Positively curved Riemannian orbifolds and Alexandrov apaces with circle aymmetry in Dimension 4

Abstract

We classify positively curved Alexandrov spaces of dimension 4 with an isometric circle action up to equivariant homeomorphism, subject to a certain additional condition on the infinitesimal geometry near fixed points which we conjecture is always satisfied. \par As a corollary, we also classify positively curved Riemannian orbifolds of dimension 4 with an isometric circle action.