Journal of the Mathematical Society of Japan

Hausdorff leaf spaces for foliations of codimension one

Szymon M. WALCZAK

Full-text: Open access

Abstract

We discuss the topology of Hausdorff leaf spaces (briefly the HLS) for foliation of codimension one. After examining the connection between HLSs and warped foliations, we describe the HLSs associated with foliations obtained by basic constructions such as transversal and tangential gluing, spinning, turbulization and suspension. We show that the HLS for any foliation of codimension one on a compact Riemannian manifold is isometric to a finite connected metric graph, and any finite connected metric graph is isometric to a certain HLS. In the final part of this paper, we discuss the condition for a sequence of warped foliations to converge the HLS.

Article information

Source
J. Math. Soc. Japan, Volume 63, Number 2 (2011), 473-502.

Dates
First available in Project Euclid: 25 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1303737795

Digital Object Identifier
doi:10.2969/jmsj/06320473

Mathematical Reviews number (MathSciNet)
MR2793108

Zentralblatt MATH identifier
1270.57070

Subjects
Primary: 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
Secondary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Keywords
foliations Gromov-Hausdorff topology Hausdorff leaf spaces codimension one foliations

Citation

WALCZAK, Szymon M. Hausdorff leaf spaces for foliations of codimension one. J. Math. Soc. Japan 63 (2011), no. 2, 473--502. doi:10.2969/jmsj/06320473. https://projecteuclid.org/euclid.jmsj/1303737795


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