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Coisotropic Submanifolds in b-symplectic Geometry

Part of: Symplectic geometry, contact geometry

Published online by Cambridge University Press:  24 February 2020

Stephane Geudens  and
Marco Zambon
Stephane Geudens
Affiliation:
KU Leuven, Department of Mathematics, Celestijnenlaan 200B box 2400, BE-3001Leuven, Belgium e-mail: stephane.geudens@kuleuven.be
Marco Zambon*
Affiliation:
KU Leuven, Department of Mathematics, Celestijnenlaan 200B box 2400, BE-3001Leuven, Belgium e-mail: stephane.geudens@kuleuven.be
*
e-mail: marco.zambon@kuleuven.be
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Abstract

We study coisotropic submanifolds of b-symplectic manifolds. We prove that b-coisotropic submanifolds (those transverse to the degeneracy locus) determine the b-symplectic structure in a neighborhood, and provide a normal form theorem. This extends Gotay’s theorem in symplectic geometry. Further, we introduce strong b-coisotropic submanifolds and show that their coisotropic quotient, which locally is always smooth, inherits a reduced b-symplectic structure.

Keywords

Poisson manifoldcoisotropic submanifold

MSC classification

Primary: 53D17: Poisson manifolds; Poisson groupoids and algebroids
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 3 , June 2021 , pp. 737 - 768
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Copyright
© Canadian Mathematical Society 2020

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