Coronae of product spaces and the Coarse Baum-Connes conjecture

Abstract

We study the coarse Baum-Connes conjecture for product spaces and product groups. We show that a product of CAT(0) groups, polycyclic groups and relatively hyperbolic groups which satisfy some assumptions on peripheral subgroups, satisfies the coarse Baum-Connes conjecture. For this purpose, we construct and analyze an appropriate compactification and its boundary, "corona", of a product of proper metric spaces.

35 pages

Cited by in corpus (6)

• Novikov's Conjecture
• A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture
• The equivariant coarse Novikov conjecture and coarse embedding
• Expanders are counterexamples to the ${\ell }^p$ coarse Baum-Connes conjecture
• Coarse compactifications and controlled products
• $L^p$ coarse Baum-Connes conjecture via $C_0$ coarse geometry