Some finiteness results for groups of automorphisms of manifolds

Kupers, Alexander

doi:10.2140/gt.2019.23.2277

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Some finiteness results for groups of automorphisms of manifolds

Alexander Kupers

Geometry & Topology 23 (2019) 2277–2333

DOI: 10.2140/gt.2019.23.2277

Abstract

We prove that in dimension $\neq 4, 5, 7$ 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 $ℝ^{n}$ 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

Volume 23, issue 5 (2019)