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Fredholm theory and transversality for the parametrized and for the -invariant symplectic action
Frédéric Bourgeois, Alexandru Oancea
We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the -gradient lines is Fredho…
A note on Reeb dynamics on the tight 3-sphere
F. Bourgeois, K. Cieliebak, T. Ekholm
We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. M…
Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces
Frédéric Bourgeois, Alexandru Oancea
We define Floer homology for a time-independent, or autonomous Hamiltonian on a symplectic manifold with contact type boundary, under the assumption that its 1-periodic orbits are…
Contact homology and homotopy groups of the space of contact structures
Frédéric Bourgeois
Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our t…