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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Existence of Lefschetz fibrations on Stein and Weinstein domains

Emmanuel Giroux and John Pardon

Geometry & Topology 21 (2017) 963–997
Abstract

We show that every Stein or Weinstein domain may be presented (up to deformation) as a Lefschetz fibration over the disk. The proof is an application of Donaldson’s quantitative transversality techniques.

Keywords
Stein manifolds, Stein domains, Weinstein manifolds, Weinstein domains, Lefschetz fibrations, quantitative transversality
Mathematical Subject Classification 2010
Primary: 32Q28
Secondary: 32E10, 53D05, 53D35
References
Publication
Received: 27 July 2015
Revised: 7 April 2016
Accepted: 20 May 2016
Published: 17 March 2017
Proposed: Simon Donaldson
Seconded: Leonid Polterovich, Ciprian Manolescu
Authors
Emmanuel Giroux
Unité de Mathématiques Pures et Appliquées
École Normale Supérieure de Lyon
69364 Lyon cedex 07
France
John Pardon
Department of Mathematics
Stanford University
450 Serra Mall
Building 380
Stanford, CA 94305
United States