Torus orbifolds with two fixed points

TL;DR

This paper investigates torus orbifolds with exactly two fixed points, analyzing their equivariant topological properties and conditions for computing their integral equivariant cohomology via orbifold torus graphs.

Contribution

It characterizes the equivariant topological type of these orbifolds and extends methods for computing their cohomology using orbifold torus graphs.

Findings

Classification of torus orbifolds with two fixed points

Conditions for applying [DKS] results to compute cohomology

Explicit descriptions of equivariant cohomology rings

Abstract

The main objects of this paper are torus orbifolds that have exactly two fixed points. We study the equivariant topological type of these orbifolds and consider when we can use the results of the paper [DKS] (arXiv:1809.03678) to compute its integral equivariant cohomology, in terms of generators and relations, coming from the corresponding orbifold torus graph.