Alexandrov spaces are CS sets
Differential Geometry
2025-08-12 v3 Geometric Topology
Metric Geometry
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.
Cite
@article{arxiv.2404.14587,
title = {Alexandrov spaces are CS sets},
author = {Tadashi Fujioka},
journal= {arXiv preprint arXiv:2404.14587},
year = {2025}
}
Comments
revised incorrect terminology on PL structure in Theorem 1.4 and Lemma 5.1 and added Remarks 1.5 and 1.7