Orbit Spaces of Gradient Vector Fields

Details Orbit Spaces of Gradient Vector Fields Orbit Spaces of Gradient Vector Fields

2011-05-26

arxiv.org/abs/1105.5286v2

Mathematics

Dynamical Systems

16 pages, 4 figures; strengthened a main result (Corollary 3.5) and updated the introduction and the conclusion

Scientific paper

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.

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