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arXiv · 2609.01819

Asymptotic dimension of 3-dimensional CAT(0) manifolds

Panos Papasoglu·Eric Swenson
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Abstract

We prove that every $3$-manifold equipped with a proper metric admitting a convex geodesic bicombing has Assouad--Nagata dimension at most $3$. In particular, every proper CAT$(0)$ $3$-manifold has Assouad--Nagata dimension at most $3$. As a corollary one obtains that the isoperimetric gap theorem of Lang-Stadler-Urech (\cite{LSU}) and Peteranderl\cite{Pet}, generalizes from 3-dimensional Hadamard manifolds to 3-dimensional CAT(0) manifolds.

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Panos Papasoglu, Eric Swenson. 2026-09-01. Asymptotic dimension of 3-dimensional CAT(0) manifolds. https://arxiv.org/abs/2609.01819

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