CAT(0) spaces of higher rank

Stephan Stadler

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arXiv · 2202.02302

CAT(0) spaces of higher rank

Stephan Stadler

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Abstract

Ballmann's Rank Rigidity Conjecture predicts that a CAT(0) space of higher rank with a geometric group action is rigid -- isometric to a Riemannian symmetric space, a Euclidean building, or splits as a direct product. We confirm this conjecture in rank 2. For CAT(0) spaces of higher rank $n\geq 2$ we prove rigidity if the space contains a periodic $n$-flat and every complete geodesic lies in some $n$-flat. This does not require a geometric group action.

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Stephan Stadler. 2022-02-04. CAT(0) spaces of higher rank. https://arxiv.org/abs/2202.02302

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