Geometry & Topology

Lefschetz fibrations on compact Stein surfaces

Selman Akbulut and Burak Özbağcı

Full-text: Open access

Abstract

Let M be a compact Stein surface with boundary. We show that M admits infinitely many pairwise nonequivalent positive allowable Lefschetz fibrations over D2 with bounded fibers.

Article information

Source
Geom. Topol., Volume 5, Number 1 (2001), 319-334.

Dates
Received: 31 January 2001
Accepted: 20 March 2001
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513882991

Digital Object Identifier
doi:10.2140/gt.2001.5.319

Mathematical Reviews number (MathSciNet)
MR1825664

Zentralblatt MATH identifier
1002.57062

Subjects
Primary: 57R55: Differentiable structures
Secondary: 57R65: Surgery and handlebodies 57R17: Symplectic and contact topology 57M50: Geometric structures on low-dimensional manifolds

Keywords
Lefschetz fibration Stein surface open book decomposition

Citation

Akbulut, Selman; Özbağcı, Burak. Lefschetz fibrations on compact Stein surfaces. Geom. Topol. 5 (2001), no. 1, 319--334. doi:10.2140/gt.2001.5.319. https://projecteuclid.org/euclid.gt/1513882991


Export citation

References

  • S Akbulut, R Matveyev, A convex decomposition theorem for $4$–manifolds, Int. Math. Research Notices No 7 (1998) 371–381.
  • S Akbulut, B Ozbagci, On the topology of compact Stein surfaces, preprint.
  • Y Eliashberg, Topological characterization of Stein manifolds in dimension $\geq 2$, Int. Journ. of Math. 1 (1990) 29–46
  • D Gabai, Detecting fibered links in $S^3$, Comment. Math. Helv. 61 (1986) 519–555
  • R Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998) 619–693
  • R Gompf, A Stipsicz, 4–manifolds and Kirby calculus, Graduate Studies in Math. 20, A.M.S. (1999)
  • J Harer, How to construct all fibered knots and links, Topology, 21 (1982) 263–280
  • K Honda, On the classification of tight contact structures I, Geometry and Topology, 4 (2000) 309–368
  • A Kas, On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math. 89 (1980) 89–104
  • A Loi, R Piergallini, Compact Stein surfaces with boundary as branched covers of $B^4$, Invent. Math. 143 (2001) 325–348.
  • H Lyon, Torus knots in the complements of links and surfaces, Michigan Math. J. 27 (1980) 39–46
  • L Rudolph, Quasipositive plumbing, Proc. Amer. Math. Soc. 126 (1998) 257–267
  • L Rudolph, A characterization of quasipositive Seifert surfaces, Topology, 31 (1992) 231–237
  • L Rudolph, Quasipositive annuli, J. Knot Theory and its Ramifications, 1 (1992) 451–466
  • L Rudolph, An obstruction to sliceness via contact geometry and classical gauge theory, Invent. Math. 119 (1995) 155–163
  • J Stallings, Construction of fibered knots and links, A.M.S. Proc. Symp. in Pure Math. 32 (1978) 55–60
  • I Torisu, Convex contact structures and fibered links in 3–manifolds, Int. Math. Research Notices, 9 (2000) 441–454