On rational homological stability for block automorphisms of connected sums of products of spheres

Grey, Matthias

doi:10.2140/agt.2019.19.3359

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On rational homological stability for block automorphisms of connected sums of products of spheres

Matthias Grey

Algebraic & Geometric Topology 19 (2019) 3359–3407

DOI: 10.2140/agt.2019.19.3359

Abstract

We show rational homological stability for the classifying spaces of the monoid of homotopy self-equivalences and the block diffeomorphism group of iterated connected sums of products of spheres. The spheres can have different dimensions, but need to satisfy a certain connectivity assumption. The main theorems of this paper extend homological stability results for automorphism spaces of connected sums of products of spheres of the same dimension by Berglund and Madsen.

Keywords

manifolds, homotopy automorphisms, block diffeomorphisms, rational homology, homological stability

Mathematical Subject Classification 2010

Primary: 55P62, 57S05

References

Publication

Received: 12 January 2018

Revised: 13 January 2019

Accepted: 2 April 2019

Published: 17 December 2019

Authors

Matthias Grey
Matematiska institutionen Stockholms universitet Stockholm Sweden

Volume 19, issue 7 (2019)