = 1.095519 + 0.786479I
1.92693 2.73519I 2.12851 + 1.17713I
u = 0.776577 0.650017I
a = 0.922024 1.023180I
b = 1.20743 + 0.85684I
9.19605 + 1.61168I 6.97481 1.32865I
u = 0.776577 + 0.650017I
a = 0.922024 + 1.023180I
b = 1.20743 0.85684I
9.19605 1.61168I 6.97481 + 1.32865I
u = 0.884444 0.447119I
a = 1.157764 0.800837I
b = 1.076266 + 0.846603I
0.17592 + 6.93073I 0.67959 5.56176I
u = 0.884444 + 0.447119I
a = 1.157764 + 0.800837I
b = 1.076266 0.846603I
0.17592 6.93073I 0.67959 + 5.56176I
u = 0.938125 0.475226I
a = 1.103093 + 0.752114I
b = 1.081183 0.871713I
5.50503 + 10.82286I 3.52361 6.15835I
u = 0.938125 + 0.475226I
a = 1.103093 0.752114I
b = 1.081183 + 0.871713I
5.50503 10.82286I 3.52361 + 6.15835I
9
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
(u
70
+ u
69
+ ··· + 7u + 1)
c
2
(u
70
+ 29u
69
+ ··· + 7u + 1)
c
3
(u
70
+ 7u
69
+ ··· + u + 1)
c
5
, c
6
(u
70
+ u
69
+ ··· + 5u + 1)
c
7
(u
70
+ 3u
69
+ ··· 23u + 1)
c
8
(u
70
+ u
69
+ ··· + 49u + 4)
c
9
(u
70
+ u
69
+ ··· + 5u + 1)
c
10
(u
70
+ u
69
+ ··· 1887u + 578)
c
11
(u
70
+ 5u
69
+ ··· + u + 1)
10
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
(y
70
+ 29y
69
+ ··· + 7y + 1)
c
2
(y
70
+ 25y
69
+ ··· + 347y + 1)
c
3
(y
70
+ 5y
69
+ ··· + 7y + 1)
c
5
(y
70
+ 61y
69
+ ··· 5y + 1)
c
6
, c
9
(y
70
+ 61y
69
+ ··· 5y + 1)
c
7
(y
70
71y
69
+ ··· 45y + 1)
c
8
(y
70
75y
69
+ ··· 401y + 16)
c
10
(y
70
15y
69
+ ··· 869601y + 334084)
c
11
(y
70
7y
69
+ ··· 5y + 1)
11