Symplectic homology. I: Open sets in \(\mathbb{C}^ n\)
type: Item
instance of: scholarly article
title: Symplectic homology. I: Open sets in \(\mathbb{C}^ n\)
zbMATH Open document ID: 0810.58013
DOI: 10.1007/BF02571699
published in: Mathematische Zeitschrift
publication date: 1994-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/174598
review text: The purpose of this paper is to construct a symplectic homology on \(\mathbb{C}^ n\) by using Floer homology and capacity theory. This theory of the symplectic homology has many important applications. As an example, the computation of the symplectic homology groups of polydisks leads to a proof of a conjecture of Gromov on the symplectic classification of open polydisks: For \(r = (r_ 1, \dots, r_ n)\) with the convention \(0 < r_ 1 \leq r_ 2 \leq \dots \leq r_ n\), let \(B^ 2(r_ i)\) be an open boule of radius \(r_ i\) in \(\mathbb{C}\) and \(D(r)\) be the polydisk \(B^ 2(r_ 1) \times \dots \times B^ 2(r_ n)\). Then \(D(r)\) and \(D(r')\) are symplectomorphic if and only if \(r = r'\).
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 567418
zbMATH Keywords: symplectic form
zbMATH Keywords: symplectic morphism
zbMATH Keywords: Floer homology
zbMATH Keywords: capacity
author: Andreas Floer
author: Helmut Hofer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 567418