Proceedings of the American Mathematical Society

Author(s): John Etnyre; Robert Ghrist
Journal: Proc. Amer. Math. Soc. 127 (1999), 3697-3706.
MSC (1991): Primary 53C15, 57M12; Secondary 58F05
Posted: August 5, 1999
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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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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: 10.1090/S0002-9939-99-05377-0
PII: S 0002-9939(99)05377-0
Keywords: Tight contact structures, Reeb flows
Received by editor(s): January 28, 1998
Posted: 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 of article: Copyright 1999, American Mathematical Society

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