Topological rigidity of quasitoric manifolds

TL;DR

This paper proves that quasitoric manifolds are uniquely determined up to T^n-homeomorphism by their T^n-homotopy type, establishing a form of topological rigidity in these manifolds.

Contribution

It establishes the equivariant rigidity of quasitoric manifolds, showing T^n-homotopy equivalence implies T^n-homeomorphism, a new result in the field.

Findings

Quasitoric manifolds are T^n-equivariantly rigid.

Any T^n-homotopy equivalent manifold is T^n-homeomorphic.

The quotient spaces are manifolds with corners.

Abstract

Quasitoric manifolds are manifolds that admit an action of the torus that is locally as the standard action of T^n on C^n. 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 T^n-homotopy equivalent to a quasitoric manifold, is T^n-homeomorphic to it.