Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Invariants of contact structures from open books

Author(s): John B. Etnyre; Burak Ozbagci
Journal: Trans. Amer. Math. Soc. 360 (2008), 3133-3151.
MSC (2000): Primary 57R17
Posted: January 25, 2008
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

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).

References:

[DGS]
F. Ding, H. Geiges, and A. I. Stipsicz, Surgery diagrams for contact $ 3$-manifolds, Turkish J. Math, 28 (2004) no. 1, 41-74. MR 2056760 (2005c:57028)

[E]
Y. Eliashberg, Filling by holomorphic discs and its applications, Geometry of low-dimensional manifolds, 2 (Durham, 1989), London Math. Soc. Lecture Note Ser., 151 (1990), 45-67. MR 1171908 (93g:53060)

[E1]
J. B. Etnyre, Planar open book decompositions and contact structures, IMRN 79 (2004), 4255-4267. MR 2126827 (2005k:57049)

[E2]
J. B. Etnyre, Lectures on open book decompositions and contact structures, Lecture notes from the Clay Mathematics Institute Summer School on Floer Homology, Gauge Theory, and Low Dimensional Topology at the Alfréd Rényi Institute; Clay Math. Proc., 5, AMS, 2006. MR 2249250 (2007g:57042)

[EF]
J. B. Etnyre and T. Fuller, Realizing $ 4$-manifolds as achiral Lefschetz fibrations, Int. Math. Res. Not. 2006, Art. ID 70272. MR 2219214 (2007d:57040)

[EO]
J. B. Etnyre and B. Ozbagci, Open books and plumbings, Int. Math. Res. Not. 2006, Art. ID 72710. MR 2272094

[Ge]
H. Geiges, Constructions of contact manifolds, Math. Proc. Cambridge Philos. Soc. 121 (1997), no. 3, 455-464. MR 1434654 (98f:53027)

[Gi]
E. Giroux, Géometrie de contact: de la dimension trois vers les dimensions supérieures, Proceedings of the International Congress of Mathematicians (Beijing 2002), Vol. II, 405-414. MR 1957051 (2004c:53144)

[G]
R. Gompf, Handlebody construction of Stein surfaces, Ann. of Math. (2), 148 (1998) no. 2, 619-693. MR 1668563 (2000a:57070)

[GS]
R. Gompf and A. Stipsicz, $ 4$-manifolds and Kirby calculus, Grad. Stud. Math., Vol. 20, AMS, 1999. MR 1707327 (2000h:57038)

[HN]
U. Hirsch and W.D. Neumann, On cyclic branched coverings of spheres, Math. Ann. 215 (1975), 289-291. MR 0375321 (51:11516)

[HKM]
K. Honda, W. Kazez and G. Matic, Right-veering diffeomorphisms of compact surfaces with boundary I, preprint 2005.

[NR]
W.D. Neumann and L. Rudolph, Difference index of vector fields and the enhanced Milnor number, Topology 29 (1990) no. 1, 83-100. MR 1046626 (91j:57010)

[OS]
B. Ozbagci and A. Stipsicz, Surgery on contact $ 3$-manifolds and Stein surfaces, Bolyai Soc. Math. Stud., Vol. 13, Springer, 2004. MR 2114165 (2005k:53171)

[OSS]
P. Ozsvath, A. Stipsicz and Z. Szabo, Planar open books and Floer homology, Int. Math. Res. Not. 2005, no. 54, 3385-3401. MR 2200085 (2006j:57056)

[Ro]
D. Rolfsen, Knots and links, Publish or Perish, 1976. MR 0515288 (58:24236)

[S]
S. Schönenberger, Planar open books and symplectic fillings, Ph.D. Dissertation, the University of Pennsylvania, 2005.

[TW]
W. Thurston and H. Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975), 345-347. MR 0375366 (51:11561)

[Vh]
J. Van Horn, Ph.D. Dissertation, the University of Texas at Austin, in preparation.

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 57R17

Retrieve articles in all Journals with MSC (2000): 57R17

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: 10.1090/S0002-9947-08-04459-0
PII: S 0002-9947(08)04459-0
Received by editor(s): May 16, 2006
Posted: 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.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google