Orientation and symmetries of Alexandrov spaces with applications in positive curvature

Click on the DOI link to access the article (may not be free).We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact Lie groups. These tools are applied to the classification of compact, positively curved Alexandrov spaces with maximal symmetry rank.US National Science Foundation. The second-named author was supported in part by CONACYT Project #SEP-106923