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Regular version of the site

Working paper

Rigid geometries and their automorphism groups on leaf spaces of foliations

math. arxive. Cornell University, 2018. No. 1704.04220.
We introduce a category of rigid geometries on singular spaces which are leaf spaces of foliations and are considered as leaf manifold. We separate out a special category F_0 of leaf manifolds containing the orbifold category as a complete subcategory. Objects of F_0 may be non-Hausdorff  unlike orbifolds. The topology of some objects of F_0 do not satisfies the separation axiom T_0. It is shown that for every object N  of F_0 a rigid geometry  on N admits a desingularization. Moreover, for every such N we prove the existence and the uniqueness of a finite-dimensional Lie group structure on the group of all automorphisms of the rigid geometry on N.