University of Florida, Department of Mathematics, P.O. Box 118105, 358 Little Hall, Gainesville, FL 32611-8105, USA
Abstract:
Gouliang Yu has introduced a property of discrete metric spaces and groups called property A which implies the coarse Baum–Connes Conjecture and hence the Novikov Higher Signature Conjecture. In this paper we extend a result of Jean-Louis Tu to conclude that a group acting by isometries on a metric space with finite asymptotic dimension whose d-stabilizers have property A, also has property A. As a result, we conclude a theorem of Tu, according to which, a fundamental group of a finite graph of groups whose vertices have property A also has property A.