Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 29, 2002 | public
Journal Article Open

Every orientable 3-manifold is a B\Gamma

Abstract

We show that every orientable 3-manifold is a classifying space B\Gamma where \Gamma 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 C^1 but not C^2. 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 = B\Gamma for some C^\infty groupoid \Gamma.

Additional Information

Submitted: 25 March 2002. Accepted: 28 May 2002. Published: 29 May 2002. In August 2001, the P.U.C. in Rio de Janeiro held a conference on Foliations and Dynamics aimed at bringing together traditional foliators and 3-manifold topologists. At this conference, Takashi Tsuboi posed the question of the existence of typical foliations on 3-manifolds. I would very much like to thank Takashi for posing this question, for reading an early draft of this paper and catching numerous errors, and for introducting me to the beautiful subject of classical foliation theory. I'd also like to thank Curt McMullen for a useful conversation which helped clarify some analytic questions for me. E-print: arXiv:math.GT/0206066

Files

CALagt02.pdf
Files (203.5 kB)
Name Size Download all
md5:3d91a83755a6c08ff281b16056e732b9
203.5 kB Preview Download

Additional details

Created:
August 21, 2023
Modified:
October 13, 2023