K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes

Lafforgue, Vincent

doi:10.1007/s002220200213

Cited by 197 publications

(316 citation statements)

References 30 publications

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“…Then 1 (G, A) is a dense subalgebra of the reduced crossed product A red G. The following lemma is proved in [36,Section 1. 7] Lemma 3.6.…”

Section: Matthey (M) Oyono-oyono (H) and Pitsch (W)mentioning

confidence: 90%

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Homotopy invariance of higher signatures and $3$-manifold groups

Matthey¹,

Oyono-Oyono²,

Pitsch³

2008

Bul. Soc. Math. France

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Abstract. -For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the "piecewise geometric" ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable 3-manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients holds. The non-oriented case is also discussed. Nous démontrons que pour des variétés fermées et orientées les signatures qui proviennent des groupes fondamentaux d'une large classe de variétés orientables de dimension 3 sont des invariants homotopiques. Cette classe, que nous décrivons soigneusement, contient en particulier les variétés géométriques par morceaux au sens de Thurston. Si la conjecture de géométrisation de Thurston s'avère vraie cette classe coïncide alors avec celle des groupes fondamentaux de variétés de dimension 3 orientables. Plus précisément nous démontrons que tous les groupes dans cette classe satisfont la conjecture de Baum-Connes avec coefficients. Nous discutons également le cas non-orientable.

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“…Then 1 (G, A) is a dense subalgebra of the reduced crossed product A red G. The following lemma is proved in [36,Section 1. 7] Lemma 3.6.…”

Section: Matthey (M) Oyono-oyono (H) and Pitsch (W)mentioning

confidence: 90%

“…Let X be a proper G-space, let A be a G X-algebra and let α ∈ KK G (C, A) and β ∈ KK G (A, C) be elements such that α⊗ A β = 1 in KK G (C, C). By [36,Section 1.7], the following diagram is commutative…”

Section: Matthey (M) Oyono-oyono (H) and Pitsch (W)mentioning

confidence: 99%

Homotopy invariance of higher signatures and $3$-manifold groups

Matthey¹,

Oyono-Oyono²,

Pitsch³

2008

Bul. Soc. Math. France

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“…Their techniques are rather different from ours, and depend on recent work of Vincent Lafforgue [26].…”

Section: Conjecture 15 (The Strong Bass Conjecture)mentioning

confidence: 97%

Whitehead groups and the Bass conjecture

Farrell

Linnell

2003

Mathematische Annalen

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“…This was proven (for a large class of groups containing G) in [Laf1]. For the groups under consideration the Baum-Connes conjecture can also be formulated and proven more algebraically [HiNi, Schn], with equivariant cosheaf homology (also known as chamber homology) [ABP,§2].…”

Section: Equivariant K-theorymentioning

confidence: 99%

Conjectures about 𝑝-adic groups and their noncommutative geometry

Aubert¹,

Baum²,

Plymen

et al. 2017

Around Langlands Correspondences

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Abstract. Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G.At the heart of these conjectures are statements about the geometric structure of Bernstein components for G, both at the level of the space of irreducible representations and at the level of the associated Hecke algebras. We relate this to two well-known conjectures: the local Langlands correspondence and the BaumConnes conjecture for G. In particular, we present a strategy to reduce the local Langlands correspondence for irreducible G-representations to the local Langlands correspondence for supercuspidal representations of Levi subgroups. Contents

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K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes

Cited by 197 publications

References 30 publications

Homotopy invariance of higher signatures and $3$-manifold groups

Homotopy invariance of higher signatures and $3$-manifold groups

Whitehead groups and the Bass conjecture

Conjectures about 𝑝-adic groups and their noncommutative geometry

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