Klein Stratification of Orbit Spaces: Examples

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GÜRER S.

International Electronic Journal of Geometry, vol.16, no.2, pp.665-671, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.36890/iejg.1364214
  • Journal Name: International Electronic Journal of Geometry
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.665-671
  • Keywords: diffeology, Orbit Spaces, stratifications
  • Galatasaray University Affiliated: Yes

Abstract

We consider the Klein stratification of orbit spaces M/G, defined by the action of local diffeomorphisms. We show that the Klein strata on M/G, where the singular orbits are isolated points and the stabilizer group acts transitively on the unit sphere, are precisely the union of the points where M/G has the same dimension.