Topology seminar

Matthias Grey, on homological stability for automorphisms of odd-dimensional manifolds.

Abstract: Given a family of (topological) groups G_i\rightarrow G_{i+1}, we say that it satisfies homological stability if the induced map H_*(G_i)\rightarrow H_*(G_{i+1}) is an isomorphism in a range depending on i. Often the homology of the colimit of the family is easier to understand than the homology of the individual groups and thus at least gives information in the so called stable range. The aim of this talk is to describe the proof of rational homological stability for the homotopy automorphisms of the iterated connected sum of S^d\times S^{d+1}, following methods by A. Berglund and I. Madsen.