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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Tight contact structures via dynamics
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by John Etnyre and Robert Ghrist PDF
Proc. Amer. Math. Soc. 127 (1999), 3697-3706 Request permission

Abstract:

We consider the problem of realizing tight contact structures on closed orientable three-manifolds. By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of (Reeb) flows transverse to the contact structure. We detail how two classical constructions, Dehn surgery and branched covering, may be performed on dynamically-constrained links in such a way as to preserve a transverse tight contact structure.
References
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Additional Information
  • John Etnyre
  • Affiliation: Department of Mathematics, Stanford University, Palo Alto, California 94305
  • MR Author ID: 619395
  • Email: etnyre@math.stanford.edu
  • Robert Ghrist
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
  • MR Author ID: 346210
  • Email: ghrist@math.gatech.edu
  • Received by editor(s): January 28, 1998
  • Published electronically: August 5, 1999
  • Additional Notes: The first author was supported in part by NSF Grant # DMS-9705949.
    The second author was supported in part by NSF Grant # DMS-9508846.
  • Communicated by: Ronald A. Fintushel
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3697-3706
  • MSC (1991): Primary 53C15, 57M12; Secondary 58F05
  • DOI: https://doi.org/10.1090/S0002-9939-99-05377-0
  • MathSciNet review: 1670438