Amenable group actions and the Novikov conjecture

Nigel Higson, John Roe

Research output: Contribution to journalArticlepeer-review

104 Scopus citations

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 languageEnglish (US)
Pages (from-to)143-153
Number of pages11
JournalJournal fur die Reine und Angewandte Mathematik
Volume519
DOIs
StatePublished - 2000

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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