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arXiv · 2212.07092

CAT(0) spaces of higher rank II

Stephan Stadler
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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.

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Stephan Stadler. 2022-12-14. CAT(0) spaces of higher rank II. https://arxiv.org/abs/2212.07092

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