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Manuel Krannich (Cambridge): (In)finiteness properties of automorphism spaces of manifolds

Abstract: After surveying the state of the art in homotopical finiteness conditions of diffeomorphism groups of manifolds, I will explain recent work with M. Bustamante and A. Kupers in which we show that the classifying space of the diffeomorphism group of a high-dimensional closed manifold M of even dimension is of finite type as long as the fundamental group of M is finite.