Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces

Abstract

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 transversally nondegenerate. Our construction is based on Morse-Bott techniques for Floer trajectories. Our main motivation is to understand the relationship between the linearized contact homology of a fillable contact manifold and the symplectic homology of its filling