On the diffeology of orbit spaces

GÜRER S., Iglesias-Zemmour P.

Differential Geometry and its Application, cilt.103, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 103
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.difgeo.2026.102391
  • Dergi Adı: Differential Geometry and its Application
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Diffeology, Isostabilizer decomposition, Klein stratification, Orbit space, Orthofold
  • Galatasaray Üniversitesi Adresli: Evet

Özet

We investigate the correspondence between the geometry of a smooth action of a compact Lie group on a manifold M and the intrinsic smooth structure of the orbit space M/G[jls-end-space/]. The latter is captured by the Klein stratification, which partitions M/G into orbits of local diffeomorphisms, classifying the space by its intrinsic singularity types. We show that this geometry maps coherently to the quotient through the isostabilizer decomposition of M, whose elements are the connected components of submanifolds where the stabilizer is constant. Our main result, the Correspondence Theorem, establishes that the canonical projection induces a surjective map from this decomposition to the Klein strata. As a corollary, we define the Inverse Klein Stratification on M by pullback, clarifying its relationship with the intrinsic geometry of the quotient.