Torus Actions on Alexandrov 4-Spaces

Abstract

We obtain an equivariant classification for orientable, closed, four-dimensional Alexandrov spaces admitting an isometric torus action. This generalizes the equivariant classification of Orlik and Raymond of closed four-dimensional manifolds with torus actions. Moreover, we show that such Alexandrov spaces are equivariantly homeomorphic to 4-dimensional Riemannian orbifolds with isometric {T^{2}}-actions. We also obtain a partial homeomorphism classification.