Orientation and symmetries of Alexandrov spaces with applications in   positive curvature
  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. 
John Harvey and Catherine Searle
math.DG