Introduction To The Baum-Connes Conjecture

By Alain Valette. 2002

184 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5b432c5d7a5cfd2811e0602312746879dffbaef2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Banach KK-theory and the Baum-Connes conjecture (2003, background): “There are many surveys on Kasparov’s KK-theory and the Baum-Connes conjecture (see [4, 48, 49, 21, 27, 13, 54]) and on Banach KK-theory ([49, 38]).”
On simplicity of reduced C*-algebras of groups (2005, background): “Today, reduced group C*-algebras and their K-theory play a fundamental role in noncommutative geometry [34], in particular in the Baum–Connes conjecture [9]; see also [100].”
Expanders, exact crossed products, and the Baum–Connes conjecture (2013, background): “All confirming examples for the original Baum-Connes conjecture remain confirming examples for the reformulated conjecture, and at present there are no known counterexamples to the reformulated conjecture.”
Lectures on Noncommutative Geometry (2005, background): “This conjecture is still open although it has now been verified for various classes of groups [120].”
Permanence properties of the Baum-Connes conjecture (2001, background): “Although BCC has been shown to be true for many groups (for a general overview of recent results we recommend the surveys [24] [28]), it seems now to be clear that there exist examples of groups for which the assembly map is not always surjective (there are counterexamples due to Higson, Lafforgue,…”
The Property of Rapid Decay for Discrete Quantum Groups (2020, background): “For a recent account on Property RD for discrete groups, including examples, counterexamples and more references, we refer the reader to Chapter 7 of [17].”
Some geometric groups with Rapid Decay (2003, background): “His result has been generalized by the first author in [4] to cocompact lattices in SL3(H) and E6(−26) as well as in a finite product of rank one Lie groups.”
Strong Haagerup inequalities for free R-diagonal elements (2005, methodology): “layed important roles in several different ﬁelds. Inthe contextof geometricgroup theory,the Haagerupinequality (and otherconstructions presented in [H]) have evolved into a-T-menability or property T [Va2]; in the context of Lie theory, Haagerup’s inequality is related to property RD [Laf2]. It has ”