Topological rigidity of quasitoric manifolds

Original · EN

Quasitoric manifolds are manifolds that admit an action of the torus that is locally as the standard action of Tⁿ on Cⁿ. It is known that the quotients of such actions are nice manifolds with corners. We prove that such manifolds are equivariantly rigid i.e., that any other manifold that is Tⁿ-homotopy equivalent to a quasitoric manifold, is Tⁿ-homeomorphic to it.