Bonn Topology Group - Abstracts

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Talk

June 5th 2018
Nathalie Wahl (Københavns Universitet, Denmark): Stability and stable homology of classical groups

Abstract

In joint work with David Sprehn, we give an improved homological stability range for the general linear groups GL_n(F), and for symplectic group Sp_{2n}(F), orthogonal group O_{n,n}(F) and unitary groups U_{2n}(F) over any field F other than F_2. Under more restricted assumptions, we deduce a stability theorem for the orthogonal group O_n(F). We also show that the stable mod p homology of the symplectic, orthogonal, and unitary groups over a finite field of odd characteristic p is trivial. I'll present these results, and give some ideas of the tools and techniques that go into proving them.

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