On Quasitoric Orbifolds

TL;DR

This paper explores the structures and invariants of quasitoric orbifolds, extending the understanding of their topological properties and relationships to smooth manifolds, with a focus on cohomology and complex structures.

Contribution

It provides new definitions, computes fundamental groups, homology, cohomology rings, and describes Chen-Ruan cohomology for quasitoric orbifolds, advancing their topological classification.

Findings

Determined orbifold fundamental group and rational homology groups.

Established conditions for quasitoric orbifolds to be quotients of smooth manifolds.

Described Chen-Ruan cohomology groups for almost complex quasitoric orbifolds.

Abstract

Quasitoric spaces were introduced by Davis and Januskiewicz in their 1991 Duke paper. There they extensively studied topological invariants of quasitoric manifolds. These manifolds are generalizations or topological counterparts of nonsingular projective toric varieties. In this article we study structures and invariants of quasitoric orbifolds. In particular, we discuss equivalent definitions and determine the orbifold fundamental group, rational homology groups and cohomology ring of a quasitoric orbifold. We determine whether any quasitoric orbifold can be the quotient of a smooth manifold by a finite group action or not. We prove existence of stable almost complex structure and describe the Chen-Ruan cohomology groups of an almost complex quasitoric orbifold.