4:00 pm Wednesday, February 6, 2013
Geometry-Analysis Seminar: Some Homology and Cohomology Theories for a Metric Space
by Robert Hardt (Rice) in HB 227
Abstract: Various classes of chains and cochains may reveal geometric as well as topological properties of metric spaces. In 1957, Whitney introduced a geometric "flat norm" on polyhedral chains in Euclidean space, completed to get flat chains, and defined flat cochains as the dual space. For variational problems, Federer and Fleming also considered these in the sixties and seventies, for homology and cohomology of Euclidean Lipschitz neighborhood retracts. These include smooth manifolds and polyhedra, but not algebraic varieties or subspaces of some Banach spaces. In works with Thierry De Pauw and Washek Pfeffer, we find generalizations and alternate topologies for flat chains and cochains in general metric spaces. With these, we homologically characterize Lipschitz path connectedness and obtain several facts about spaces that satisfy local linear isoperimetric inequalities. Host Department: Rice University-Mathematics
Submitted by hardt@rice.edu |
