Rational Homological Stability for Automorphisms of Manifolds

Abstract

We show rational homological stability for the homotopy automorphisms and block diffeomorphims of iterated connected sums of products of spheres. The spheres can have different dimension, 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.

References in corpus (2)

• Homological stability for moduli spaces of high dimensional manifolds. I
• Linking forms and stabilization of diffeomorphism groups of manifolds of dimension 4n+1

Cited by in corpus (6)

• Mapping class groups of highly connected $(4k+2)$-manifolds
• The stable cohomology of self-equivalences of connected sums of products of spheres
• Algebraic models for classifying spaces of fibrations
• A note on rational homological stability for automorphisms of manifolds
• Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
• Representation stability for homotopy automorphisms