Algebra/Topology Seminar

Speaker: Erik Lindell

Title: Stable homology of Aut(F_n) with bivariant twisted coefficients

Abstract: The stable homology of the automorphism group of the free group on n generators, i.e. the homology groups where n is large compared to the homological degree, has been studied by several authors. With trivial rational coefficients, the stable homology groups were proven to be trivial by Galatius, and by building on the same methods, Randal-Williams managed to compute the stable homology groups with coefficients in tensor powers of the standard representation H=H_1(F_n,Q), or of its dual. Using functor homology methods, these have also been independently computed by Djament and Vespa. For mixed tensor powers of H and H*, a conjectural description has been given by Djament. In this talk, we will see how this conjecture can be proven, by pushing the geometric methods of Galatius and Randal-Williams a bit further.

On request, we will broadcast this talk via Zoom. If you would like to attend online and need the password, please contact the organisers.