The homotopy theory of equivariant posets

J. P. May; Marc Stephan; Inna Zakharevich

The homotopy theory of equivariant posets

Algebraic Topology 2018-05-18 v3 Combinatorics Category Theory

Authors: J. P. May , Marc Stephan , Inna Zakharevich

Abstract

Let $G$ be a discrete group. We prove that the category of $G$ -posets admits a model structure that is Quillen equivalent to the standard model structure on $G$ -spaces. As is already true nonequivariantly, the three classes of maps defining the model structure are not well understood calculationally. To illustrate, we exhibit some examples of cofibrant and fibrant posets and an example of a non-cofibrant finite poset.

Keywords

equivariant posets model structure Quillen equivalence G-spaces cofibrant objects fibrant objects homotopy theory

Cite

@article{arxiv.1601.02521,
  title  = {The homotopy theory of equivariant posets},
  author = {J. P. May and Marc Stephan and Inna Zakharevich},
  journal= {arXiv preprint arXiv:1601.02521},
  year   = {2018}
}

Comments

22 pages; minor improvements suggested by the referee, final version, to appear in Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques

The homotopy theory of equivariant posets

Abstract

Keywords

Cite

Comments

Related papers