Coisotropic submanifolds in $b$-symplectic geometry

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.

arXiv commentMinor stylistic modifications. Version to be published

References in corpus (5)

• Symplectic and Poisson geometry on b-manifolds
• Toric actions on b-symplectic manifolds
• Examples and counter-examples of log-symplectic manifolds
• Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures
• Fibrations and log-symplectic structures

Cited by in corpus (1)

• Reduction theory for singular symplectic manifolds and singular forms on moduli spaces