Abstract
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.
Original language | English (US) |
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Pages (from-to) | 143-153 |
Number of pages | 11 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 519 |
DOIs | |
State | Published - 2000 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics