Toric actions on b-symplectic manifolds

TL;DR

This paper classifies b-symplectic manifolds with Hamiltonian torus actions using a Delzant-type theorem, extending symplectic geometry concepts to manifolds with boundary-like singularities.

Contribution

It introduces a classification theorem for b-symplectic manifolds under torus actions, generalizing Delzant's theorem to this singular setting.

Findings

Classification of b-symplectic manifolds via polytopes

Extension of Delzant theorem to b-symplectic case

Introduction of decorated polytopes in the dual Lie algebra

Abstract

We study Hamiltonian actions on $b$-symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem that classifies these manifolds using polytopes that reside in a certain enlarged and decorated version of the dual of the Lie algebra of the torus.