Complex Cobordism of quasitoric orbifolds

TL;DR

This paper constructs orbifolds with quasitoric boundary, demonstrates their stable almost complex structures, and shows their complex cobordism relation to complex orbifold projective spaces, including computations in the cobordism ring.

Contribution

It introduces a method to relate quasitoric orbifolds to complex projective spaces via cobordism, expanding understanding of their topological classification.

Findings

Quasitoric orbifolds have stable almost complex structures.

Quasitoric orbifolds are complex cobordant to disjoint unions of complex orbifold projective spaces.

Provides explicit computations in the complex cobordism ring.

Abstract

We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some computations in the complex cobordism ring for manifolds are given.