arXiv math/04103322004-10math.DGmath.GTmath.SG

Singular Lefschetz pencils

Denis Auroux, Simon K Donaldson, Ludmil Katzarkov

备注：: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper24.abs.html
发表信息：: Geom. Topol. 9 (2005) 1043-1114
DOI：: 10.2140/gt.2005.9.1043

英文摘要：

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,omega) 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.

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