CAT(0) spaces of higher rank II

Stephan Stadler

CAT(0) spaces of higher rank II

Metric Geometry 2022-12-15 v1 Differential Geometry Dynamical Systems Geometric Topology

Authors: Stephan Stadler

Abstract

This belongs to a series of papers motivated by Ballmann's Higher Rank Rigidity Conjecture. We prove the following. Let $X$ be a CAT(0) space with a geometric group action. Suppose that every geodesic in $X$ lies in an $n$ -flat, $n\geq 2$ . If $X$ contains a periodic $n$ -flat which does not bound a flat $(n+1)$ -half-space, then $X$ is a Riemannian symmetric space, a Euclidean building or non-trivially splits as a metric product. This generalizes the Higher Rank Rigidity Theorem for Hadamard manifolds with geometric group actions.

Keywords

cat(0) space higher rank rigidity geometric group action n-flat symmetric space euclidean building metric product

Cite

@article{arxiv.2212.07092,
  title  = {CAT(0) spaces of higher rank II},
  author = {Stephan Stadler},
  journal= {arXiv preprint arXiv:2212.07092},
  year   = {2022}
}

CAT(0) spaces of higher rank II

Abstract

Keywords

Cite

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