The Structure of Stable Vector Fields on Surfaces
Differential Geometry
2015-03-19 v1
Abstract
The Poincare-Hopf theorem tells us that given a smooth, structurally stable vector field on a surface of genus g, the number of saddles is 2-2g less than the number of sinks and sources. We generalize this result by introducing a more complex combinatorial invariant. Using this tool, we demonstrate that many such structurally stable vector fields are equivalent up to a set of basic operations. We show in particular that for the sphere, all such vector fields are equivalent.
Cite
@article{arxiv.1108.2643,
title = {The Structure of Stable Vector Fields on Surfaces},
author = {John Berman and Sergei Bernstein},
journal= {arXiv preprint arXiv:1108.2643},
year = {2015}
}
Comments
13 pages, 13 figures