Mathematical Sciences: Geometric Topology

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The project of F. Connolly covers a variety of topics related to topological rigidity properties of crystallographic, arithmetic, and negatively curved groups. His investigations also include related questions about Nil-K-theory of such groups as well as the study of groups which act freely and cocompactly on the product of real n-space and an m-sphere. This work is related to a number of famous open problems, e.g., the Borel conjecture, the Novikov conjecture, and it draws upon a broad range of techniques.