# Presymplectic convexity and (ir)rational polytopes

## TL;DR

This paper generalizes convexity theorems and classification results from symplectic to presymplectic manifolds, introducing Morita equivalence and exploring the structure of associated polytopes, including non-rational cases.

## Contribution

It extends key symplectic convexity and classification theorems to presymplectic manifolds and introduces Morita equivalence for presymplectic toric manifolds and their polytopes.

## Key findings

- Extended convexity theorem to presymplectic manifolds
- Defined Morita equivalence for presymplectic toric manifolds
- Analyzed rational and non-rational polytopes in this context

## Abstract

In this paper, we extend the Atiyah--Guillemin--Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their corresponding framed momentum polytopes, which may be rational or non-rational. Toric orbifolds, quasifolds and non-commutative toric varieties may be viewed as the quotient of our presymplectic toric manifolds by the kernel isotropy foliation of the presymplectic form.