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Automorphism groups of rigid geometries on leaf spaces of foliations

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 نشر من قبل Nina Zhukova
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Nina I. Zhukova




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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 $mathfrak F_0$ of leaf manifolds containing the orbifold category as a full subcategory. Objects of $mathfrak F_0$ may have non-Hausdorff topology unlike the orbifolds. The topology of some objects of $mathfrak F_0$ does not satisfy the separation axiom $T_0$. It is shown that for every ${mathcal N}in Ob(mathfrak F_0)$ a rigid geometry $zeta$ 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 $Aut(zeta)$ of the rigid geometry $zeta$ on $mathcal{N}$.



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