Cohomology of decomposition and the multiplicity theorem with applications to dynamical systems
type: Item
instance of: scholarly article
title: Cohomology of decomposition and the multiplicity theorem with applications to dynamical systems
zbMATH Open document ID: 1246.55002
published in: Illinois Journal of Mathematics
publication date: 2011-11-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ijm/1318598669
review text: The main result of this paper is a description of lower bounds for the sectional category of a map and the Lusternik-Schnirelmann category of a space in terms of the cohomology of the base space and the total space. These results are based on an assumption on the multiplicity of maps of CW complexes which are unions of a finite number of closed sets. Some applications to equilibria of flows of dynamical systems on manifolds are given.
reviewed by: Hellen Colman
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 55R10
zbMATH DE Number: 5981640
zbMATH Keywords: sectional category
zbMATH Keywords: cohomology
author: Leonid A. Luxemburg
MaRDI profile type: Publication
cites work: Q5522742
cites work: The sectional category of a map
cites work: On category, in the sense of Lusternik-Schnirelmann
cites work: The category of a map and of a cohomology class
cites work: Morse inequalities for a dynamical system
cites work: On the Lusternik-Schnirelmann category
cites work: On the Lusternik-Schnirelmann category of abstract groups
cites work: Cohomology theories and infinite CW-complexes
description: scientific article; zbMATH DE number 5981640