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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, the isoperimetric results of Lang--Stadler--Urech \cite{LSU} and Peteranderl \cite{Pet}, previously applicable to $3$-dimensional Hadamard manifolds, also apply to proper CAT(0) $3$-manifolds of asymptotic rank at most $2$.

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Cite

BibTeXRIS
BibTeX
@misc{papasoglu2026asymptotic,
  title = {{Asymptotic dimension of 3-dimensional CAT(0) manifolds}},
  author = {Panos Papasoglu and Eric Swenson},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01819},
  eprint = {2609.01819},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01819},
}
RIS
TY  - UNPB
TI  - Asymptotic dimension of 3-dimensional CAT(0) manifolds
AU  - Panos Papasoglu
AU  - Eric Swenson
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.01819
UR  - https://arxiv.org/abs/2609.01819
AB  - 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, the isoperimetric results of Lang--Stadler--Urech \cite{LSU} and Peteranderl \cite{Pet}, previously applicable to $3$-dimensional Hadamard manifolds, also apply to proper CAT(0) $3$-manifolds of asymptotic rank at most $2$.
ER  -