Proving homological stability for homeomorphisms of manifolds

2015/10/08 by Alexander Kupers, Kupers, Alexander · 2 citations
Mathematics · #55R40 #57N65 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1510.02456

openalex publication_date 2015/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Following the argument for diffeomorphisms by Galatius and Randal-Williams, we prove that homeomorphisms of 1-connected manifolds of even dimension at least 6 exhibit homological stability. We deduce similar results for PL homeomorphisms and homeomorphisms as a discrete group.

Cited by

• The asphericity of locally finite infinite configuration spaces and Weierstrass entire coverings
• A local to global argument on low dimensional manifolds

Related

• Homological stability of diffeomorphism groups of high dimensional manifolds via E_k-algebras
• Homological stability of diffeomorphism groups
• Set theory, logic, and homeomorphism groups of manifolds
• Actions of groups of homeomorphisms on one-manifolds
• Homological stability for moduli spaces of high dimensional manifolds