Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry 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. As a corollary, we also classify positively curved Riemannian orbifolds of dimension 4 with an isometric circle action.

arXiv comment42 pages, 7 figures. In v2 there is some improvement to the exposition and a closer focus on the application to orbifolds. To be published in Documenta Mathematica