Homological stability of diffeomorphism groups.

Alexander Berglund; Ib Henning Madsen

doi:10.4310/PAMQ.2013.v9.n1.a1

Homological stability of diffeomorphism groups.

Alexander Berglund, Ib Henning Madsen

Department of Mathematical Sciences

16 Citations (Scopus)

Abstract

In this paper we prove a stability theorem for block diffeomorphisms of 2d -dimensional manifolds that are connected sums of S d ×S d . Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet’s lemma of disjunction, we determine the homology of the classifying space of their diffeomorphism groups relative to an embedded disk in a stable range.

Original language	English
Journal	Pure and Applied Mathematics Quarterly
Volume	9
Issue number	1
Pages (from-to)	1-48
ISSN	1558-8599
DOIs	https://doi.org/10.4310/PAMQ.2013.v9.n1.a1
Publication status	Published - 2013

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10.4310/PAMQ.2013.v9.n1.a1

Cite this

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AB - In this paper we prove a stability theorem for block diffeomorphisms of 2d -dimensional manifolds that are connected sums of S d ×S d . Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet’s lemma of disjunction, we determine the homology of the classifying space of their diffeomorphism groups relative to an embedded disk in a stable range.

U2 - 10.4310/PAMQ.2013.v9.n1.a1

DO - 10.4310/PAMQ.2013.v9.n1.a1

M3 - Journal article

SN - 1558-8599

VL - 9

SP - 1

EP - 48

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 1

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