Contact structures with singularities: From local to global
In this article we introduce and analyze in detail singular contact structures, with an emphasis on bm-contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth di...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/536853 |
| Acceso en línea: | http://hdl.handle.net/2072/536853 |
| Access Level: | acceso abierto |
| Palabra clave: | b-Symplectic manifolds Contact structures Jacobi manifolds Singularities |
| Sumario: | In this article we introduce and analyze in detail singular contact structures, with an emphasis on bm-contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential forms, called bm-contact forms, having an associated critical hypersurface Z. We provide several constructions, prove local normal forms, and study the induced structure on the critical hypersurface. The topology of manifolds endowed with such singular contact forms are related to smooth contact structures via desingularization. The problem of existence of bm-contact structures on a given manifold is also tackled in this paper. We prove that a connected component of a convex hypersurface of a contact manifold can be realized as a connected component of the critical set of a bm-contact structure. In particular, given an almost contact manifold M with a hypersurface Z, this yields the existence of a b2k-contact structure on M realizing Z as a critical set. As a consequence of the desingularization techniques in [21], we prove the existence of folded contact forms on any almost contact manifold. © 2023 The Author(s) |
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