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2002 Every orientable 3–manifold is a $\mathrm{B}\Gamma$
Danny Calegari
Algebr. Geom. Topol. 2(1): 433-447 (2002). DOI: 10.2140/agt.2002.2.433

Abstract

We show that every orientable 3–manifold is a classifying space BΓ where Γ is a groupoid of germs of homeomorphisms of . This follows by showing that every orientable 3–manifold M admits a codimension one foliation such that the holonomy cover of every leaf is contractible. The we construct can be taken to be C1 but not C2. The existence of such an answers positively a question posed by Tsuboi [Classifying spaces for groupoid structures, notes from minicourse at PUC, Rio de Janeiro (2001)], but leaves open the question of whether M= BΓ for some C groupoid Γ.

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Danny Calegari. "Every orientable 3–manifold is a $\mathrm{B}\Gamma$." Algebr. Geom. Topol. 2 (1) 433 - 447, 2002. https://doi.org/10.2140/agt.2002.2.433

Information

Received: 25 March 2002; Accepted: 28 May 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 0991.57028
MathSciNet: MR1917061
Digital Object Identifier: 10.2140/agt.2002.2.433

Subjects:
Primary: 57R32
Secondary: 58H05

Rights: Copyright © 2002 Mathematical Sciences Publishers

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