Torus actions on Alexandrov 4-spaces
Differential Geometry
2023-06-23 v2 Metric Geometry
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 -dimensional Riemannian orbifolds with isometric -actions. We also obtain a partial homeomorphism classification.
Cite
@article{arxiv.1902.09402,
title = {Torus actions on Alexandrov 4-spaces},
author = {Diego Corro and Jesús Núñez-Zimbrón and Masoumeh Zarei},
journal= {arXiv preprint arXiv:1902.09402},
year = {2023}
}
Comments
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