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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Invariants of contact structures from open books


Authors: John B. Etnyre and Burak Ozbagci
Journal: Trans. Amer. Math. Soc. 360 (2008), 3133-3151
MSC (2000): Primary 57R17
Published electronically: January 25, 2008
MathSciNet review: 2379791
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Abstract: In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages) and the norm (which is minus the maximal Euler characteristic of a page of a supporting open book).


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Additional Information

John B. Etnyre
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: etnyre@math.gatech.edu

Burak Ozbagci
Affiliation: Department of Mathematics, Koç University, Istanbul, Turkey
Email: bozbagci@ku.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04459-0
PII: S 0002-9947(08)04459-0
Received by editor(s): May 16, 2006
Published electronically: January 25, 2008
Additional Notes: The first author was partially supported by the NSF CAREER Grant DMS-0239600 and NSF Focused Research Grant FRG-024466.
The second author was partially supported by the Turkish Academy of Sciences and by the NSF Focused Research Grant FRG-024466. The authors thank the referee for many useful comments concerning the original version of this paper.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.