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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Coisotropic embeddings in Poisson manifolds


Authors: A. S. Cattaneo and M. Zambon
Journal: Trans. Amer. Math. Soc. 361 (2009), 3721-3746
MSC (2000): Primary 53D17; Secondary 53D55
Published electronically: February 10, 2009
MathSciNet review: 2491897
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Abstract: We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.


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A. S. Cattaneo
Affiliation: Institut für Mathematik, Universität Zürich-Irchel, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
Email: alberto.cattaneo@math.unizh.ch

M. Zambon
Affiliation: Departamentos de Matematica Pura, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Email: mzambon@fc.up.pt

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04667-4
PII: S 0002-9947(09)04667-4
Received by editor(s): May 25, 2007
Published electronically: February 10, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.