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arXiv · 2404.14587

Alexandrov spaces are CS sets

Tadashi Fujioka
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Abstract

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.

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Tadashi Fujioka. 2024-04-22. Alexandrov spaces are CS sets. https://arxiv.org/abs/2404.14587

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