A twisted homology fibration criterion and the twisted group-completion theorem
with Jeremy Miller

The Quarterly Journal of Mathematics vol. 66 no. 1 (2015) pp. 265-284
arXiv: abs — pdf
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 "Scanning for oriented configuration spaces".

Abstract

The purpose of this note is to clarify some details in McDuff and Segal's proof of the group-completion theorem and to generalize both this and the homology fibration criterion of McDuff to homology with twisted coefficients. This will be used in forthcoming work to identify the limiting homology of "oriented" configuration spaces, which doubly cover the classical configuration spaces of distinct unordered points in a manifold.