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Whitney stratifications are conically smooth.

Authors :
Nocera, Guglielmo
Volpe, Marco
Source :
Selecta Mathematica, New Series; Nov2023, Vol. 29 Issue 5, p1-20, 20p
Publication Year :
2023

Abstract

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10221824
Volume :
29
Issue :
5
Database :
Complementary Index
Journal :
Selecta Mathematica, New Series
Publication Type :
Academic Journal
Accession number :
172971757
Full Text :
https://doi.org/10.1007/s00029-023-00877-4