Which singular tangent bundles are isomorphic?
Logarithmic and -tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these resolve singularities by reframing singular vector fields as well-behaved sections of these. This approach has gained significant attention in symplectic...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:dnet:upcommonspor::b8e844f5483333d76a1e2bb616ea0ff9 |
| Acesso em linha: | https://hdl.handle.net/2117/461225 https://dx.doi.org/10.1112/jlms.70550 |
| Access Level: | acceso abierto |
| Palavra-chave: | Algebraic topology Fiber spaces in algebraic topology Differential geometry Poisson manifolds Poisson groupoids and algebroids Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica |
| Resumo: | Logarithmic and -tangent bundles provide a versatile framework for addressing singularities in geometry. Introduced by Deligne and Melrose, these resolve singularities by reframing singular vector fields as well-behaved sections of these. This approach has gained significant attention in symplectic geometry, particularly through its applications to the study of Poisson manifolds that are symplectic away from a hypersurface (-symplectic forms). In this paper, we investigate the conditions under which these singular tangent bundles are isomorphic to the tangent bundle or other singular bundles, analyzing in detail the low-dimensional case and the case of spheres. We also examine the existence of geometric structures in light of these conditions. Furthermore, we establish a Poincaré–Hopf theorem for the -tangent bundle, offering new insights into the interplay between singular structures and topological invariants. |
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