A twisted homology fibration criterion and the twisted group-completion theorem

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.

21 pages. This note supersedes Section 2 of arXiv:1306.6896v1, which has been split in half for length reasons

References in corpus (4)

• Homological stability for moduli spaces of high dimensional manifolds. I
• Homological stability for moduli spaces of high dimensional manifolds
• The homotopy type of a topological stack
• Homology fibrations and "group-completion" revisited

Cited by in corpus (3)

• Semi-simplicial spaces
• Homological stability of topological moduli spaces
• Toward a Galois theory of the integers over the sphere spectrum