dc.contributor.author |
Cardona, Robert |
dc.contributor.author |
Miranda, Eva |
dc.date.accessioned |
2020-11-27T08:35:25Z |
dc.date.available |
2020-11-27T08:35:25Z |
dc.date.issued |
2019-04-01 |
dc.identifier.uri |
http://hdl.handle.net/2072/378030 |
dc.format.extent |
197 p. |
dc.language.iso |
eng |
dc.relation.ispartof |
Regular and Chaotic Dynamics (Springer) |
dc.rights |
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons:http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.source |
RECERCAT (Dipòsit de la Recerca de Catalunya) |
dc.subject.other |
Matemàtiques |
dc.title |
On the Volume Elements of a Manifold with Transverse Zeroes |
dc.type |
info:eu-repo/semantics/article |
dc.type |
info:eu-repo/semantics/draft |
dc.subject.udc |
51 - Matemàtiques |
dc.embargo.terms |
cap |
dc.identifier.doi |
10.1134/s1560354719020047 |
dc.rights.accessLevel |
info:eu-repo/semantics/openAccess |
dc.description.abstract |
Moser proved in 1965 in his seminal paper [15] that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in the top cohomology group of a manifold coincide. In particular, this yields a classification of compact symplectic surfaces in terms of De Rham cohomology. In this paper we generalize these results for volume forms admitting transversal zeroes. In this case there is also a cohomology capturing the classification: the relative cohomology with respect to the critical hypersurface. We compare this classification scheme with the classification of Poisson structures on surfaces which are symplectic away from a hypersurface where they fulfill a transversality assumption (b-Poisson structures). We do this using the desingularization technique introduced in [10] and extend it to bm-Nambu structures. |