Title

Orbit spaces of gradient vector fields

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.

Publisher

Cambridge University Press

Publication Date

1-1-2013

Publication Title

Ergodic Theory and Dynamical Systems

Department

Mathematics

Document Type

Article

DOI

10.1017/etds.2012.123

Language

English

Format

text

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