Pure and Applied Mathematics Quarterly

Volume 9 (2013)

Number 1

Special Issue: In Honor of Dennis Sullivan, Part 1 of 2

Homological stability of diffeomorphism groups

Pages: 1 – 48

DOI: http://dx.doi.org/10.4310/PAMQ.2013.v9.n1.a1

Authors

Alexander Berglund (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Ib Madsen (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Abstract

In this paper we prove a stability theorem for block diffeomorphisms of $2d$-dimensional manifolds that are connected sums of $S^d \times S^d$. 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.

Keywords

algebraic topology of manifolds, rational homotopy theory, block bundles

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