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Property A and CAT(0) cubical groups
Abstract
The main results of the paper are:
- A finite dimensional CAT(0) cube complex has Property A
- A discrete group acting properly on a CAT(0) cube complex fixing
a vertex at infinity is amenable
Property A is a non-equivariant analog of amenability defined for metric
spaces by Yu in his work on the Novikov conjecture. The first result
above is proven by directly constructing the `Folner sets' called for in
Yu's original definition. The result applies to non-locally finite
complexes.
The same construction, suitably adapted to allow a basepoint at
infinity, is the essential ingredient in the proof of the second result
above.