Geometry & Topology Monographs, Vol. 7 (2004),
Proceedings of the Casson Fest,
Paper no. 11, pages 267--290.

Symplectic structures from Lefschetz pencils in high dimensions

Robert E Gompf

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

AMS subject classification. Primary: 57R17.

E-print: arXiv:math.SG/0409370

Submitted to GT on 4 June 2004. (Revised 2 August 2004.) Paper accepted 20 July 2004. Paper published 20 September 2004.

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

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