Automorphism groups of rigid geometries on leaf spaces of foliations

2017/04/13 by Н. И. Жукова, Zhukova, Nina I.
Mathematics · #18F15 #53C12 #57R30 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1704.04220

openalex publication_date 2017/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifolds. We single out a special category \mathfrak F₀ of leaf manifolds containing the orbifold category as a full subcategory. Objects of \mathfrak F₀ may have non-Hausdorff topology unlike the orbifolds. The topology of some objects of \mathfrak F₀ does not satisfy the separation axiom T₀. It is shown that for every \mathcal N∈ Ob(\mathfrak F₀) a rigid geometry ζ on \mathcal N admits a desingularization. Moreover, for every such \mathcal N we prove the existence and the uniqueness of a finite dimensional Lie group structure on the automorphism group Aut(ζ) of the rigid geometry ζ on N.

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