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Lusternik-Schnirelmann category and Morse decompositions

Part of: Classical Topics in Algebraic Topology

Published online by Cambridge University Press:  26 February 2010

José M. R. Sanjurjo
José M. R. Sanjurjo
Affiliation:
Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain. E-mail: Jose_Sanjurjo@mat.ucm.es
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Extract

§1. Introduction. We study in this paper some properties of the Lusternik-Schnirelmann category of isolated invariant sets of continuous dynamical systems. There are several different definitions of this coefficient, although most of them agree in the important case of ANR's (Absolute Neighbourhood Retracts). We refer to the review articles [10] by R. H. Fox and [15, 16] by I. M. James for general information about this topological invariant. We shall use in this paper the definition of the Lusternik-Schnirelmann category of a compactum introduced by K. Borsuk in [4].

MSC classification

Secondary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space

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Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 299 - 305
Copyright
Copyright © University College London 2000

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