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Coisotropic Submanifolds in b-symplectic Geometry

Published online by Cambridge University Press:  24 February 2020

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

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.

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Article
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© Canadian Mathematical Society 2020

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