Toric contact geometry in arbitrary codimension

TL;DR

This paper introduces a new framework for toric contact manifolds in any codimension, describing them via labelled polytopes in Grassmannians, extending the classical Delzant polytope concept from symplectic geometry.

Contribution

It generalizes the notion of toric contact manifolds to arbitrary codimension and provides a polytope-based classification analogous to Delzant polytopes.

Findings

Defined toric contact manifolds in arbitrary codimension

Developed a labelled polytope description in Grassmannians

Extended classical symplectic results to contact geometry

Abstract

We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.