Higher algebraic structures in Hamiltonian Floer theory
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.
Cite
@article{arxiv.1412.2682,
title = {Higher algebraic structures in Hamiltonian Floer theory},
author = {Oliver Fabert},
journal= {arXiv preprint arXiv:1412.2682},
year = {2020}
}
Comments
55 pages; published final version, containing also results from 1310.6014. arXiv admin note: substantial text overlap with arXiv:1206.1564