A wide variety of problems in algebraic and geometric topology will be investigated by the four faculty investigators and one of their advanced graduate students. Professor Milgram plans to work on geometric and algebraic problems connected to the relations between Poincare duality bordism groups and surgery theory. He also plans to study the geometry of certain classifying spaces related to topological bundles and deleted symmetric products. Professor Brumfiel is interested in the relations between real algebraic geometry and the Thurston compactification of Teichmuller space. He also wants to extend these techniques to the moduli spaces of Riemann surfaces. Professor Cohen wants to continue a collaboration with G. Carlsson and W. C. Hsiang on the homotopy type of the Waldhausen algebraic K-theory space. He also wants to continue his study of the consequences of his recent reduction of the Novikov conjecture to a question about the Waldhausen space for a point. Finally, he and A. Adem are also working on applying homological techniques to equivariant homotopy theory. Professor Kerckhoff plans to study the automorphisms of free groups using some new complexes constructed by Vogtmann and Culler. He also wants to study the geometry of certain 3- dimensional manifolds related to closed surfaces.
