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2011 | 9 | 4 | 752-756
Tytuł artykułu

On the Heegaard genus of contact 3-manifolds

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is well-known that the Heegaard genus is additive under connected sum of 3-manifolds. We show that the Heegaard genus of contact 3-manifolds is not necessarily additive under contact connected sum. We also prove some basic properties of the contact genus (a.k.a. open book genus [Rubinstein J.H., Comparing open book and Heegaard decompositions of 3-manifolds, Turkish J. Math., 2003, 27(1), 189–196]) of 3-manifolds, and compute this invariant for some 3-manifolds.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
4
Strony
752-756
Opis fizyczny
Daty
wydano
2011-08-01
online
2011-05-26
Twórcy
Bibliografia
  • [1] Ding F., Geiges H., Stipsicz A., Surgery diagrams for contact 3-manifolds, Turkish J. Math., 2004, 28(1), 41–74
  • [2] Eliashberg Y., Contact 3-manifolds twenty years since J. Martinet’s work, Ann. Inst. Fourier (Grenoble), 1992, 42(1–2), 165–192
  • [3] Etnyre J.B., Lectures on open book decompositions and contact structures, In: Floer Homology, Gauge Theory, and Low-Dimensional Topology, Clay Math. Proc., 5, American Mathematical Society, Providence, 2006, 103–141
  • [4] Etnyre J.B., Ozbagci B., Invariants of contact structures from open books, Trans. Amer. Math. Soc., 2008, 360(6), 3133–3151 http://dx.doi.org/10.1090/S0002-9947-08-04459-0
  • [5] Giroux E., Géométrie de contact: de la dimension trois vers les dimensions supérieures, In: Proceedings of the International Congress of Mathematicians, Beijing 2002, Vol. II, Higher Ed. Press, Beijing, 2002, 405–414
  • [6] Gompf R.E., Handlebody construction of Steinsurfaces, Ann. of Math., 1998, 148(2), 619–693 http://dx.doi.org/10.2307/121005
  • [7] Ozbagci B., Stipsicz A.I., Surgery on Contact 3-manifolds and Stein Surfaces, Bolyai Soc. Math. Stud., 13, Springer, Berlin, 2004
  • [8] Rubinstein J.H., Comparing open book and Heegaard decompositions of 3-manifolds, Turkish J. Math., 2003, 27(1), 189–196
  • [9] Torisu I., Convex contact structures and fibered links in 3-manifolds, Internat. Math. Res. Notices, 2000, 9, 441–454 http://dx.doi.org/10.1155/S1073792800000246
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0038-7
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