Volume 7 (2004)

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Symplectic structures from Lefschetz pencils in high dimensions

Robert E Gompf

Geometry & Topology Monographs 7 (2004) 267–290

DOI: 10.2140/gtm.2004.7.267

Abstract

A symplectic structure is canonically constructed on any manifold endowed with a topological linear k–system whose fibers carry suitable symplectic data. As a consequence, the classification theory for Lefschetz pencils in the context of symplectic topology is analogous to the corresponding theory arising in differential topology.

Keywords

linear system, vanishing cycle, monodromy

Publication

Received: 4 June 2004
Revised: 2 August 2004
Accepted: 20 July 2004
Published: 20 September 2004

Authors
Robert E Gompf
Department of Mathematics
The University of Texas at Austin
1 University Station C1200
Austin TX 78712–0257
USA