Symplectic toric stratified spaces with isolated singularities

TL;DR

This paper extends the classification of symplectic toric stratified spaces with isolated singularities and contact toric manifolds beyond the compact connected case, providing a broader understanding of their structure.

Contribution

It generalizes existing classifications to include non-compact and singular cases, linking symplectic and contact toric geometries.

Findings

Classification of symplectic toric cones

Extension of contact toric manifold classification

Broader classification including isolated singularities

Abstract

The goal of this paper is to classify symplectic toric stratified spaces with isolated singularities. This extends a result of Burns, Guillemin, and Lerman which carries out this classification in the compact connected case. In making this classification, it is necessary to classify symplectic toric cones. Via a well-known equivalence between symplectic toric cones and contact toric manifolds, this allows for the classification of contact toric manifolds as well, extending Lerman's classification of compact connected contact toric manifolds.