Spherical contact toric manifolds

TL;DR

This paper investigates conditions under which regular contact toric manifolds of Reeb type are topologically equivalent to spheres, specifically focusing on the case where the manifold is compact and connected.

Contribution

It provides new criteria for identifying when a regular contact toric manifold of Reeb type is homeomorphic to a sphere.

Findings

Identifies conditions for $M$ to be homeomorphic to $S^{2n+1}$

Focuses on regular contact forms in contact toric manifolds

Advances understanding of the topology of contact toric manifolds

Abstract

Let $(M, \alpha)$ be a $2n+1$-dimensional connected compact contact toric manifold of Reeb type. Suppose the contact form $\alpha$ is regular, we find conditions under which $M$ is homeomorphic to $S^{2n+1}$.