#### Volume 16, issue 2 (2016)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Equivariant diagrams of spaces

### Emanuele Dotto

Algebraic & Geometric Topology 16 (2016) 1157–1202
##### 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
Primary: 55P91
Secondary: 55Q91