Expanders are counterexamples to the ${\ell }^p$ coarse Baum-Connes conjecture

Abstract

We consider an ${\ell }^p$ coarse Baum-Connes assembly map for $1<p<\infty$, and show that it is not surjective for expanders arising from residually finite hyperbolic groups.

25 pages. Final version, to appear in Journal of Noncommutative Geometry. Subsection 2.2 in the previous version has been moved to the appendix

References in corpus (6)

• Group algebras acting on $L^p$-spaces
• A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
• Coronae of product spaces and the Coarse Baum-Connes conjecture
• K-theory of group Banach algebras and Banach property RD
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Cited by in corpus (1)

• $L^p$ coarse Baum-Connes conjecture via $C_0$ coarse geometry