The homotopy classification of four-dimensional toric orbifolds

Abstract

Let X be a 4-dimensional toric orbifold. If H 3 (X) has a non-trivial odd primary torsion, then we show that X is homotopy equivalent to the wedge of a Moore space and a CW-complex. As a corollary, given two 4-dimensional toric orbifolds having no 2-torsion in the cohomology, we prove that they have the same homotopy type if and only their integral cohomology rings are isomorphic.Question 1.1. Are two toric orbifolds homotopy equivalent if their integral cohomology rings are isomorphic as graded rings?This paper aims to answer this question for certain 4-dimensional toric orbifolds. We first study certain CW-complexes which model 4-dimensional toric orbifolds and investigate