A discrete model of $S^1$-homotopy theory

Details A discrete model of $S^1$-homotopy theory A discrete model of $S^1$-homotopy theory

2004-11-09

arxiv.org/abs/math/0411183v1

Mathematics

Algebraic Topology

Scientific paper

We construct a discrete model of the homotopy theory of $S^1$-spaces. We define a category $\sP$ with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. $\sP$ 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 $\sP$ 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.

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