Convexity of the moment map image for torus actions on $b^m$-symplectic manifolds

TL;DR

This paper proves a convexity theorem for the moment map image in the context of Hamiltonian torus actions on $b^m$-symplectic manifolds, extending classical convexity results to this broader setting.

Contribution

It introduces a convexity theorem for the moment map image specific to $b^m$-symplectic manifolds, a novel class of geometric structures.

Findings

Established convexity of the moment map image for $b^m$-symplectic manifolds.

Extended classical convexity theorems to the $b^m$-symplectic setting.

Provided new insights into Hamiltonian torus actions on singular symplectic structures.

Abstract

We prove a convexity theorem for the image of the moment map of a Hamiltonian torus action on a $b^m$-symplectic manifold.