2024/04/22 by Tadashi Fujioka, Fujioka, Tadashi
Engineering · #52B70 #53C20 #53C23 #57N16 #57N80 #57P99 #57Q99 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2404.14587
openalex publication_date 2024/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.