A quantum cup-length estimate for symplectic fixed points
type: Item
instance of: scholarly article
title: A quantum cup-length estimate for symplectic fixed points
zbMATH Open document ID: 0951.53053
author: Matthias Schwarz
published in: Inventiones Mathematicae
publication date: 2001-01-02T00:00:00Z
review text: The author presents an approach which replaces the cup-action of singular cohomology on Floer homology by the deformed cohomology ring known as its quantum cohomology. The classical cup-length is extended to the quantum cup-length of the quantum cohomology ring. It is proved that for arbitrary closed symplectic manifolds with rational symplectic class the cup-length estimate holds true if the Hofer energy of the Hamiltonian automorphism is sufficiently small.
Mathematics Subject Classification ID: 53D40
Mathematics Subject Classification ID: 53D45
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 37J10
Mathematics Subject Classification ID: 37N20
zbMATH DE Number: 1199916
zbMATH Keywords: symplectic manifold
zbMATH Keywords: quantum cohomology
zbMATH Keywords: Cauchy-Riemann equation
zbMATH Keywords: singular cohomology
MaRDI profile type: Publication
full work available at URL: s002220050248
OpenAlex ID: W2040072336
DOI: 10.1007/S002220050248
description: scientific article; zbMATH DE number 1199916