Mathematical Sciences: The Geometry and Topology of Free Group Automorphisms

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Although it is customary for geometry and topology to benefit from the application of algebraic methods, it is increasingly true that ideas find application in the other direction as well. Professor Cohen is one of a growing cohort of mathematicians investigating group theory with much of the inspiration derived from geometry and topology. He will continue work on the dynamics of free group automorphisms, with questions concerning the fixed subgroup as one of the intended realms of application. In addition, the question of whether a certain "Teichmuller space" for the outer automorphism group is simply connected at infinity will be investigated. Finally (with lowest priority) a question about free products modulo a single relator will be studied.