The geometry of e-manifolds
Motivated by the study of symplectic Lie algebroids, we focus on a type of algebroid (called an E-tangent bundle) which is particularly well suited to the study of singular differential forms and their cohomology. This setting generalizes b-symplectic manifolds, foliat ed manifolds, and a wide class...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| 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:2117/332421 |
| Acceso en línea: | https://hdl.handle.net/2117/332421 https://dx.doi.org/10.4171/rmi/1232 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Hamiltonian systems b-symplectic manifolds Foliations Lie algebroids Poisson manifolds Moser path method Normal forms Cohomology Sistemes dinàmics diferenciables Sistemes hamiltonians Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | Motivated by the study of symplectic Lie algebroids, we focus on a type of algebroid (called an E-tangent bundle) which is particularly well suited to the study of singular differential forms and their cohomology. This setting generalizes b-symplectic manifolds, foliat ed manifolds, and a wide class of Poisson manifolds. We generalize Moser’s theorem to this setting, and use it to construct symplec tomorphisms between singular symplectic forms. We give applications of this machinery (including the study of Poisson cohomology), and study specificexamples of a few of them in depth. |
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