Equivariant classification of bm-symplectic surfaces
Inspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of bm-Poiss...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:2117/121250 |
| Acceso en línea: | https://hdl.handle.net/2117/121250 https://dx.doi.org/10.1134/S1560354718040019 |
| Access Level: | acceso abierto |
| Palabra clave: | Topological manifolds Poisson distribution Geometry, Differencial Moser path method singularities b-symplectic manifolds group actions Varietats topològiques Geometria diferencial Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Varietats topològiques Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial |
| Sumario: | Inspired by Arnold’s classification of local Poisson structures [1] in the plane using the hierarchy of singularities of smooth functions, we consider the problem of global classification of Poisson structures on surfaces. Among the wide class of Poisson structures, we consider the class of bm-Poisson structures which can be also visualized using differential forms with singularities as bm-symplectic structures. In this paper we extend the classification scheme in [24] for bm-symplectic surfaces to the equivariant setting. When the compact group is the group of deck-transformations of an orientable covering, this yields the classification of these objects for nonorientable surfaces. The paper also includes recipes to construct bm-symplectic structures on surfaces. The feasibility of such constructions depends on orientability and on the colorability of an associated graph. The desingularization technique in [10] is revisited for surfaces and the compatibility with this classification scheme is analyzed in detail. |
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