Rigidity of Hamiltonian actions on Poisson manifolds
This paper is about the rigidity of compact group actions in the Poisson context. The main result is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This Nash-Moser normal form has other applications to...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2011 |
| 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:2117/12645 |
| Acceso en línea: | https://hdl.handle.net/2117/12645 |
| Access Level: | acceso abierto |
| Palabra clave: | Geometry, Differencial Geometria diferencial Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial |
| Sumario: | This paper is about the rigidity of compact group actions in the Poisson context. The main result is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This Nash-Moser normal form has other applications to stability results that we will explore in a future paper. We also review some classical rigidity results for differentiable actions of compact Lie groups and export it to the case of symplectic actions of compact Lie groups on symplectic manifolds. |
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