An approach to Hamiltonian Floer theory for maps from surfaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914760353644544 |
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| author | Brilleslijper, Ronen Fabert, Oliver |
| author_facet | Brilleslijper, Ronen Fabert, Oliver |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An approach to Hamiltonian Floer theory for maps from surfaces Brilleslijper, Ronen Fabert, Oliver Symplectic Geometry Mathematical Physics 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. |
| title | An approach to Hamiltonian Floer theory for maps from surfaces |
| topic | Symplectic Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2404.12249 |