Títol:
|
On the Volume Elements of a Manifold with Transverse Zeroes
|
Autor/a:
|
Cardona, Robert; Miranda, Eva
|
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. |
Data de publicació:
|
01-04-2019 |
Matèries (CDU):
|
51 - Matemàtiques |
Matèries:
|
Matemàtiques |
Drets:
|
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/ |
Pàgines:
|
197 p. |
Tipus de document:
|
Article Article - Esborrany |
DOI:
|
10.1134/s1560354719020047
|
Publicat a:
|
Regular and Chaotic Dynamics (Springer)
|
Compartir:
|
|