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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 pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation
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by R. Roberts, J. Shareshian and M. Stein PDF
J. Amer. Math. Soc. 16 (2003), 639-679 Request permission

Abstract:

We investigate group actions on simply-connected (second countable but not necessarily Hausdorff) 1-manifolds and describe an infinite family of closed hyperbolic 3-manifolds whose fundamental groups do not act nontrivially on such 1-manifolds. As a corollary we conclude that these 3-manifolds contain no Reebless foliation. In fact, these arguments extend to actions on oriented $\mathbb R$-order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken.
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Additional Information
  • R. Roberts
  • Affiliation: Department of Mathematics, Washington University, St Louis, Missouri 63130
  • MR Author ID: 600757
  • Email: roberts@math.wustl.edu
  • J. Shareshian
  • Affiliation: Department of Mathematics, Washington University, St Louis, Missouri 63130
  • MR Author ID: 618746
  • Email: shareshi@math.wustl.edu
  • M. Stein
  • Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
  • Email: Melanie.Stein@mail.cc.trincoll.edu
  • Received by editor(s): June 2, 2002
  • Published electronically: March 3, 2003
  • Additional Notes: The first author was partially supported by National Science Foundation grant DMS-9971333
    The second author was partially supported by National Science Foundation grant DMS-0070757
    The third author was partially supported by a Trinity College Faculty Research Grant
  • © Copyright 2003 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 639-679
  • MSC (2000): Primary 57M25; Secondary 57R30
  • DOI: https://doi.org/10.1090/S0894-0347-03-00426-0
  • MathSciNet review: 1969207