Equivariant K-theory of toric orbifolds

TL;DR

This paper studies the equivariant cohomology of a class of toric orbifolds called retractable, extending known results from weighted projective spaces by establishing conditions for invariant cell structures.

Contribution

It introduces sufficient combinatorial conditions for the existence of invariant cell structures on toric orbifolds and analyzes their equivariant cohomology.

Findings

Extended results on equivariant cohomology to retractable toric orbifolds.

Provided combinatorial criteria for invariant cell structures.

Generalized previous work on divisive weighted projective spaces.

Abstract

Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an invariant cell structure on it and call such a toric orbifold retractable. In this paper, our main goal is to study equivariant cohomology theories of retractable toric orbifolds. Our results extend the corresponding results on divisive weighted projective spaces.