10
94
(K10a
91
)
1
Arc Sequences
5 6 8 1 9 3 10 2 7 4
Solving Sequence
2,6
3
7,9
10 5 1 4 8
c
2
c
6
c
9
c
5
c
1
c
4
c
8
c
3
, c
7
, c
10
Representation Ideals
I = I
u
1
I
u
1
= hu
35
+ u
34
+ ··· + 3u
2
1, 1.92548 × 10
23
u
34
+ 4.50591 × 10
24
u
33
+ ··· + 1.94056 × 10
26
b + 5.00911 × 10
25
,
1.47187 × 10
25
u
34
5.55497 × 10
25
u
33
+ ··· + 1.94056 × 10
26
a + 1.26325 × 10
26
i
There are 1 irreducible components with 35 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
35
+u
34
+· · ·+3u
2
1, 1.93×10
23
u
34
+4.51×10
24
u
33
+· · ·+1.94×10
26
b+
5.01× 10
25
, 1.47×10
25
u
34
5.55 ×10
25
u
33
+· · · +1.94 ×10
26
a + 1.26× 10
26
i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
7
=
u
u
3
+ u
a
9
=
0.0758476u
34
+ 0.286255u
33
+ ··· 2.05345u 0.650973
0.000992225u
34
0.0232196u
33
+ ··· + 1.94515u 0.258127
a
10
=
0.207071u
34
+ 0.496531u
33
+ ··· 2.86737u 0.313795
u
3
+ u
a
5
=
4.17860u
34
+ 10.2576u
33
+ ··· + 6.57083u + 7.30621
0.0762066u
34
+ 0.0320312u
33
+ ··· 0.719210u + 0.551477
a
1
=
6.68171u
34
+ 13.7176u
33
+ ··· + 6.41454u + 8.47300
0.378893u
34
0.258591u
33
+ ··· 0.386101u 0.293395
a
4
=
6.53158u
34
10.3927u
33
+ ··· 5.31388u 1.03456
0.143069u
34
0.242790u
33
+ ··· + 0.233712u 0.348632
a
8
=
0.0748554u
34
+ 0.309475u
33
+ ··· 3.99860u 0.392847
0.000992225u
34
0.0232196u
33
+ ··· + 1.94515u 0.258127
(ii) Obstruction class = 1
(iii) Cusp Shapes =
685604431393501191149801996
194056291140393639670155049
u
34
+
1265614220419500138897629840
194056291140393639670155049
u
33
+
··· +
1347136378071411012980246724
194056291140393639670155049
u +
476504741445014011926263206
194056291140393639670155049
2
(iv) Complex Volumes and Cusp Shapes
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.32253 0.58471I
a = 0.555617 1.083367I
b = 1.16179 1.18148I
7.4557 + 13.3116I 5.56191 7.05476I
u = 1.32253 + 0.58471I
a = 0.555617 + 1.083367I
b = 1.16179 + 1.18148I
7.4557 13.3116I 5.56191 + 7.05476I
u = 1.28980 0.70883I
a = 0.085002 0.663986I
b = 0.675701 0.598517I
0.51201 + 4.13357I 2.56649 6.25203I
u = 1.28980 + 0.70883I
a = 0.085002 + 0.663986I
b = 0.675701 + 0.598517I
0.51201 4.13357I 2.56649 + 6.25203I
u = 1.239282 0.234249I
a = 0.406708 + 0.513046I
b = 0.780134 + 0.364822I
2.98343 + 0.70642I 1.79862 + 1.96555I
u = 1.239282 + 0.234249I
a = 0.406708 0.513046I
b = 0.780134 0.364822I
2.98343 0.70642I 1.79862 1.96555I
u = 1.153346 0.400330I
a = 0.560318 + 0.975567I
b = 1.33659 + 1.39229I
2.83088 + 6.77803I 3.49538 6.10276I
u = 1.153346 + 0.400330I
a = 0.560318 0.975567I
b = 1.33659 1.39229I
2.83088 6.77803I 3.49538 + 6.10276I
u = 0.925847 0.149168I
a = 0.69237 + 1.98607I
b = 0.343369 + 0.493773I
0.118043 + 0.668153I 2.12828 + 10.66433I
u = 0.925847 + 0.149168I
a = 0.69237 1.98607I
b = 0.343369 0.493773I
0.118043 0.668153I 2.12828 10.66433I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.886211 0.403329I
a = 0.395589 + 0.026121I
b = 1.09496 + 1.70151I
7.88737 + 3.84000I 8.41305 5.49307I
u = 0.886211 + 0.403329I
a = 0.395589 0.026121I
b = 1.09496 1.70151I
7.88737 3.84000I 8.41305 + 5.49307I
