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arXiv · 2010.01438

Local Symplectic Homology of Reeb Orbits

Elijah Fender
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Abstract

In this paper we prove two isomorphisms in the local symplectic homology of a simple, which is to say non iterated, isolated Reeb orbit. The isomorphisms are in $S^1$-equivariant and nonequivariant symplectic homology, relating the local Floer homology group of the orbit to that of the return map. The isomorphism we prove in $S^1$-equivariant symplectic homology can be stated succinctly as the local $S^1$-equivariant symplectic homology of a simple isolated Reeb orbit is isomorphic to the local Hamiltonian Floer homology of the return map. We also prove the equivalence of two different definitions of a Reeb orbit being a symplectically degenerate maximum.

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Elijah Fender. 2020-10-03. Local Symplectic Homology of Reeb Orbits. https://arxiv.org/abs/2010.01438

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