Journal of Noncommutative Geometry
Full-Text PDF (211 KB) | Metadata | Table of Contents | JNCG summary
Published online: 2015-10-29
Property A and uniform embedding for locally compact groupsSteven Deprez and Kang Li (1) University of Copenhagen, Denmark
(2) University of Copenhagen, Denmark
For locally compact groups, we define an analogue to Yu’s property A that he defined for discrete metric spaces.We show that our property A for locally compact groups agrees with Roe’s notion of property A for proper metric spaces, defined in . We prove that many of the results that are known to hold in the discrete setting, hold also in the locally compact setting. In particular, we show that property A is equivalent to amenability at infinity (see  for the discrete case), and that a locally compact group with property A embeds uniformly into a Hilbert space (see  for the discrete case). We also prove that the Baum–Connes assembly map with coecients is split-injective, for every locally compact group that embeds uniformly into a Hilbert space. This extends results by Skandalis, Tu and Yu , and by Chabert, Echterho and Oyono-Oyono .
Keywords: Property A, Baum–Connes conjecture, uniform embeddability, locally compact groups
Deprez Steven, Li Kang: Property A and uniform embedding for locally compact groups. J. Noncommut. Geom. 9 (2015), 797-819. doi: 10.4171/JNCG/208