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dc.contributor.authorCardona Aguilar, Robert
dc.contributor.authorMiranda Galcerán, Eva
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2022-03-29T14:11:26Z
dc.date.available2022-09-23T00:27:26Z
dc.date.issued2021-09-22
dc.identifier.citationCardona, R.; Miranda, E. Integrable systems on singular symplectic manifolds: from local to global. "International mathematics research notices", 22 Setembre 2021,
dc.identifier.issn1073-7928
dc.identifier.urihttp://hdl.handle.net/2117/364971
dc.description.abstractIn this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes either to infinity or to zero transversally, yielding either a b-symplectic form or a folded symplectic form. The hypersurface where the form degenerates is called critical set. We give a new impulse to the investigation of the existence of action-angle coordinates for these structures initiated in [34] and [35] by proving an action-angle theorem for folded symplectic integrable systems. Contrary to expectations, the action-angle coordinate theorem for folded symplectic manifolds cannot be presented as a cotangent lift as done for symplectic and b-symplectic forms in [34]. Global constructions of integrable systems are provided and obstructions for the global existence of action-angle coordinates are investigated in both scenarios. The new topological obstructions found emanate from the topology of the critical set Z of the singular symplectic manifold. The existence of these obstructions in turn implies the existence of singularities for the integrable system on Z¿.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
dc.subject.lcshSymplectic geometry
dc.titleIntegrable systems on singular symplectic manifolds: from local to global
dc.typeArticle
dc.subject.lemacGeometria simplèctica
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.identifier.doi10.1093/imrn/rnab253
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
dc.relation.publisherversionhttps://academic.oup.com/imrn
dc.rights.accessOpen Access
local.identifier.drac32837780
dc.description.versionPreprint
local.citation.authorCardona, R.; Miranda, E.
local.citation.publicationNameInternational mathematics research notices


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