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Orbit spaces of gradient vector fields

Published online by Cambridge University Press:  30 October 2012

JACK S. CALCUT  and
ROBERT E. GOMPF
JACK S. CALCUT
Affiliation:
Department of Mathematics, Oberlin College, Oberlin, OH 44074, USA (email: jcalcut@oberlin.edu)
ROBERT E. GOMPF
Affiliation:
Department of Mathematics, University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA (email: gompf@math.utexas.edu)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 6 , December 2013 , pp. 1732 - 1747
Copyright
Copyright © 2012 Cambridge University Press 

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