Volume 16, issue 2 (2016)

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Equivariant diagrams of spaces

Emanuele Dotto

Algebraic & Geometric Topology 16 (2016) 1157–1202

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.

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equivariant, connectivity, homotopy limits
Mathematical Subject Classification 2000
Primary: 55P91
Secondary: 55Q91
Received: 19 June 2015
Accepted: 23 July 2015
Published: 26 April 2016
Emanuele Dotto
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Cambridge, MA 02139-4307