Geometry & Topology 9 (2005) 1043–1114

DOI: 10.2140/gt.2005.9.1043

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 S¹ 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.

Keywords

near-symplectic manifolds, singular Lefschetz pencils

Mathematical Subject Classification

Primary: 53D35

Secondary: 57M50, 57R17

References

Publication

Received: 1 November 2004
Accepted: 30 May 2005
Published: 1 June 2005
Proposed: Robion Kirby
Seconded: Dieter Kotschick, Ronald Stern

Authors