Journal of Symplectic Geometry

Volume 18 (2020)

Number 5

Symplectic toric stratified spaces with isolated singularities

Pages: 1391 – 1473



Seth Wolbert (Department of Mathematics and Statistics, Minnesota State University, Mankato, Minn., U.S.A.)


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.

Received 8 November 2015

Accepted 1 December 2018

Published 29 October 2020