Modèle de Segal pour les structures multifeuilletées. (Segal model for multifoliated structures)
type: Item
instance of: scholarly article
title: Modèle de Segal pour les structures multifeuilletées. (Segal model for multifoliated structures)
zbMATH Open document ID: 0603.57018
DOI: 10.1007/BF01174014
author: Pirouze Djoharian
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155092
review text: Let \(\Gamma \subset \Gamma_ n\) be a subgroupoid containing the diagonal of the topological groupoid of local smooth diffeomorphisms of \({\mathbb{R}}^ n\). Then \(B\Gamma_ n\) is Haefliger's classifying space for codimension-n smooth foliations. The main result of this paper is that \(B\Gamma_ n\) is weakly homotopy equivalent to the discrete monoid of self-embeddings of \({\mathbb{R}}^ n\) all of whose germs are in \(\Gamma\). This generalizes a result of \textit{G. Segal} [Topology 17, 367-382 (1978; Zbl 0398.57018)]. The generalization comes out of carefully investigating and working out details of Segal's main lemma: an almost locally trivial map with contractible fibres is a weak homotopy equivalence. The author relates his result to the classification of multifoliations.
Mathematics Subject Classification ID: 57R32
Mathematics Subject Classification ID: 55R35
zbMATH DE Number: 3973867
zbMATH Keywords: topological groupoid of local smooth diffeomorphisms of \({bbfR}^ n\)
zbMATH Keywords: Haefliger's classifying space for codimension-n smooth foliations
zbMATH Keywords: discrete monoid of self-embeddings of \({bbfR}^ n\)
zbMATH Keywords: almost locally trivial map with contractible fibres
zbMATH Keywords: classification of multifoliations
reviewed by: Solomon Jekel
MaRDI profile type: Publication
cites work: Q5545247
cites work: Q5607712
cites work: Classifying spaces and spectral sequences
cites work: Categories and cohomology theories
cites work: Classifying spaces related to foliations
OpenAlex ID: W2084045237
description: scientific article; zbMATH DE number 3973867