# Coisotropic submanifolds in $b$-symplectic geometry

## TL;DR

This paper extends symplectic geometry concepts to $b$-symplectic manifolds, proving normal form theorems for coisotropic submanifolds and introducing strong $b$-coisotropic submanifolds with reduced $b$-symplectic structures.

## Contribution

It establishes a normal form theorem for $b$-coisotropic submanifolds and introduces strong $b$-coisotropic submanifolds with inherited reduced structures.

## Key findings

- $b$-coisotropic submanifolds determine local $b$-symplectic structure.
- Normal form theorem extends Gotay's theorem to $b$-symplectic geometry.
- Reduced $b$-symplectic structures exist on quotients of strong $b$-coisotropic submanifolds.

## 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.