Isometry groups of Alexandrov spaces

Abstract

For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also determine a gap in the possible dimensions of the isometry groups and show that if the Alexandrov space is symmetric, then it is isometric to a Riemannian manifold.

Final version of the paper, accepted for publication at the Bulletin of the London Mathematical Society. It improves the proof of the Principal Orbit Theorem in section 2, and completes the missing cases in section 6 on dimension gaps

Cited by in corpus (10)

• On quotients of spaces with Ricci curvature bounded below
• Orientation and symmetries of Alexandrov spaces with applications in positive curvature
• Structure of Submetries
• Closed three-dimensional Alexandrov spaces with isometric circle actions
• Three-dimensional Alexandrov spaces with local isometric circle actions
• Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces
• Isospectral Alexandrov Spaces
• Lifting isometries of orbit spaces
• Torus actions on Alexandrov 4-spaces
• On geodesic extendibility and the space of compact balls of length spaces