## Algebraic & Geometric Topology

### Equivariant diagrams of spaces

Emanuele Dotto

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 2 (2016), 1157-1202.

Dates
Accepted: 23 July 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.agt/1510841163

Digital Object Identifier
doi:10.2140/agt.2016.16.1157

Mathematical Reviews number (MathSciNet)
MR3493418

Zentralblatt MATH identifier
1339.55015

Subjects

#### Citation

Dotto, Emanuele. Equivariant diagrams of spaces. Algebr. Geom. Topol. 16 (2016), no. 2, 1157--1202. doi:10.2140/agt.2016.16.1157. https://projecteuclid.org/euclid.agt/1510841163

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