Alexandrov spaces are CS sets
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916888618991616 |
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| author | Fujioka, Tadashi |
| author_facet | Fujioka, Tadashi |
| contents | We prove that the extremal stratification of an Alexandrov space introduced by Perelman-Petrunin is a CS stratification in the sense of Siebenmann. We also show that every space of directions of an Alexandrov space without proper extremal subsets is homeomorphic to a sphere. In the polyhedral case, the same holds for every iterated space of directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14587 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alexandrov spaces are CS sets Fujioka, Tadashi Differential Geometry Geometric Topology Metric Geometry 53C20, 53C23, 57N16, 57N80, 57P99, 57Q99, 52B70 We prove that the extremal stratification of an Alexandrov space introduced by Perelman-Petrunin is a CS stratification in the sense of Siebenmann. We also show that every space of directions of an Alexandrov space without proper extremal subsets is homeomorphic to a sphere. In the polyhedral case, the same holds for every iterated space of directions. |
| title | Alexandrov spaces are CS sets |
| topic | Differential Geometry Geometric Topology Metric Geometry 53C20, 53C23, 57N16, 57N80, 57P99, 57Q99, 52B70 |
| url | https://arxiv.org/abs/2404.14587 |