Spaces with local equivalence relations, and their monodromy
type: Item
instance of: scholarly article
title: Spaces with local equivalence relations, and their monodromy
zbMATH Open document ID: 0973.54012
DOI: 10.1016/0166-8641(95)00101-8
published in: Topology and its Applications
publication date: 2001-11-23T00:00:00Z
full work available at URL: http://hdl.handle.net/2066/129061
review text: The authors study a suggestion of A. Grothendieck [\textit{A. Grothendieck} and \textit{J. L. Verdier}, Lect. Notes Math. 269, 1-217 (1972; Zbl 0249.18021)] regarding invariant sheaves arising from a local equivalance relation on a given space, especially on a foliation. They compare it with the standard model obtained by taking the quotient space of foliations defined by the action of holonomy groupoid. Among other things, they prove that under suitable conditions of connectedness, the above invariant sheaves can be described by the usual monodromy groupoids. As an answer to the realization question, the authors show that every etale topological groupoid arises as the monodromy groupoid of a local equivalence relation on a suitable space \(M\). In an appendix, the authors also provide the topos theoretic aspects of local equivalence relation described above.
Mathematics Subject Classification ID: 54B40
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 20L05
zbMATH DE Number: 937156
zbMATH Keywords: invariant sheaf
zbMATH Keywords: foliation
zbMATH Keywords: etale groupoid
author: Anders Kock
author: Ieke Moerdijk
MaRDI profile type: Publication
OpenAlex ID: W2073153734
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description: scientific article; zbMATH DE number 937156