u = 0.508893 0.400402I
a = 1.31387 1.37047I
b = 1.57728 0.56731I
8.87322 0.26521I 9.98023 1.43782I
u = 0.508893 + 0.400402I
a = 1.31387 + 1.37047I
b = 1.57728 + 0.56731I
8.87322 + 0.26521I 9.98023 + 1.43782I
u = 0.093357 1.125481I
a = 0.601295 + 0.969793I
b = 0.735626 + 1.123217I
11.27947 7.30532I 9.07114 + 4.61200I
u = 0.093357 + 1.125481I
a = 0.601295 0.969793I
b = 0.735626 1.123217I
11.27947 + 7.30532I 9.07114 4.61200I
u = 0.082503 0.452801I
a = 0.841430 0.897374I
b = 0.348083 0.564419I
0.134869 + 1.085583I 2.08723 6.10429I
u = 0.082503 + 0.452801I
a = 0.841430 + 0.897374I
b = 0.348083 + 0.564419I
0.134869 1.085583I 2.08723 + 6.10429I
u = 0.064302 0.587556I
a = 1.58195 1.12504I
b = 0.504472 1.180242I
5.91469 2.99202I 7.69164 + 2.94469I
u = 0.064302 + 0.587556I
a = 1.58195 + 1.12504I
b = 0.504472 + 1.180242I
5.91469 + 2.99202I 7.69164 2.94469I
4
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.167144 1.250920I
a = 0.353770 + 0.562838I
b = 0.399400 + 0.679964I
3.73588 + 3.17966I 9.01884 7.80623I
u = 0.167144 + 1.250920I
a = 0.353770 0.562838I
b = 0.399400 0.679964I
3.73588 3.17966I 9.01884 + 7.80623I
u = 0.463958 0.092112I
a = 2.27468 0.41119I
b = 0.845374 0.090842I
2.28660 + 0.00327I 6.71199 + 0.85350I
u = 0.463958 + 0.092112I
a = 2.27468 + 0.41119I
b = 0.845374 + 0.090842I
2.28660 0.00327I 6.71199 0.85350I
u = 0.911512 0.305208I
a = 0.076946 + 0.554057I
b = 0.605384 + 1.144651I
1.17815 2.75086I 5.83679 + 7.59594I
u = 0.911512 + 0.305208I
a = 0.076946 0.554057I
b = 0.605384 1.144651I
1.17815 + 2.75086I 5.83679 7.59594I
u = 0.917235 0.218298I
a = 1.198315 0.162879I
b = 0.322177 + 0.266185I
3.14805 + 0.11237I 1.93831 + 1.19079I
u = 0.917235 + 0.218298I
a = 1.198315 + 0.162879I
b = 0.322177 0.266185I
3.14805 0.11237I 1.93831 1.19079I
u = 1.03793
a = 14.7138
b = 0.161473
4.96247 155.292
u = 1.185871 0.342420I
a = 0.441712 + 0.819560I
b = 1.111956 + 0.867646I
3.42076 4.23935I 1.57284 + 6.50170I
5
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 1.185871 + 0.342420I
a = 0.441712 0.819560I
b = 1.111956 0.867646I
3.42076 + 4.23935I 1.57284 6.50170I
u = 1.30365 0.61580I
a = 0.319124 0.958070I
b = 0.995035 0.894449I
0.17363 9.53352I 2.89594 + 8.02980I
u = 1.30365 + 0.61580I
a = 0.319124 + 0.958070I
b = 0.995035 + 0.894449I
0.17363 + 9.53352I 2.89594 8.02980I
u = 1.59774 0.61668I
a = 0.257294 0.089867I
b = 0.159067 0.606648I
6.16860 + 1.10468I 14.8768 5.2183I
u = 1.59774 + 0.61668I
a = 0.257294 + 0.089867I
b = 0.159067 + 0.606648I
6.16860 1.10468I 14.8768 + 5.2183I
6
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
4
, c
10
(u
35
+ 3u
34
+ ··· + 3u
2
1)
c
2
, c
6
(u
35
+ u
34
+ ··· + 3u
2
1)
c
3
(u
35
+ 17u
34
+ ··· + 214u + 23)
c
5
(u
35
+ 13u
34
+ ··· + 12u + 7)
c
7
, c
9
(u
35
+ u
34
+ ··· 2u 1)
c
8
(u
35
+ 3u
34
+ ··· + 4u + 1)
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
4
, c
10
(y
35
37y
34
+ ··· + 6y 1)
c
2
, c
6
(y
35
21y
34
+ ··· + 6y 1)
c
3
(y
35
233y
34
+ ··· + 5914y 529)
c
5
(y
35
237y
34
+ ··· + 942y 49)
c
7
, c
9
(y
35
25y
34
+ ··· 70y 1)
c
8
(y
35
+ 3y
34
+ ··· + 34y 1)
8