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Alexandrov spaces are CS sets

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arxiv 2404.14587 v3 pith:JIFWCIGL submitted 2024-04-22 math.DG math.GTmath.MG

Tadashi Fujioka This is my paper · ORCID
classification math.DGmath.GTmath.MG
keywords spacealexandrovdirectionseveryextremalstratificationcaseholds
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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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Cited by 1 Pith paper

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  1. Regularity of Resolutions and Limits of Manifolds with a Uniform Contractibility Function

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    If a compact ANR is a Gromov-Hausdorff limit of closed n-manifolds with bounded contractibility functions, then it is an open cell-like image of each sufficiently close approximating manifold, resolving Moore's conjec...

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