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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Constructions preserving Hilbert space uniform embeddability of discrete groups
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by Marius Dadarlat and Erik Guentner PDF
Trans. Amer. Math. Soc. 355 (2003), 3253-3275 Request permission


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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Additional Information
  • Marius Dadarlat
  • Affiliation: Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395
  • MR Author ID: 53925
  • Email:
  • Erik Guentner
  • Affiliation: Mathematics Department, University of Hawaii, Manoa, 2565 McCarthy Mall, Honolulu, Hawaii 96822
  • Email:
  • Received by editor(s): July 22, 2002
  • Received by editor(s) in revised form: December 26, 2002
  • Published electronically: April 8, 2003
  • Additional Notes: The first author was supported in part by an MSRI Research Professorship and NSF Grant DMS-9970223. The second author was supported in part by an MSRI Postdoctoral Fellowship and NSF Grant DMS-0071402.
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3253-3275
  • MSC (2000): Primary 46L89, 20F65
  • DOI:
  • MathSciNet review: 1974686