11a
183
(K11a
183
)
1
Arc Sequences
7 1 11 10 9 2 3 4 5 6 8
Solving Sequence
2,7
1 3 8 6 11 4 9 5 10
c
1
c
2
c
7
c
6
c
11
c
3
c
8
c
5
c
10
c
4
, c
9
Representation Ideals
I = I
u
1
I
u
1
= hu
57
u
56
+ ··· u + 1i
There are 1 irreducible components with 57 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
57
u
56
+ · · · u + 1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
1
=
1
u
2
a
3
=
u
2
+ 1
u
4
a
8
=
u
5
2u
3
u
u
7
u
5
+ u
a
6
=
u
u
a
11
=
u
10
+ 3u
8
+ 4u
6
+ 3u
4
+ u
2
+ 1
u
12
+ 2u
10
+ 2u
8
u
4
a
4
=
u
18
+ 5u
16
+ 12u
14
+ 17u
12
+ 15u
10
+ 9u
8
+ 4u
6
+ 2u
4
+ u
2
+ 1
u
20
+ 4u
18
+ 8u
16
+ 8u
14
+ 3u
12
2u
10
2u
8
+ u
4
a
9
=
u
31
+ 8u
29
+ ··· + 12u
7
+ 4u
5
u
33
+ 7u
31
+ ··· + 2u
13
+ u
a
5
=
u
48
+ 11u
46
+ ··· + 2u
4
+ 1
u
48
12u
46
+ ··· 20u
10
8u
8
a
10
=
u
14
3u
12
4u
10
u
8
+ 2u
6
+ 2u
4
+ 1
u
14
+ 4u
12
+ 7u
10
+ 6u
8
+ 2u
6
+ u
2
a
10
=
u
14
3u
12
4u
10
u
8
+ 2u
6
+ 2u
4
+ 1
u
14
+ 4u
12
+ 7u
10
+ 6u
8
+ 2u
6
+ u
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 = 0.757271 0.363158I
4.65256 5.23405I 10.45155 + 4.02810I
u = 0.757271 + 0.363158I
4.65256 + 5.23405I 10.45155 4.02810I
u = 0.707423 0.280338I
5.26507 3.02226I 0.93578 + 3.10778I
u = 0.707423 + 0.280338I
5.26507 + 3.02226I 0.93578 3.10778I
u = 0.672902 0.557091I
2.38357 1.16168I 8.69132 + 0.25547I
u = 0.672902 + 0.557091I
2.38357 + 1.16168I 8.69132 0.25547I
u = 0.665622 0.613891I
1.41577 + 7.09232I 7.22236 6.42230I
u = 0.665622 + 0.613891I
1.41577 7.09232I 7.22236 + 6.42230I
u = 0.579530 0.956820I
0.40457 2.25231I 5.63793 + 0.50011I
u = 0.579530 + 0.956820I
0.40457 + 2.25231I 5.63793 0.50011I
u = 0.579073 1.001247I
1.07430 + 6.01691I 6.28925 6.05831I
u = 0.579073 + 1.001247I
1.07430 6.01691I 6.28925 + 6.05831I
u = 0.575214 1.115481I
2.43881 + 10.27358I 7.12723 7.98252I
u = 0.575214 + 1.115481I
2.43881 10.27358I 7.12723 + 7.98252I
u = 0.548264
1.27831 8.28663
u = 0.539048 1.122593I
7.68595 + 7.77424I 2.23653 6.71754I
u = 0.539048 + 1.122593I
7.68595 7.77424I 2.23653 + 6.71754I
u = 0.529993 0.461580I
0.979056 + 0.679070I 8.79507 4.86357I
u = 0.529993 + 0.461580I
0.979056 0.679070I 8.79507 + 4.86357I
u = 0.509062 1.066915I
0.85109 + 3.57978I 5.03586 1.38706I
u = 0.509062 + 1.066915I
0.85109 3.57978I 5.03586 + 1.38706I
u = 0.382626 1.083860I
1.62790 + 3.37240I 3.27495 5.30685I
u = 0.382626 + 1.083860I
1.62790 3.37240I 3.27495 + 5.30685I
u = 0.293305 1.121981I
9.34182 0.07828I 5.13184 0.08231I
u = 0.293305 + 1.121981I
9.34182 + 0.07828I 5.13184 + 0.08231I
u = 0.210597 1.105412I
0.04467 2.73028I 4.01382 + 2.71873I
u = 0.210597 + 1.105412I
0.04467 + 2.73028I 4.01382 2.71873I
