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Topological rigidity of quasitoric manifolds

Vassilis Metaftsis, Stratos Prassidis

Abstract


Quasitoric manifolds are manifolds that admit an action of the torus that is locally the same as the standard action of $T^n$ on $\mathbb{C}^n$. It is known that the quotients of such actions are nice manifolds with corners. We prove that a class of locally standard manifolds, that contains the quasitoric manifolds, is equivariantly rigid, i.e., that any manifold that is $T^n$-homotopy equivalent to a quasitoric manifold is $T^n$-homeomorphic to it.


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DOI: http://dx.doi.org/10.7146/math.scand.a-97303

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