Classifying toposes and foliations
type: Item
instance of: scholarly article
title: Classifying toposes and foliations
zbMATH Open document ID: 0727.57029
author: Ieke Moerdijk
publication date: 1991-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74913
review text: For any étale topological groupoid G (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal's theorem on Haefliger's classifying space \(B\Gamma^ q\).
Mathematics Subject Classification ID: 57R32
Mathematics Subject Classification ID: 18F10
zbMATH DE Number: 4201177
zbMATH Keywords: étale topological groupoid
zbMATH Keywords: classifying topos
zbMATH Keywords: classifying space
zbMATH Keywords: fundamental group
zbMATH Keywords: Haefliger's classifying space
MaRDI profile type: Publication
OpenAlex ID: W1968902436
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DOI: 10.5802/AIF.1254
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4201177