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Regular version of the site

Book chapter

Жесткие геометрии на пространстве слоев слоений и группы их автоморфизмов

С. 48-51.

We introduce a category of rigid geometries on smooth singular spaces of leaves of foliations.

A special category $\mathfrak F_0$ containing orbifolds is allocated. Unlike orbifolds, objects

of $\mathfrak F_0$ can have non-Hausdorff topology and can even not satisfy the separability axiom $T_0$. 

It is shown that the rigid geometry $(N,\zeta)$, where $N\in (\mathfrak F_0)$, allows a desingularization. For each such geometry $( N,\zeta)$ we prove the existence and uniqueness of the structure of a finite-dimensional Lie group in the group of all automorphisms $Aut (N},\zeta)$.

The applications to the orbifolds are considered.