A major theme of twentieth century mathematics has been the deep connections between group theory and geometry and topology. This connection began with Poincare's discovery of the notion of the fundamental group of a space. One of the most interesting aspects of this connection is the relationship between group theory and curvature in particular, nonpositive curvature. The 1980's saw a new influx of ideas in this last area including the following: (1) work on "word hyperbolic groups," that is, a class which contains all groups which can act properly and cocompactly on negatively curved spaces, (2) the recognition of the algorithmic character of such groups leading to the introduction of the notion of "automatic groups," (3) the study of groups acting on trees and R-trees, (4) work on polyhedra and orbihedra of nonpositive curvature and applications to complexes of groups, and (5) the Novikov conjecture for word hyperbolic groups and work on topological rigidity of nonpositively curved manifolds. This project will support a research quarter in Nonpositive Curvature and Geometric Group Theory to be held at the Ohio State University during the Spring Quarter of 1992. The activity will include both long and short term visitors, as well as a conference which will be held during the first week of June 1992.
