Singular Lefschetz pencils

Denis Auroux, Simon K. Donaldson, Ludmil Katzarkov

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

We consider structures analogous to symplectic Lefschetz pencils in the context of a closed 4-manifold equipped with a "near-symplectic" structure (ie, a closed 2-form which is symplectic outside a union of circles where it vanishes transversely). Our main result asserts that, up to blowups, every near-symplectic 4-manifold (X, ω) can be decomposed into (a) two symplectic Lefschetz fibrations over discs, and (b) a fibre bundle over S 1 which relates the boundaries of the Lefschetz fibrations to each other via a sequence of fibrewise handle additions taking place in a neighbourhood of the zero set of the 2-form. Conversely, from such a decomposition one can recover a near-symplectic structure.

Original languageEnglish (US)
JournalGeometry and Topology
Volume9
DOIs
StatePublished - Jun 1 2005

ASJC Scopus subject areas

  • Geometry and Topology

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