Orientation and symmetries of Alexandrov spaces with applications in positive curvature

Abstract

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.

34 pages. Simplified proofs throughout and a new proof of the Slice Theorem, correcting omissions in the previous version

References in corpus (1)

• A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry

Cited by in corpus (16)

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• Teichmüller theory and collapse of flat manifolds
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• Closed three-dimensional Alexandrov spaces with isometric circle actions
• Positively curved Killing foliations via deformations
• Alexandrov Spaces with Maximal Radius
• Three-dimensional Alexandrov spaces with local isometric circle actions
• Inradius collapsed manifolds
• Torus actions on Alexandrov 4-spaces
• Distributional category of manifolds
• Lifting isometries of orbit spaces
• Almost non-negatively curved 4-manifolds with torus symmetry
• Stability of Tori under Lower Sectional Curvature
• The Injectivity Radius of Souls of Alexandrov Spaces
• Leaf closures of Riemannian foliations: a survey on topological and geometric aspects of Killing foliations