Coherent orientations for periodic orbit problems in symplectic geometry
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.
scientific article; zbMATH DE number 549736
scientific article