Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article

The $K$ -theory of Gromov's translation algebras and the amenability of discrete groups

Author(s): Gábor Elek
Journal: Proc. Amer. Math. Soc. 125 (1997), 2551-2553.
MSC (1991): Primary 20F38
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We prove the following theorem. A finitely generated group $\Gamma$ is amenable if and only if $\boldsymbol {1}\neq \boldsymbol {0}$ in $K_0(T(\Gamma ))$ , the algebraic $K$ -theory group of its translation algebra.

References:

1.: J. Block, S. Weinberger, Aperiodic tilings, positive scalar curvature and amenability of spaces, Journal of the Amer. Math. Soc. 5 (1992), 907-918 MR 93d:53054
2.: W.A.Deuber,M.Simonovits and V.T.Sós, A note on paradoxical metric spaces, Studia Sci.Hung.Math. 30 (1995), 17-23 MR 96i:54025
3.: M.Gromov, Asymptotic Invariants of Infinite Groups, London Math. Society, Lecture Note Series 182 (1993) MR 95m:20041
4.: J. Roe, An index theorem on open manifolds I-II, Journal of Differential Geometry 27 (1988), 87-136 MR 89a:58102
5.: P.M.Soardi, Potential Theory on Infinite Networks, Lecture Notes in Mathematics 1590 MR 96i:31005


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS