393 research outputs found
Shadowing and Expansivity in Sub-Spaces
We address various notions of shadowing and expansivity for continuous maps
restricted to a proper subset of their domain. We prove new equivalences of
shadowing and expansive properties, we demonstrate under what conditions
certain expanding maps have shadowing, and generalize some known results in
this area. We also investigate the impact of our theory on maps of the
interval, in which context some of our results can be extended.Comment: 18 page
A Simple Organic Solar Cell
Finding renewable sources of energy is becoming an increasingly important component of scientific research. Greater competition for existing sources of energy has strained the world’s supply and demand balance and has increased the prices of traditional sources of energy such as oil, coal, and natural gas. The experiment discussed in this paper is designed to identify and build an inexpensive and simple method for creating an effective organic solar cell
From continua to R-trees
We show how to associate an R-tree to the set of cut points of a continuum.
If X is a continuum without cut points we show how to associate an R-tree to
the set of cut pairs of X.Comment: This is the version published by Algebraic & Geometric Topology on 1
November 200
The fundamental groups of subsets of closed surfaces inject into their first shape groups
We show that for every subset X of a closed surface M^2 and every basepoint
x_0, the natural homomorphism from the fundamental group to the first shape
homotopy group, is injective. In particular, if X is a proper compact subset of
M^2, then pi_1(X,x_0) is isomorphic to a subgroup of the limit of an inverse
sequence of finitely generated free groups; it is therefore locally free, fully
residually free and residually finite.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-67.abs.htm
Paper folding, Riemann surfaces, and convergence of pseudo-Anosov sequences
A method is presented for constructing closed surfaces out of Euclidean
polygons with infinitely many segment identifications along the boundary. The
metric on the quotient is identified. A sufficient condition is presented which
guarantees that the Euclidean structure on the polygons induces a unique
conformal structure on the quotient surface, making it into a closed Riemann
surface. In this case, a modulus of continuity for uniformizing coordinates is
found which depends only on the geometry of the polygons and on the
identifications. An application is presented in which a uniform modulus of
continuity is obtained for a family of pseudo-Anosov homeomorphisms, making it
possible to prove that they converge to a Teichm\"uller mapping on the Riemann
sphere.Comment: 75 pages, 18 figure
Parabolic groups acting on one-dimensional compact spaces
Given a class of compact spaces, we ask which groups can be maximal parabolic
subgroups of a relatively hyperbolic group whose boundary is in the class. We
investigate the class of 1-dimensional connected boundaries. We get that any
non-torsion infinite f.g. group is a maximal parabolic subgroup of some
relatively hyperbolic group with connected one-dimensional boundary without
global cut point. For boundaries homeomorphic to a Sierpinski carpet or a
2-sphere, the only maximal parabolic subgroups allowed are virtual surface
groups (hyperbolic, or virtually ).Comment: 10 pages. Added a precision on local connectedness for Lemma 2.3,
thanks to B. Bowditc
Surface homeomorphisms with zero dimensional singular set
We prove that if f is an orientation-preserving homeomorphism of a closed
orientable surface M whose singular set is totally disconnected, then f is
topologically conjugate to a conformal transformation.Comment: 22 page
Constructing near-embeddings of codimension one manifolds with countable dense singular sets
The purpose of this paper is to present, for all , very simple
examples of continuous maps from closed -manifolds
into closed -manifold such that even though the singular set
of is countable and dense, the map can nevertheless be
approximated by an embedding, i.e. is a {\sl near-embedding}
- …