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Some finiteness results for groups of automorphisms of manifolds

Alexander Kupers

Geometry & Topology 23 (2019) 2277–2333
Abstract

We prove that in dimension 4,5,7 the homology and homotopy groups of the classifying space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses homological stability, embedding calculus and the arithmeticity of mapping class groups. From this we deduce similar results for the homeomorphisms of n and various types of automorphisms of 2–connected manifolds.

Keywords
diffeomorphisms, embeddings
Mathematical Subject Classification 2010
Primary: 57S05
References
Publication
Received: 15 January 2017
Revised: 7 November 2018
Accepted: 15 December 2018
Published: 13 October 2019
Proposed: Yasha Eliashberg
Seconded: Peter Teichner, Benson Farb
Authors
Alexander Kupers
Department of Mathematics
Harvard University
Cambridge, MA
United States