Classifying toposes and foliations

Ieke Moerdijk

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 1, page 189-209
  • ISSN: 0373-0956

Abstract

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For any etale 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 Γ q .

How to cite

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Moerdijk, Ieke. "Classifying toposes and foliations." Annales de l'institut Fourier 41.1 (1991): 189-209. <http://eudml.org/doc/74913>.

@article{Moerdijk1991,
abstract = {For any etale 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 $B\Gamma ^ q$.},
author = {Moerdijk, Ieke},
journal = {Annales de l'institut Fourier},
keywords = {étale topological groupoid; classifying topos; classifying space; fundamental group; Haefliger's classifying space},
language = {eng},
number = {1},
pages = {189-209},
publisher = {Association des Annales de l'Institut Fourier},
title = {Classifying toposes and foliations},
url = {http://eudml.org/doc/74913},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Moerdijk, Ieke
TI - Classifying toposes and foliations
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 1
SP - 189
EP - 209
AB - For any etale 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 $B\Gamma ^ q$.
LA - eng
KW - étale topological groupoid; classifying topos; classifying space; fundamental group; Haefliger's classifying space
UR - http://eudml.org/doc/74913
ER -

References

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