On the equivariant Morse chain complex of the space of closed curves
type: Item
instance of: scholarly article
title: On the equivariant Morse chain complex of the space of closed curves
zbMATH Open document ID: 0652.58020
DOI: 10.1007/BF01160683
author: Hans-Bert Rademacher
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174053
review text: Closed geodesics on a compact Riemannian manifold M can be described as critical points of the energy functional on the free loop space \(\Lambda\) M. This space carries a canonical O(2)-action. We modify the concept of an equivariant (or G-) CW complex for a compact Lie group G in the case \(G=S^ 1\) resp. \(G=O(2)\). Using the energy functional as Morse function this allows the definition of the equivariant Morse chain complex of \(\Lambda\) M. As application we study homology classes in M and in the quotients \(\Lambda M/S^ 1\) and \(\Lambda\) M/O(2) for certain manifolds M. The paper is a condensed version of the author's thesis (``Der Äquivariante Morse-Kettenkomplex des Raums der geschlossenen Kurven'', Bonner Mathematische Schriften Nr. 178 (1987)).
reviewed by: Hans-Bert Rademacher
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 57Q05
zbMATH DE Number: 4064099
zbMATH Keywords: equivariant Morse theory on loop spaces
zbMATH Keywords: equivariant CW complexes
zbMATH Keywords: closed geodesics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4064099