Coherent orientations for periodic orbit problems in symplectic geometry
type: Item
instance of: scholarly article
title: Coherent orientations for periodic orbit problems in symplectic geometry
zbMATH Open document ID: 0789.58022
DOI: 10.1007/BF02571639
published in: Mathematische Zeitschrift
publication date: 1994-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/174470
review text: Finding periodic solutions of a Hamiltonian system is a variational problem. The merger of Gromov's theory of pseudoholomorphic curves and Conley's variant of Morse theory has lead to the first author's instanton homology in symplectic geometry. Algebraic invariants for a Hamiltonian system are obtained from the combinatorics of solution sets of suitable nonlinear first order systems of Cauchy-Riemann type. Their linearisations along the solution sets give parametrized families of Fredholm maps. The orientability of the associated determinant bundles compatible with a linear variant of Taubes' glueing procedure is a crucial ingredient for defining instanton homology with general coefficients. The present article describes a solution of this orientation problem. This will be important for a forthcoming series of joint papers on a symplectic homology theory.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58J20
Mathematics Subject Classification ID: 58J52
zbMATH DE Number: 549736
zbMATH Keywords: periodic orbit problems
zbMATH Keywords: symplectic geometry
zbMATH Keywords: Cauchy-Riemann type operators
zbMATH Keywords: determinant bundle
zbMATH Keywords: glueing
zbMATH Keywords: Fredholm index
zbMATH Keywords: orientation
zbMATH Keywords: instanton homology
author: Andreas Floer
author: Helmut Hofer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549736