Mathematical Sciences: Topology and Manifolds

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D. McDuff will continue her research on the structure of symplectic manifolds, concentrating in particular on the problem of constructing symplectic forms on compact manifolds. These manifolds play an important role in formulating mechanics as a mathematical theory. L. Jones will continue his joint research (with F. T. Farrell of Columbia University) into the computation of the algebraic K-groups and L-groups of discrete subgroups of connected Lie groups. One of their aims is to show that any manifold which is homotopy equivalent to a compact closed Riemannian manifold of constant sectional curvature equal to -1 is actually homeomorphic to it. Understanding the interplay between geometry and topology in this situation should have wide repercussions.