About homotopy classes of non-singular vector fields on the three-sphere
Dynamical Systems
2007-05-23 v1 Geometric Topology
Abstract
Generically, the set of points along which two non-singular vector fields on the three-sphere are positively (resp. negatively) collinear form a link. We prove that the two vector fields are homotopic if and only if the linking number of those links is zero. We use this criterion to give a new proof of a result of Yano: every non-singular vector field on the three-sphere is homotopic to a non-singular Morse-Smale vector field.
Keywords
Cite
@article{arxiv.math/0303315,
title = {About homotopy classes of non-singular vector fields on the three-sphere},
author = {Emmanuel Dufraine},
journal= {arXiv preprint arXiv:math/0303315},
year = {2007}
}
Comments
16 pages, 6 figures