Equivariant cohomology of torus orbifolds

TL;DR

This paper computes the integral equivariant cohomology of certain torus orbifolds with specific topological properties, using GKM theory and focusing on half-dimensional torus actions.

Contribution

It provides a detailed calculation of equivariant cohomology for locally standard torus orbifolds, extending GKM methods to orbifold settings.

Findings

Explicit generators and relations for cohomology rings

Extension of GKM theory to orbifolds

Characterization of cohomology in cases with vanishing odd-degree cohomology

Abstract

We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin by studying GKM-orbifolds, which are more general, before specialising to half-dimensional torus actions.