G-invariante Morse-Funktionen. (G-invariant Morse functions)
type: Item
instance of: scholarly article
title: G-invariante Morse-Funktionen. (G-invariant Morse functions)
zbMATH Open document ID: 0672.58007
DOI: 10.1007/BF01173705
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155371
review text: For compact G-manifolds (G is a compact Lie group) a special class of invariant Morse functions is introduced, which is shown to be dense (hence nonempty) in the space of invariant Morse functions with respect to the \({\mathcal C}^ 1\)-topology. It is proved that if f is a special Morse function on M then M is homotopy equivalent to a G-CW complex the equivariant \(\lambda\)-cells of which correspond to the critical orbits of f with index \(\lambda\). Applications deal with the Euler number of the fixed point set of the G action and Morse inequalities in the equivariant homology theory.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 57R91
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 4100211
zbMATH Keywords: equivariant Morse theory
zbMATH Keywords: equivariant CW complex
zbMATH Keywords: invariant Morse functions
zbMATH Keywords: equivariant homology theory
author: K. H. Mayer
reviewed by: Balázs Csikós
MaRDI profile type: Publication
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cites work: Seminar on Transformation Groups. (AM-46)
cites work: Lectures on Morse theory, old and new
cites work: Equivariant cohomology theories
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cites work: Q4150865
cites work: Equivariant differential topology
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description: scientific article; zbMATH DE number 4100211