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arXiv · 2404.12249

An approach to Hamiltonian Floer theory for maps from surfaces

Ronen Brilleslijper·Oliver Fabert
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Abstract

In $n$-dimensional classical field theory one studies maps from $n$-dimensional manifolds in such a way that classical mechanics is recovered for $n=1$. In previous papers we have shown that the standard polysymplectic framework in which field theory is described, is not suitable for variational techniques. In this paper, we introduce for $n=2$ a Lagrange-Hamilton formalism that allows us to define a generalization of Hamiltonian Floer theory. As an application, we prove a cuplength estimate for our Hamiltonian equations that yields a lower bound on the number of solutions to Laplace equations with nonlinearity. We also discuss the relation with holomorphic Floer theory.

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Ronen Brilleslijper, Oliver Fabert. 2024-04-18. An approach to Hamiltonian Floer theory for maps from surfaces. https://arxiv.org/abs/2404.12249

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