Homological stability for moduli spaces of high dimensional manifolds

2012/03/30 by Søren Galatius, Galatius, Soren, Oscar Randal‐Williams +1
Mathematics · #55P47 #57R15 #57R56 #57R90 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1203.6830

openalex publication_date 2012/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(Sⁿ x Sⁿ), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a calculation of the homology of these moduli spaces in a range of degrees.

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