Rational Homological Stability for Automorphisms of Manifolds
Matthias Grey
TL;DR
This paper proves rational homological stability for automorphisms of certain high-dimensional manifolds formed by connected sums of products of spheres, extending previous stability results to more general cases.
Contribution
It extends homological stability results to automorphisms of manifolds formed by connected sums of products of spheres with varying dimensions under specific connectivity conditions.
Findings
Rational homological stability established for automorphisms of these manifolds.
Generalization of previous stability results to more complex manifold structures.
Applicable to manifolds with spheres of different dimensions satisfying connectivity assumptions.
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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra