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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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A Higman embedding preserving asphericity
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by Mark Sapir
J. Amer. Math. Soc. 27 (2014), 1-42
Published electronically: July 9, 2013


We prove that every finitely generated group with recursive aspherical presentation embeds into a group with finite aspherical presentation. This and several known facts about groups and manifolds imply that there exists a 4-dimensional closed aspherical manifold $M$ such that the fundamental group $\pi _1(M)$ coarsely contains an expander. Thus it has infinite asymptotic dimension, is not coarsely embeddable into a Hilbert space, does not satisfy G. Yu’s property A, and does not satisfy the Baum-Connes conjecture with coefficients. Closed aspherical manifolds with any of these properties were previously unknown.
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Bibliographic Information
  • Mark Sapir
  • Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
  • MR Author ID: 189574
  • Email:
  • Received by editor(s): April 26, 2011
  • Received by editor(s) in revised form: September 22, 2011, November 29, 2011, and April 29, 2013
  • Published electronically: July 9, 2013
  • Additional Notes: This research was supported in part by NSF grant DMS-0700811.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 27 (2014), 1-42
  • MSC (2010): Primary 20F65; Secondary 20F69, 20F38, 22F50
  • DOI:
  • MathSciNet review: 3110794