Singular Lefschetz pencils
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.
引用
@article{arxiv.math/0410332,
title = {Singular Lefschetz pencils},
author = {Denis Auroux and Simon K Donaldson and Ludmil Katzarkov},
journal= {arXiv preprint arXiv:math/0410332},
year = {2014}
}
备注
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper24.abs.html