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Structures bifeuilletées en codimension 1

Abstract : This thesis has for goal the study of pairs of complex foliations. More precisely, we will discuss pairs of codimension 1 complex foliations in two different situations: on one side we will have germs of foliations in the neighborhood of the origin of C (the "local" situation), on the other side the foliations will be defined on a dimension 2 neighborhood of a complex curve (the "semi-global" situation). The semi-global problem has for goal the understanding of neighborhoods of curves in complex surfaces; we will thus obtain classification results for the particular neighborhoods that are equipped with two foliations. In order to obtain this classification, we will first need to study pairs of foliations from a local point of view. Hence, we will present some results about classification of pairs of germs of foliations in a neighborhood of a point in C2. Some of the local results give by generalisation classification results for pairs of germs of functions in any dimension; in particular, we will present a detailed study of pairs of germs of Morse functions in any dimension.
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Submitted on : Wednesday, January 31, 2018 - 3:44:07 PM
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Olivier Thom. Structures bifeuilletées en codimension 1. Topologie géométrique [math.GT]. Université Rennes 1, 2017. Français. ⟨NNT : 2017REN1S064⟩. ⟨tel-01697856⟩



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