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Fredholm theory and transversality for the parametrized and for the $S^{1}$ -invariant symplectic action

Frédéric Bourgeois; Alexandru Oancea — 2010

Journal of the European Mathematical Society

We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the $L^{2}$ -gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic $S^{1}$ -invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define $S^{1}$ -equivariant...

Contact homology of toroidal manifolds. (Homologie de contact des variétés toroïdales.)

Bourgeois, Frédéric; Colin, Vincent — 2005

Geometry & Topology

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Fredholm theory and transversality for the parametrized and for the S 1 -invariant symplectic action

Contact homology of toroidal manifolds. (Homologie de contact des variétés toroïdales.)

Fredholm theory and transversality for the parametrized and for the $S^{1}$ -invariant symplectic action