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Longitudinal smoothness of the holonomy groupoid.
- Source :
-
Comptes Rendus. Mathématique . Aug2013, Vol. 351 Issue 15/16, p613-616. 4p. - Publication Year :
- 2013
-
Abstract
- Abstract: Iakovos Androulidakis and Georges Skandalis have defined a holonomy groupoid for any singular foliation. This groupoid, whose topology is usually quite bad, is the starting point for the study of longitudinal pseudodifferential calculus on such foliation and its associated index theory. These studies can be highly simplified under the assumption of the holonomy groupoid being longitudinally smooth. In this note, we rephrase the period bounding lemma that asserts that a vector field on a compact manifold admits a strictly positive lower bound for its periodic orbits in order to prove that the holonomy groupoid is always longitudinally smooth. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 1631073X
- Volume :
- 351
- Issue :
- 15/16
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 91727120
- Full Text :
- https://doi.org/10.1016/j.crma.2013.07.025