Orbit Spaces of Gradient Vector Fields
Dynamical Systems
2014-08-06 v2 Algebraic Topology
General Topology
Abstract
We study orbit spaces of generalized gradient vector fields for Morse functions. Typically, these orbit spaces are non-Hausdorff. Nevertheless, they are quite structured topologically and are amenable to study. We show that these orbit spaces are locally contractible. We also show that the quotient map associated to each such orbit space is a weak homotopy equivalence and has the path lifting property.
Keywords
Cite
@article{arxiv.1105.5286,
title = {Orbit Spaces of Gradient Vector Fields},
author = {Jack S. Calcut and Robert E. Gompf},
journal= {arXiv preprint arXiv:1105.5286},
year = {2014}
}
Comments
16 pages, 4 figures; strengthened a main result (Corollary 3.5) and updated the introduction and the conclusion