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Indices analytiques à support compact pour des groupoïdes de Lie

Abstract : For any Lie groupoid, we construct an analytic index morphism taking values in a modified K-theory group which involves the convolution algebra of compactly supported smooth functions over the groupoid. The construction is performed by using a suitable deformation algebra of smooth functions over the tangent groupoid, constructed in this work. This allows in particular to prove a more primitive version of the Connes-Skandalis Longitudinal index Theorem for foliations, that is, an index theorem taking values in a group that can still paired with Cyclic cocycles. As another application, let D be a G-PDO elliptic operator with associated index ind(D)€ K_0(A) (with A the convolution algebra), we have that the pairing of ind(D) with a bounded continuous cyclic cocycle, only depends on the principal symbol class of D. The result is completely general for Etale groupoids.
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Contributor : Paulo Carrillo Rouse <>
Submitted on : Tuesday, April 8, 2008 - 3:06:41 PM
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  • HAL Id : tel-00271219, version 1


Paulo Carrillo Rouse. Indices analytiques à support compact pour des groupoïdes de Lie. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2007. Français. ⟨tel-00271219⟩



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