Infinite Families of Equivariantly Formal Toric Orbifolds

TL;DR

This paper extends the simplicial wedge construction to toric orbifolds, producing infinite families with torsion-free, even-degree cohomology, and provides explicit descriptions of their cohomology rings.

Contribution

It introduces a method to generate infinite families of integrally equivariantly formal toric orbifolds from a given orbifold, expanding the understanding of their cohomological properties.

Findings

Infinite families of toric orbifolds with torsion-free, even-degree cohomology.

Explicit descriptions of cohomology rings related to original orbifolds.

Extension of simplicial wedge construction to orbifolds.

Abstract

The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and more generally, polyhedral products. In this paper we extend the analysis to include toric orbifolds. Our main results yield infinite families of toric orbifolds, derived from a given one, whose integral cohomology is free of torsion and is concentrated in even degrees, a property which might be termed \emph{integrally equivariantly formal}. In all cases, it is possible to give a description of the cohomology ring and to relate it to the cohomology of the original orbifold.