Homology, Homotopy and Applications

Volume 17 (2015)

Number 1

Scanning for oriented configuration spaces

Pages: 35 – 66

DOI: http://dx.doi.org/10.4310/HHA.2015.v17.n1.a2

Authors

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

Martin Palmer (Mathematisches Institut, Westfälisch Wilhelms Universität, Münster, Germany)

Abstract

In [Pal13] the second author proved that the sequence of “oriented” configuration spaces on an open connected manifold exhibits homological stability as the number of particles goes to infinity. To complement that result we identify the corresponding limiting space, up to homology equivalence, as a certain explicit double cover of a section space. Along the way we also prove that the scanning map of [McD75] for unordered configuration spaces is acyclic in the limit.

Keywords

oriented configuration space, alternating group, scanning, homology fibration, local coefficients, group completion

2010 Mathematics Subject Classification

55R65, 55R80, 57N65

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Published 18 May 2015