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Rank Rigidity for CAT(0) spaces without 3-flats

Metric Geometry 2022-12-15 v1 Differential Geometry Group Theory Geometric Topology

Abstract

If a group Γ\Gamma acts geometrically on a CAT(0) space XX without 3-flats, then either XX contains a Γ\Gamma-periodic geodesic which does not bound a flat half-plane, or else XX is a rank 2 Riemannian symmetric space, a 2-dimensional Euclidean building or non-trivially splits as a metric product. Consequently all such groups satisfy a strong form of the Tits Alternative.

Keywords

Cite

@article{arxiv.2212.07100,
  title  = {Rank Rigidity for CAT(0) spaces without 3-flats},
  author = {Stephan Stadler},
  journal= {arXiv preprint arXiv:2212.07100},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2202.02302

R2 v1 2026-06-28T07:33:58.427Z