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arXiv · 1412.2682

Higher algebraic structures in Hamiltonian Floer theory

Oliver Fabert
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Abstract

In this paper we show how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures in Hamiltonian Floer theory. Using the SFT of Hamiltonian mapping tori we show how to define a homotopy extension of the well-known Lie bracket and discuss how it can be used to prove the existence of multiple closed Reeb orbits. Furthermore we show how to define the analogue of rational Gromov-Witten theory in the Hamiltonian Floer theory of open symplectic manifolds. More precisely, we introduce a so-called cohomology F-manifold structure in Hamiltonian Floer theory and prove that it generalizes the well-known Frobenius manifold structure in rational Gromov-Witten theory.

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Oliver Fabert. 2014-12-08. Higher algebraic structures in Hamiltonian Floer theory. https://doi.org/10.1515/advgeom-2019-0017

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