Proposal for a Conference on the Geometry and Topology of Manifolds

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AbstractAward: DMS-0406314Principal Investigator: Crichton L. OgleThis award provides partial support for participant costs of aconference on the "Geometry and Topology of Manifolds" at OhioState University. The main themes of the meeting are invariantsof manifolds arising in square-integrable cohomology, K-theory,and geometric group theory. Invited speakers and otherparticipants include a number of female mathematicians, recentPhDs, and graduate students.A manifold is a geometric space in which every point hasneighborhoods that can be identified with Euclidean space of somedimension. For example, every point on the surface of a2-dimensional sphere lies in an open hemisphere that can beflattened onto the Euclidean plane by a map projection. Anexample of a higher dimensional manifold would be the space ofphysical coordinates for three particles moving in the planewithout collisions: each particle's dynamical data consists oftwo position and two velocity coordinates, thus each of the threeparticles requires four numbers to record its dynamics and toreport all three moving particles simultaneously calls for twelvecoordinates. "Invariants" of manifolds are computable objects(not necessarily numbers) that help us tell one space fromanother, and some of the known invariants can be constructed bymethods of calculus (such as square-integrable cohomology),algebraic tools (K-theory), and by looking at very long-rangebehavior of the manifold or of algebraic objects associated to it(geometric group theory).