Algebraic & Geometric Topology 2 (2002) 433–447

DOI: 10.2140/agt.2002.2.433

arXiv: math.GT/0206066

Abstract

We show that every orientable 3--manifold is a classifying space BΓ where Γ is a groupoid of germs of homeomorphisms of R. This follows by showing that every orientable 3--manifold M admits a codimension one foliation F such that the holonomy cover of every leaf is contractible. The F we construct can be taken to be C¹ but not C². The existence of such an F 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.

Keywords

foliation, classifying space, groupoid, germs of homeomorphisms

Mathematical Subject Classification

Primary: 57R32

Secondary: 58H05

References

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Publication

Received: 25 March 2002
Accepted: 28 May 2002
Published: 29 May 2002

Authors