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Constructions preserving Hilbert space uniform embeddability of discrete
groups, written with M. Dadarlat.
This paper appeared in Transactions of the AMS, 355 (2003), 3253--3275.
Abstract (from the preprint)
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 to the Novikov
conjecture. Exactness, introduced and studied extensively by
Kirchberg-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.