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

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

2010-02-26

arxiv.org/abs/1002.5040v2

Mathematics

Geometric Topology

Scientific paper

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.

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