Assembling homology classes of free group automorphisms

Abstract

The goal of this talk is to give a gentle introduction to the recent work of Conant, Hatcher, Kassabov and Vogtmann on free group automorphisms and their homology. We will first set the scene by defining group homology, introducing free group automorphisms and sketching what is known of their homology, in particular, the Morita classes. Low rank computations of Euler characteristic suggest that this picture is far from representative, motivating the need for a different idea. The new approach taken here will be to understand certain groups \Gamma_{n,s} that arise as natural generalisations of free group automorphisms. Using nothing but the simplest examples of these groups we will reconstruct the Morita classes via an assembly map, and point to further applications of these techniques.

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