A Morse-Bott approach to contact homology

Frédéric Bourgeois (1)

1 Department of Mathematics [Stanford]

Contact homology was introduced by Eliashberg, Givental and Hofer; this contact invariant is based on J-holomorphic curves in the symplectization of a contact manifold. We expose an extension of contact homology to Morse-Bott situations, in which closed Reeb orbits form submanifolds of the contact manifold. We then illustrate how to use this to compute contact homology with several examples.

Domaines: Géométrie symplectique [math.SG]

Frédéric Bourgeois. A Morse-Bott approach to contact homology. Yakov Eliashberg, Boris Khesin and François Lalonde. Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society, pp.55-77, 2003, Fields Institute Communications, Vol. 35, 978-0-8218-3162-5. ⟨hal-01011022⟩