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

By Frederick J. Bourgeois III, A. Oancea. 2007

150 citations recorded by the source corpus.

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 linearized contact homology of a fillable contact manifold and symplectic homology of its filling.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e93e4af1757854b7638b7918815b511eab94336c

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Cylindrical contact homology for dynamically convex contact forms in three dimensions (2014, unknown): “ew in §2.1. The parity 1One can correct for this failure of gluing, but one is then naturally led to a “Morse-Bott” version of the chain complex, with two generators for each Reeb orbit, analogous to [5]. The homology of this Morse-Bott chain complex is not the desired cylindrical contact homology, ”
A biased view of symplectic cohomology (2007, unknown): “20 55 v6 [ m at h. SG ] 1 5 Fe b 20 10”
Brieskorn manifolds in contact topology (2013, background): “Theorem 5.19 (Espina, Bourgeois–Oancea).”
Rabinowitz Floer homology and symplectic homology (2009, methodology): “plex structure JM on M×R +. By Gromov’s Monotonicity Lemma [23, Proposition 4.3.1], there exists an ε>0 such that every JM-holomorphic curve in M×R + which meets the level M×{3}and exits the set M×[2,4] has symplectic area at least ε. Rescaling by R>1, it follows that every JM-holomorphic curv”