Codimension-one foliations calibrated by nondegenerate closed 2-forms

David Martínez Torres

Vol. 261 (2013), No. 1, 165–217

DOI: 10.2140/pjm.2013.261.165

Abstract

A class of codimension-one foliations has been recently introduced by imposing a natural compatibility condition with a closed maximally nondegenerate 2-form. In this paper we study for such foliations the information captured by a Donaldson-type submanifold. In particular we deduce that their leaf spaces are homeomorphic to leaf spaces of 3-dimensional taut foliations. We also introduce surgery constructions to show that this class of foliations is broad enough. Our techniques come mainly from symplectic geometry.

Keywords

codimension-one foliation, three-dimensional taut foliation, leaf space, symplectic structure, Lagrangian sphere, generalized Dehn twist, Legendrian surgery, Lefschetz pencil

Mathematical Subject Classification 2010

Primary: 53C12, 53D17, 57R17, 57R30

Secondary: 57R65, 53D12

Milestones

Received: 19 August 2011

Revised: 10 June 2012

Accepted: 27 August 2012

Published: 28 February 2013