A $b$-symplectic slice theorem

TL;DR

This paper establishes a slice theorem for Lie group actions on $b$-symplectic manifolds, advancing the understanding of symplectic structures in manifolds with boundary.

Contribution

It introduces a slice theorem specifically tailored for $b$-symplectic manifolds, filling a gap in the geometric theory of these structures.

Findings

Proves a slice theorem for $b$-symplectic manifolds

Provides tools for analyzing symmetries in $b$-symplectic geometry

Enhances understanding of boundary behavior in symplectic manifolds

Abstract

In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of $b$-symplectic manifolds started in [12], we prove a slice theorem for Lie group actions on $b$-symplectic manifolds.