Topological median algebra structures on ER homology manifolds I: local cubulation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915666646269952 |
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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 |