Topological rigidity of quasitoric manifolds

2013/01/03 by Metaftsis, V., Prassidis, S.
#57R19 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.0469

Abstract

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.

Related

• Topological rigidity of quoric manifolds
• Strong cohomological rigidity of quasitoric manifolds over the 3-cube
• Homotopy rigidity for quasitoric manifolds over a product of d-simplices
• Hirzebruch genera of manifolds with torus action
• Some examples in toric geometry