Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Improved homological stability for configuration spaces after inverting $2$

Pages: 255 – 266

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n1.a12

Authors

Alexander Kupers (Department of Mathematics Stanford University, Stanford, California, U.S.A.)

Jeremy Miller (Department of Mathematics Stanford University, Stanford, California, U.S.A.)

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 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 $\mathbb{Z}[1/2]$ coefficients, and clarify some aspects of Segal’s proof for topological manifolds.

Keywords

configuration space, homological stability, topological manifold

2010 Mathematics Subject Classification

55R40, 55R80

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Published 18 May 2015