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Main Authors: Bestvina, Mladen, Bromberg, Kenneth, Sageev, Michah
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.09875
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author Bestvina, Mladen
Bromberg, Kenneth
Sageev, Michah
author_facet Bestvina, Mladen
Bromberg, Kenneth
Sageev, Michah
contents We study topological median algebra structures on Euclidean spaces and, more generally, ER homology manifolds. We show that all such median structures have a local CAT(0) cubulation structure. We also show that topological median algebra structures are completely metrizable as median metric spaces if and only if intervals are compact. We give examples of both metrizable and non-metrizable such structures, as well as provide a construction for producing many non-locally cubulated topological median algebra structures on the unit ball in Euclidean space.
format Preprint
id arxiv_https___arxiv_org_abs_2512_09875
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Topological median algebra structures on ER homology manifolds I: local cubulation
Bestvina, Mladen
Bromberg, Kenneth
Sageev, Michah
Geometric Topology
20F65, 57P05
We study topological median algebra structures on Euclidean spaces and, more generally, ER homology manifolds. We show that all such median structures have a local CAT(0) cubulation structure. We also show that topological median algebra structures are completely metrizable as median metric spaces if and only if intervals are compact. We give examples of both metrizable and non-metrizable such structures, as well as provide a construction for producing many non-locally cubulated topological median algebra structures on the unit ball in Euclidean space.
title Topological median algebra structures on ER homology manifolds I: local cubulation
topic Geometric Topology
20F65, 57P05
url https://arxiv.org/abs/2512.09875