Mathematical Sciences: Topology

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This project covers a wide range of topics in algebraic and geometric topology. More specifically, the researchers study the following: (a) Combinatorial and geometric properties of various classes of discrete groups, including finitely presented infinite simple groups, groups presented by a rewriting system, groups presented by a triangle of groups, and the automorphism group of a free or free-by-finite group; (b) laminations in 3-manifolds; (c) equivariant and controlled topology, including the equivariant topology of locally linearizable actions and the topological equivalence of linear representations. Topology addresses geometric properties which do not depend in an essential way on distances or angles. It nevertheless attempts to find ways to compare topological objects and to reduce their study to computations in many cases. The instant project is engaged in different aspects of this multifarious effort.