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Explore a mathematical lecture that delves into the complex relationships between foliations on the plane R², pre-laminations on the circle S¹, and group actions. Learn about the compactification of countable families of pairwise transverse foliations on the plane R² into a disc D² with a circle at infinity, and understand how every leaf corresponds to a pair of points on the circle. Examine four key questions addressing realization and completion problems for both singular and nonsingular foliations, including the conditions under which sets of point pairs on a circle correspond to foliation endpoints and the uniqueness of group actions preserving these structures. Recorded during the thematic meeting "Foliations and Diffeomorphism Groups" at the Centre International de Rencontres Mathématiques in Marseille, France, this hour-long presentation offers access to enriched content through CIRM's Audiovisual Mathematics Library, complete with chapter markers, keywords, abstracts, and comprehensive mathematical classifications.
