The fundamental groups of contact toric manifolds

TL;DR

This paper investigates the fundamental groups of contact toric manifolds, showing that those of Reeb type have finite cyclic fundamental groups and providing a method to determine their order from the moment map image.

Contribution

It establishes that contact toric manifolds of Reeb type have finite cyclic fundamental groups and offers a way to compute their order from the moment map image.

Findings

Fundamental group of Reeb type contact toric manifolds is finite cyclic.

Order of the fundamental group can be derived from the moment map image.

Most contact toric manifolds are of Reeb type.

Abstract

Let $M$ be a connected compact contact toric manifold. Most of such manifolds are of Reeb type. We show that if $M$ is of Reeb type, then $\pi_1(M)$ is finite cyclic, and we describe how to obtain the order of $\pi_1(M)$ from the moment map image.