K-théorie équivariante et groupoïdes

Abstract : The etale groupoid are the central subject of this thesis. We first study the proper action of a discrete group on a locally compact and Hausdorff space, which gives an example of proper etale groupoid and we find some conditions for which the group of equivariant K-theory defined by phillips is completely described by equivariant complex bundles of finite dimension. In the second part of the thesis, we consider locally compact, sigma-compact and Hausdorff etale groupoid and we give a definition of amenability at infinity of such groupoid. We study in some cases the relation between the exactness of the reduced C*-algebra of the groupoid and the amenability at infinity. In the last part of the thesis, we consider K oriented immersion between etales groupoids and we associate a morphism between group of K-theory of the reduced C* algebras of this etales groupoids. We study the functoriality of such morphism. This part contains a proof of a conjecture of Hilsum and Skandalis
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Ivan Lassagne. K-théorie équivariante et groupoïdes. Mathématiques générales [math.GM]. Université de Lorraine, 2013. Français. ⟨NNT : 2013LORR0359⟩. ⟨tel-01751827⟩

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