Orbifolds as stratified diffeologies

GÜRER S., Iglesias-Zemmour P.

Differential Geometry and its Application, vol.86, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 86
  • Publication Date: 2023
  • Doi Number: 10.1016/j.difgeo.2022.101969
  • Journal Name: Differential Geometry and its Application
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Keywords: Orbifolds, Diffeology, Stratification
  • Galatasaray University Affiliated: Yes

Abstract

We discuss general properties of stratified spaces in diffeology. This leads to a formal framework for the theory of stratifications. In particular, we consider the Klein stratification of diffeological orbifolds, defined by the action of local diffeomorphisms. We show that it is a standard stratification in the sense that the partition of the space into orbits of local diffeomorphisms is locally finite (for orbifolds with locally finite atlases), it satisfies the frontier condition and the orbits are locally closed manifolds.