9504913 Calabi The proposed research involves various aspects of differential geometry and differential topology: variational problems in surface theory, knot theory in the presence of curvature, topological classification of representations, homology manifolds, Einstein metrics on homogeneous spaces, equivariant K-theory, and Poisson manifolds are among the topics proposed. Differential geometry studies shapes in space keeping in mind their distance and curvature properties; differential topology concentrates on relative positions in space whilst ignoring distance or curvature. This group proposal then seeks to establish a connection between these two areas of research by asking such questions as how the topology of a space determines its geometry.
