The cellular structure of the classifying spaces of finite groups

Abstract

In this paper we obtain a description of the BZ/p-cellularization (in the sense of Dror-Farjoun) of the classifying spaces of all finite groups, for all primes p.

Torsion homology and cellular approximation

“…There is an immediate corollary concerning the position of the classifying space of this Burnside group in the BZ/p-cellular and acyclic hierarchies, which have deserved some interest in the last years (see for example [19], [11] or [25]). Proof.…”

Cellular approximations of p‐local compact groups

“…In later work , the description of was completed for every prime and finite group . The culminating result of that paper uses a previous classification of strongly closed subgroups of finite groups , emphasizing the tight relationship between the ‐cellular approximation of and the ‐local information of (or fusion system at the prime ).…”

“…In later work [22], the description of CW BZ/p BG was completed for every prime and finite group G. The culminating result of that paper uses a previous classification of strongly closed subgroups of finite groups [21], emphasizing the tight relationship between the BZ/p-cellular approximation of BG and the p-local information of G (or fusion system at the prime p). This key observation opened the way to the description of the BZ/p-cellular approximation of classifying spaces of p-local finite groups, the mod p homotopical analogues of classifying spaces of finite groups defined by Broto-Levi-Oliver in [7], and constructed from abstract fusion systems on finite p-groups.…”

Cellular approximations of infinite loop spaces

“…Many authors have contributed to the development of A-homotopy when the spaces involved are classifying spaces (see [5,[12][13][14]20]). Recently, important results have been obtained by Chachólski, Dror-Farjoun, Flores and Scherer [7] in describing cellular covers of nilpotent Postnikov stages.…”