Foliated vector fields without periodic orbits
Dynamical Systems
2015-03-10 v2 Differential Geometry
Abstract
In this article parametric versions of Wilson's plug and Kuperberg's plug are discussed. We show that there is a weak homotopy equivalence induced by the inclusion between the space of non-singular vector fields tangent to a foliation and the subspace of those without closed orbits, as long as the leaves of the foliation have dimension at least 3. We contrast this with the case of foliations by surfaces in 3-manifolds.
Keywords
Cite
@article{arxiv.1412.0123,
title = {Foliated vector fields without periodic orbits},
author = {Daniel Peralta-Salas and Alvaro del Pino and Francisco Presas},
journal= {arXiv preprint arXiv:1412.0123},
year = {2015}
}
Comments
9 pages, 2 figures