An isovariant Elmendorf's theorem

Abstract

An isovariant map between spaces with a group action is an equivariant map which preserves isotropy groups. In this paper, we show that for a finite group $G$, the category of $G$-spaces with isovariant maps has a Quillen model structure. We prove a Piacenza-style model theoretic proof of an isovariant Elmendorf's theorem, showing that this model structure is Quillen equivalent to a model category of diagrams.

13 pages, many minor corrections, significant revisions: corrected definition of link orbit category and a lemma proof, switched to compactly generated spaces, added proposition in section 2 on adding a terminal object. journal version