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.

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Selman Akbulut, Burak Ozbagci
Department of Mathematics
Michigan State University
MI, 48824, USA

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