Invariant stably complex structures on topological toric manifolds

TL;DR

This paper proves that invariant stably complex structures on topological toric manifolds are integrable and that such manifolds are essentially equivalent to toric manifolds under certain symmetries.

Contribution

It establishes the integrability of invariant stably complex structures and their isomorphism to toric manifolds, advancing understanding of topological toric manifolds.

Findings

Invariant stably complex structures are integrable.

Such manifolds are weakly equivariantly isomorphic to toric manifolds.

Provides a classification of topological toric manifolds with invariant structures.

Abstract

We show that any $(\C ^*)^n$-invariant stably complex structure on a topological toric manifold of dimension $2n$ is integrable. We also show that such a manifold is weakly $(\C ^*)^n$-equivariantly isomorphic to a toric manifold.