u = 0.199807 1.058798I
2.98923 1.15216I 0.80462 + 1.21860I
u = 0.199807 + 1.058798I
2.98923 + 1.15216I 0.80462 1.21860I
u = 0.216608 1.126051I
4.56299 + 6.72032I 0.77416 4.45102I
3
Solution to I
u
1
1(vol +
1CS) Cusp shape
u = 0.216608 + 1.126051I
4.56299 6.72032I 0.77416 + 4.45102I
u = 0.299547 1.062427I
3.37572 0.51768I 1.48190 0.98551I
u = 0.299547 + 1.062427I
3.37572 + 0.51768I 1.48190 + 0.98551I
u = 0.374506 1.121010I
6.25104 6.75305I 2.19787 + 6.33264I
u = 0.374506 + 1.121010I
6.25104 + 6.75305I 2.19787 6.33264I
u = 0.477299 1.108061I
5.56866 0.84775I 1.26082 + 1.06200I
u = 0.477299 + 1.108061I
5.56866 + 0.84775I 1.26082 1.06200I
u = 0.481283 0.697287I
3.68835 1.96306I 2.33316 + 4.18175I
u = 0.481283 + 0.697287I
3.68835 + 1.96306I 2.33316 4.18175I
u = 0.541711 1.095358I
1.72047 6.62089I 2.54306 + 8.39817I
u = 0.541711 + 1.095358I
1.72047 + 6.62089I 2.54306 8.39817I
u = 0.573731 1.103792I
0.58525 6.08343I 4.24879 + 4.25279I
u = 0.573731 + 1.103792I
0.58525 + 6.08343I 4.24879 4.25279I
u = 0.575008 1.122840I
2.1926 14.4304I 2.47128 + 9.78434I
u = 0.575008 + 1.122840I
2.1926 + 14.4304I 2.47128 9.78434I
u = 0.578383 0.978439I
4.63483 1.87363I 10.12440 + 2.27509I
u = 0.578383 + 0.978439I
4.63483 + 1.87363I 10.12440 2.27509I
u = 0.628429 0.102623I
2.86692 3.28224I 2.61623 + 2.85377I
u = 0.628429 + 0.102623I
2.86692 + 3.28224I 2.61623 2.85377I
u = 0.654325 0.347004I
0.42908 + 1.95168I 6.05217 4.83311I
u = 0.654325 + 0.347004I
0.42908 1.95168I 6.05217 + 4.83311I
u = 0.667619 0.589150I
5.78308 2.96634I 12.01643 + 3.84738I
u = 0.667619 + 0.589150I
5.78308 + 2.96634I 12.01643 3.84738I
u = 0.739554 0.382882I
1.53395 + 1.08977I 7.57234 0.12382I
u = 0.739554 + 0.382882I
1.53395 1.08977I 7.57234 + 0.12382I
u = 0.767988 0.350139I
0.08340 + 9.36804I 5.68221 6.01169I
u = 0.767988 + 0.350139I
0.08340 9.36804I 5.68221 + 6.01169I
4
II. u-Polynomials
Crossings u-Polynomials at each crossings
c
1
, c
6
(u
57
+ u
56
+ ··· u 1)
c
2
(u
57
+ 27u
56
+ ··· + u 1)
c
3
(u
57
+ 7u
56
+ ··· + 49u + 5)
c
4
(u
57
+ u
56
+ ··· + u + 1)
c
5
(u
57
+ u
56
+ ··· + u + 1)
c
7
(u
57
+ u
56
+ ··· + 231u + 53)
c
8
, c
10
(u
57
+ u
56
+ ··· 29u 17)
c
9
(u
57
+ u
56
+ ··· + u + 1)
c
11
(u
57
+ 5u
56
+ ··· 264u 112)
5
III. Riley Polynomials
Crossings Riley Polynomials at each crossings
c
1
, c
6
(y
57
+ 27y
56
+ ··· + y 1)
c
2
(y
57
+ 7y
56
+ ··· 3y 1)
c
3
(y
57
+ 3y
56
+ ··· 519y 25)
c
4
(y
57
+ 47y
56
+ ··· + y 1)
c
5
, c
9
(y
57
+ 47y
56
+ ··· + y 1)
c
7
(y
57
13y
56
+ ··· + 82617y 2809)
c
8
, c
10
(y
57
37y
56
+ ··· 1267y 289)
c
11
(y
57
+ 15y
56
+ ··· 381664y 12544)
6