Scanning for oriented configuration spaces
with Jeremy Miller

Homology, Homotopy and Applications vol. 17 no. 1 (2015) pp. 35-66
arXiv: abs — pdf
v2 — v1

Note: this was formerly part of the preprint "Twisted homology fibrations and scanning for oriented configuration spaces" (arxiv), which was subsequently split into this paper and the paper "A twisted homology fibration criterion and the twisted group-completion theorem".

Abstract

In [Palmer] 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 [McDuff] for unordered configuration spaces is acyclic in the limit.

• [McDuff] D. McDuff. (1975) Configuration spaces of positive and negative particles. Topology, 14, pp. 91–107.
• [Palmer] M. Palmer. (2013) Homological stability for oriented configuration spaces. Trans. Amer. Math. Soc., 365.7, pp. 3675–3711.