PreprintarXiv licencearXiv
Dimension of CAT spaces
Abstract
We prove that the covering dimension of a metric space with curvature bounded above equals its geometric dimension, without a separability assumption. This resolves a conjecture formulated by Kleiner that goes back to Gromov's work.
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BibTeX
@misc{lytchak2026dimension,
title = {{Dimension of CAT spaces}},
author = {Alexander Lytchak},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07567},
eprint = {2609.07567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07567},
}
RIS
TY - UNPB
TI - Dimension of CAT spaces
AU - Alexander Lytchak
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07567
UR - https://arxiv.org/abs/2609.07567
AB - We prove that the covering dimension of a metric space with curvature bounded above equals its geometric dimension, without a separability assumption. This resolves a conjecture formulated by Kleiner that goes back to Gromov's work.
ER -