Proposal for a Conference on the Geometry and Topology of Manifolds

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

Abstract Award: DMS-0406314 Principal Investigator: Crichton L. Ogle This award provides partial support for participant costs of a conference on the "Geometry and Topology of Manifolds" at Ohio State University. The main themes of the meeting are invariants of manifolds arising in square-integrable cohomology, K-theory, and geometric group theory. Invited speakers and other participants include a number of female mathematicians, recent PhDs, and graduate students. A manifold is a geometric space in which every point has neighborhoods that can be identified with Euclidean space of some dimension. For example, every point on the surface of a 2-dimensional sphere lies in an open hemisphere that can be flattened onto the Euclidean plane by a map projection. An example of a higher dimensional manifold would be the space of physical coordinates for three particles moving in the plane without collisions: each particle's dynamical data consists of two position and two velocity coordinates, thus each of the three particles requires four numbers to record its dynamics and to report all three moving particles simultaneously calls for twelve coordinates. "Invariants" of manifolds are computable objects (not necessarily numbers) that help us tell one space from another, and some of the known invariants can be constructed by methods of calculus (such as square-integrable cohomology), algebraic tools (K-theory), and by looking at very long-range behavior of the manifold or of algebraic objects associated to it (geometric group theory).