On the Heegaard genus of contact 3-manifolds

• Autorzy: Burak Ozbagci
• 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.

Słowa kluczowe

EN

Heegaard genus; Contact genus; Open book genus; Contact connected sum; Contact manifold

Kategorie tematyczne

• 57R17: Symplectic and contact topology

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 752-756

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Burak Ozbagci

• Koç University

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

Identyfikatory

DOI

10.2478/s11533-011-0038-7