The investigator will work on three projects. The first is a continuation of work with Mladen Bestvina (U.C.L.A.) on automorphisms of the free group. They hope to prove a classification theorem for subgroups of polynomial growth automorphisms and thereby complete the proof of the Tits Alternative for Out(Fn). Secondly, the investigator hopes to prove that there are no minimal homeomorphisms of the once punctured plane, which would answer a question of Besicovitch and of Herman. Finally, the investigator, in collaboration with Bruce Kitchens (I.B.M.), will explore the relationship between two natural definitions of topological entropy for homeomorphisms of non- compact spaces. The topology of surfaces is a highly developed subject, addressing properties which remain invariant when a surface is stretched or twisted without tearing it, so-called rubber sheet geometry. The theory of dynamical systems is another highly developed subject, addressing questions about transformations of a space into itself, such simple things as rotations of spheres, but also far more complicated transformations. For transformations of surfaces, the topology is intimately involved and says a great deal about what kinds of transformations are possible. Extracting this information by combining the topology of surfaces with the theory of dynamical systems is a sophisticated endeavor which forms a large part of this project.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9204292
Program Officer
Ralph M. Krause
Project Start
Project End
Budget Start
1992-08-15
Budget End
1996-07-31
Support Year
Fiscal Year
1992
Total Cost
$88,500
Indirect Cost
Name
CUNY Herbert H Lehman College
Department
Type
DUNS #
City
Bronx
State
NY
Country
United States
Zip Code
10468