@MISC{Blumberg04adiscrete, author = {Andrew J. Blumberg}, title = {A DISCRETE MODEL OF S 1-HOMOTOPY THEORY}, year = {2004} }

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Abstract

Abstract. We construct a discrete model of the homotopy theory of S 1-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. P inherits a model structure from the model structures on the categories of simplicial sets and cyclic sets. We then show that there is a Quillen equivalence between P and the model category of S 1-spaces in which weak equivalences and fibrations are maps inducing weak equivalences and fibrations on passage to all fixed point sets. 1.