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.

30 pages, 6 figures, 2 tables. We added subsections 2.4 and 2.5 for convenience of the reader, and modified sections 3, 4, 5, 6, and 7, to improve the clarity of the proof of the main results