Volume 9, issue 2 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Singular Lefschetz pencils

Denis Auroux, Simon K Donaldson and Ludmil Katzarkov

Geometry & Topology 9 (2005) 1043–1114

arXiv: math.DG/0410332


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.

near-symplectic manifolds, singular Lefschetz pencils
Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 57M50, 57R17
Forward citations
Received: 1 November 2004
Accepted: 30 May 2005
Published: 1 June 2005
Proposed: Robion Kirby
Seconded: Dieter Kotschick, Ronald Stern
Denis Auroux
Department of Mathematics
Massachusetts Institute of Technology
Massachusetts 02139
Simon K Donaldson
Department of Mathematics
Imperial College
London SW7 2BZ
United Kingdom
Ludmil Katzarkov
Department of Mathematics
University of Miami
Coral Gables
Florida 33124
Department of Mathematics
UC Irvine
California 92612