Invariant stably complex structures on topological toric manifolds

Abstract

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