Homotopy groups of K-contact toric manifold

TL;DR

This paper calculates the first and second homotopy groups of certain contact toric manifolds using the properties of their moment maps, providing new insights into their topological structure.

Contribution

It introduces a method to determine homotopy groups of contact toric manifolds based on the images of their moment maps, a novel approach in this area.

Findings

Explicit formulas for the first and second homotopy groups

Connection between homotopy groups and moment map images

Enhanced understanding of contact toric manifold topology

Abstract

We compute the first and second homotopy groups of a class of contact toric manifolds in terms of the images of the associated moment map.