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Closure of singular foliations: the proof of Molino’s conjecture

Part of: Differential topology Global differential geometry

Published online by Cambridge University Press:  13 September 2017

Marcos M. Alexandrino  and
Marco Radeschi
Marcos M. Alexandrino
Affiliation:
Universidade de São Paulo, Instituto de Matemática e Estatística, Rua do Matão 1010, 05508 090 São Paulo, Brazil email [email protected], [email protected]
Marco Radeschi
Affiliation:
University of Notre Dame, Department of Mathematics, 255 Hurley, Notre Dame, IN 46556, USA email [email protected]
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Abstract

In this paper we prove the conjecture of Molino that for every singular Riemannian foliation $(M,{\mathcal{F}})$, the partition $\overline{{\mathcal{F}}}$ given by the closures of the leaves of ${\mathcal{F}}$ is again a singular Riemannian foliation.

Keywords

singular Riemannian foliationlinearizationMolino’s conjecture

MSC classification

Primary: 53C12: Foliations (differential geometric aspects)
Secondary: 57R30: Foliations; geometric theory
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 12 , December 2017 , pp. 2577 - 2590
Copyright
© The Authors 2017 

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