Guoliang Yu has introduced a property of discrete metric spaces which guarantees the existence of a uniform embedding into Hilbert space. We show that the metric space underlying a finitely generated discrete group has this property if and only if the action of the group on its Stone-Čech compactification is topologically amenable. It follows from Yu's work that if BG is a finite complex, and if G acts amenably on some compact Hausdorff space, then the Novikov higher signature conjecture is true for G.
All Science Journal Classification (ASJC) codes
- Applied Mathematics