A cohomological characterisation of Yu's Property A for metric spaces

Abstract

Property A was introduced by Yu as a non-equivariant analogue of amenability. Nigel Higson posed the question of whether there is a homological characterisation of property A. In this paper we answer Higson's question affirmatively by constructing analogues of group cohomology and bounded cohomology for a metric space X, and show that property A is equivalent to vanishing cohomology. Using these cohomology theories we also give a characterisation of property A in terms of the existence of an asymptotically invariant mean on the space.

References in corpus (2)

• Invariant expectations and vanishing of bounded cohomology for exact groups
• Expanders and Property A

Cited by in corpus (3)

• Coarse amenability versus paracompactness
• Relative property A and relative amenability for countable groups
• Expanders and Property A