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...

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Detalles Bibliográficos
Autores: Miranda Galcerán, Eva|||0000-0001-9518-5279, Scott, Geoffrey
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
Descripción
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.