Whitney stratifications are conically smooth

• Guglielmo Nocera ^[2] ; Marco Volpe ^[1]
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  2. [2] Université Sorbonne Paris Nord, Francia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 5, 2023
• Idioma: inglés
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• Resumen

  • The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is a very well behaved analogue of a differential structure in the context of stratified topological spaces, satisfying good properties such as the existence of resolutions of singularities and handlebody decompositions. In this paper we prove Ayala, Francis and Tanaka’s conjecture that any Whitney stratified space admits a canonical conically smooth structure. We thus establish a connection between the theory of conically smooth spaces and the classical examples of stratified spaces from differential topology.