Title: Homological Stability for Diffeomorphism Groups Made Discrete



Abstract

In 2007, Morita posed a question about homological stability of surface diffeomorphism groups with discrete topology. Using techniques, mainly due to Thurston, J. Bowden could show homological stability of these groups in low degrees. In this talk we will see why the high dimensional analogue of Morita's problem can be solved by virtue of the usual Quillen's stability machine. Although homology of Diff groups with discrete topology are gigantic, we can "compute" them in low homological degrees. Whether or not the limit of the homology of these groups comes from the homology of an infinite loop space remains to be understood.