Equivariant diagrams of spaces

Dotto, Emanuele

doi:10.2140/agt.2016.16.1157

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Equivariant diagrams of spaces

Emanuele Dotto

Algebraic & Geometric Topology 16 (2016) 1157–1202

DOI: 10.2140/agt.2016.16.1157

Abstract

We generalize two classical homotopy theory results, the Blakers–Massey theorem and Quillen’s Theorem B, to $G$ –equivariant cubical diagrams of spaces, for a discrete group $G$ . We show that the equivariant Freudenthal suspension theorem for permutation representations is a direct consequence of the equivariant Blakers–Massey theorem. We also apply this theorem to generalize to $G$ –manifolds a result about cubes of configuration spaces from embedding calculus. Our proof of the equivariant Theorem B involves a generalization of the classical Theorem B to higher-dimensional cubes, as well as a categorical model for finite homotopy limits of classifying spaces of categories.

Keywords

equivariant, connectivity, homotopy limits

Mathematical Subject Classification 2000

Primary: 55P91

Secondary: 55Q91

References

Publication

Received: 19 June 2015

Accepted: 23 July 2015

Published: 26 April 2016

Authors

Emanuele Dotto
Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA

Volume 16, issue 2 (2016)