Improved homological stability for configuration spaces after inverting 2

Abstract

In Appendix A of his article on rational functions, Segal proved homological stability for configuration spaces with a stability slope of 1/2. This was later improved to a slope of 1 by Church and Randal-Williams if one works with rational coefficients and manifolds of dimension at least $3$. In this note we prove that the stability slope of 1 holds even with Z[1/2] coefficients, and clarify some aspects of Segal's proof for topological manifolds.

11 pages, 1 figure. Minor mistakes fixed

References in corpus (1)

• $E_n$-cell attachments and a local-to-global principle for homological stability

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