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Article

Сильная трансверсальная эквивалентность полных трансверсально аффинных слоений

Complete transversely affine foliations are studied. The strong transversal equivalence of
complete affine foliations is investigated, which is a more refined notion than the transverse
equivalence of foliations in the sense of Molino. A global holonomy group of a complete
affine foliations is determined and it is proved that this group is the complete invariant
of the foliation relatively strong transversal equivalence. A representative of an arbitrary
equivalence class is constructed on its complete invariant. This representative is a twodimensional
complete transversely affine foliation (𝑀, 𝐹), where 𝑀 is the space of Elenberg-
McLane of the type 𝐾(𝜋, 1).