Volume 19, issue 7 (2019)

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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

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.

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manifolds, homotopy automorphisms, block diffeomorphisms, rational homology, homological stability
Mathematical Subject Classification 2010
Primary: 55P62, 57S05
Received: 12 January 2018
Revised: 13 January 2019
Accepted: 2 April 2019
Published: 17 December 2019
Matthias Grey
Matematiska institutionen
Stockholms universitet