## Geometry & Topology

### Lefschetz fibrations on compact Stein surfaces

#### 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
Accepted: 20 March 2001
First available in Project Euclid: 21 December 2017

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

#### 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

#### 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