Constructions preserving Hilbert space uniform embeddability of discrete groups

Dadarlat, Marius; Guentner, Erik

doi:10.1090/S0002-9947-03-03284-7

Constructions preserving Hilbert space uniform embeddability of discrete groups
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by Marius Dadarlat and Erik Guentner

Trans. Amer. Math. Soc. 355 (2003), 3253-3275

DOI: https://doi.org/10.1090/S0002-9947-03-03284-7

Published electronically: April 8, 2003

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Abstract:

Uniform embeddability (in a Hilbert space), introduced by Gromov, is a geometric property of metric spaces. As applied to countable discrete groups, it has important consequences for the Novikov conjecture. Exactness, introduced and studied extensively by Kirchberg and Wassermann, is a functional analytic property of locally compact groups. Recently it has become apparent that, as properties of countable discrete groups, uniform embeddability and exactness are closely related. We further develop the parallel between these classes by proving that the class of uniformly embeddable groups shares a number of permanence properties with the class of exact groups. In particular, we prove that it is closed under direct and free products (with and without amalgam), inductive limits and certain extensions.

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