#### Geometry & Topology, Vol. 5 (2001)
Paper no. 10, pages 319--334.

## Lefschetz fibrations on compact Stein surfaces

### Selman Akbulut, Burak Ozbagci

**Abstract**.
The existence of a positive allowable Lefschetz fibration on a compact
Stein surface with boundary was established by Loi and Piergallini by
using branched covering techniques. Here we give an alternative simple
proof of this fact and construct explicitly the vanishing cycles of
the Lefschetz fibration, obtaining a direct identification of the set
of compact Stein manifolds with positive allowable Lefschetz
fibrations over a 2-disk. In the process we associate to every compact
Stein manifold infinitely many nonequivalent such Lefschetz
fibrations.
**Note:** (25 September 2001) The authors have notified
the editors that there are errors in the last two sections of this
paper due to insufficient care with framing conventions. There is an
erratum (published 12 December 2001) which comprises verbatim
corrections to these sections starting at the heading "General case"
on page 330. This should be downloaded and used as a substitute.

**Keywords**.
Lefschetz fibration, Stein surface, open book decomposition

**AMS subject classification**.
Primary: 57R55.
Secondary: 57R65, 57R17, 57M50.

**DOI:** 10.2140/gt.2001.5.319

**E-print:** `arXiv:math.GT/0012239`

Submitted to GT on 31 January 2001.
Paper accepted 20 March 2001.
Paper published 25 March 2001.

Notes on file formats
** Erratum:**

Selman Akbulut, Burak Ozbagci

Department of Mathematics

Michigan State University

MI, 48824, USA

Email: akbulut@math.msu.edu, bozbagci@math.msu.edu

GT home page
## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**