# Equivariant cobordism of torus orbifolds

## TL;DR

This paper studies the equivariant cobordism classes of torus orbifolds, showing they are related to orbifold complex projective spaces, and introduces a construction method for such orbifolds using toric topology.

## Contribution

It provides a new construction of smooth orbifolds with torus actions and establishes their cobordism relations to orbifold complex projective spaces.

## Key findings

- Any orientable locally standard torus orbifold is equivariantly cobordant to orbifold complex projective spaces.
- The paper introduces a toric topological construction method for orbifolds with boundary.
- Includes results on equivariant cobordism when orbifolds are torus manifolds.

## Abstract

Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result, we show that any orientable locally standard torus orbifold is equivariantly cobordant to some copies of orbifold complex projective spaces. We also discuss some further equivariant cobordism results including the cases when torus orbifolds are actually torus manifolds.