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Singular Lefschetz
pencils
Denis Auroux, Simon K Donaldson and Ludmil Katzarkov |
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Geometry & Topology 9 (2005) 1043–1114
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arXiv: math.DG/0410332 |
Abstract |
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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 can be decomposed into (a) two symplectic Lefschetz fibrations over discs, and (b) a fibre bundle over 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
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Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 57M50, 57R17
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References |
Forward citations |
Publication
Received: 1 November 2004
Accepted: 30 May 2005
Published: 1 June 2005
Proposed: Robion Kirby
Seconded: Dieter Kotschick, Ronald Stern
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Authors |
| Denis Auroux | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA |
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| Simon K Donaldson | |
| Department of Mathematics Imperial College London SW7 2BZ United Kingdom |
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| Ludmil Katzarkov | |
| Department of Mathematics University of Miami Coral Gables Florida 33124 USA |
Department of Mathematics UC Irvine Irvine California 92612 USA |
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