The Arnold conjecture for singular symplectic manifolds
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of bm-symplectic manifolds. More precisely, we prove a lower bound on the number 1-periodic Hamiltonian orbits for b2m-symplectic manifolds depending only on the topo...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/386255 |
| Acceso en línea: | https://hdl.handle.net/2117/386255 https://dx.doi.org/10.48550/arXiv.2212.01344 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of bm-symplectic manifolds. More precisely, we prove a lower bound on the number 1-periodic Hamiltonian orbits for b2m-symplectic manifolds depending only on the topology of the manifold. Moreover, for bm-symplectic surfaces, we improve the lower bound depending on the topology of the pair (M, Z). We then venture into the study of Floer homology to this singular realm and we conclude with a list of open questions. |
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