Transversality in elliptic Morse theory for the symplectic action
type: Item
instance of: scholarly article
title: Transversality in elliptic Morse theory for the symplectic action
zbMATH Open document ID: 0846.58025
DOI: 10.1215/S0012-7094-95-08010-7
author: Andreas Floer
author: Dietmar A. Salamon
author: Helmut Hofer
published in: Duke Mathematical Journal
publication date: 1996-05-01T00:00:00Z
review text: The goal of this paper is to settle some transversality questions for the perturbed nonlinear Cauchy-Riemann equations on the cylinder. These results play a central role in the definition of symplectic Floer homology and hence in the proof of the Arnold conjecture. The precise definition involves an infinite-dimensional analogue of Witten's approach to Morse theory. In the finite-dimensional context, this construction requires the Morse-Smale transversality condition, namely, that the stable and unstable manifolds of any two critical points intersect transversally. The infinite-dimensional analogue of this condition is presented in the paper.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 850807
zbMATH Keywords: symplectic action
zbMATH Keywords: Floer homology
zbMATH Keywords: Arnold conjecture
zbMATH Keywords: Morse theory
zbMATH Keywords: Morse-Smale transversality condition
reviewed by: Vitaly Moroz
MaRDI profile type: Publication
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full work available at URL: s0012-7094-95-08010-7
OpenAlex ID: W1574390900
description: scientific article; zbMATH DE number 850807