Théorie de l'indice et géométrie basique d'un feuilletage riemannien

Abstract : In this paper we study the basic geometry of a Riemannian foliation. First we return on A. El Kacimi's point of view on transversally elliptic basic differential operator. We study the particular case of fibration and foliation defined by suspension. We study some examples of computation of basic index and study invariance property for the basic signature. After, we study a Riemannian foliation with the action of a compact Lie group. We prove then that a basic differential operator which is transversally elliptic to the foliation and to the group action has a distributional basic index. We study the particular case of free action and prove the multiplicativity and excision property. We end by study the link with El Kacimi's point of view
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Alexandre Rey Alcantara. Théorie de l'indice et géométrie basique d'un feuilletage riemannien. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2011. Français. ⟨NNT : 2011METZ022S⟩. ⟨tel-01749059⟩

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