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Tight contact structures via dynamics


Authors: John Etnyre and Robert Ghrist
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
Published electronically: August 5, 1999
MathSciNet review: 1670438
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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.


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Additional Information

John Etnyre
Affiliation: Department of Mathematics, Stanford University, Palo Alto, California 94305
Email: etnyre@math.stanford.edu

Robert Ghrist
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: ghrist@math.gatech.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05377-0
Keywords: Tight contact structures, Reeb flows
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
Article copyright: © Copyright 1999 American Mathematical Society

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