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On the classification of complete affine foliations respectively the strong transversal equivalence

TitleOn the classification of complete affine foliations respectively the strong transversal equivalence
AuthorsN. I. Zhukova1
1National Research University Higher School of Economics
AnnotationComplete affine foliations (i.e., foliations admitting the affine geometry as the transversal structure) are investigated. The strong transversal equivalence of complete affine foliations is considered, which is a more refined notion than the transverse equivalence of foliations in the sense of Molino. The classification of complete affine foliations with respect to the strong transversal equivalence is reduced to the classification up to conjugacy of countable subgroups of the affine group $Aff(A^q)$. It is shown that each equivalence class contains a two-dimensional suspended foliation on the manifold, which is an Elenberg--MacLane space of type $K(\pi,1)$.
Keywordsfoliation, Serre fibration, strong transversal equivalence of foliations, transversely affine foliation, global holonomy group
CitationZhukova N. I. ''On the classification of complete affine foliations respectively the strong transversal equivalence'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 403-407. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper57.pdf. - Date of access: 17.09.2019.