Mathematical Sciences: Topology

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This project deals with a broad range of topics in and around topology, from algebraic K-theory, studied by Swan, to knot theory, studied by Orr. The central foci are homotopy theory and high-dimensional manifold theory. Hopkins and Devinatz study the global structure of stable homotopy theory. Stover studies the structure of unstable homotopy theory. May and Liulevicius study a variety of topics in equivariant algebraic topology. Rothenberg and Weinberger study group actions on manifolds and related areas of geometric topology. Madsen, visiting from Denmark, will continue joint work with Rothenberg on finite group actions. Four advanced graduate students are also engaged in related research under faculty direction.