Dotto, Emanuele (2016) Equivariant diagrams of spaces. Algebraic & Geometric Topology, 16 (2). pp. 1157-1202. doi:10.2140/agt.2016.16.1157 ISSN 1472-2747.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Algebraic & Geometric Topology
Publisher:	Mathematical Sciences Publishers
ISSN:	1472-2747
Official Date:	26 April 2016
Dates:	Date Event 26 April 2016 Published 23 July 2015 Accepted
Volume:	16
Number:	2
Page Range:	pp. 1157-1202
DOI:	10.2140/agt.2016.16.1157
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	17 September 2019
Open Access Version:	ArXiv

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