Discrete gradient fields on infinite complexes

Rafael Ayala; Jose Antonio Vilches; Gregor Jerše; Neža Mramor Kosta

doi:10.3934/dcds.2011.30.623

Article Contents

2011, Volume 30, Issue 3: 623-639. Doi: 10.3934/dcds.2011.30.623

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Discrete gradient fields on infinite complexes

1.
Dpto. de Geometría y Topología, Universidad de Sevilla, 41080, Sevilla
2.
Dpto. de Geometrĺa y Topologĺa, Universidad de Sevilla, 41080, Sevilla
3.
The Faculty of Computer and Information Science, University of Ljubljana, Tržaška 25, 1000 Ljubljana

Received: December 2009

Revised: November 2010

Published: September 2011

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Abstract

The aim of this work is to characterize the discrete gradient vector fields on infinite and locally finite simplicial complexes which are induced by a proper discrete Morse function. This characterization is essentially given by the non-existence of closed trajectories and the absence of a certain kind of incidence between monotonous rays in the given field.

Keywords:

Mathematics Subject Classification: 57M20, 57Q15, 68R10.

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