Existence of Lefschetz fibrations on Stein and Weinstein domains

Giroux, Emmanuel; Pardon, John

doi:10.2140/gt.2017.21.963

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Existence of Lefschetz fibrations on Stein and Weinstein domains

Emmanuel Giroux and John Pardon

Geometry & Topology 21 (2017) 963–997

DOI: 10.2140/gt.2017.21.963

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

Volume 21, issue 2 (2017)