Volume 4, issue 1 (2000)

Download this article
For printing
Recent Issues

Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540

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
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Symplectic Lefschetz fibrations on $S^1 \times M^3$

Weimin Chen and Rostislav Matveyev

Geometry & Topology 4 (2000) 517–535

arXiv: math.DG/0002022

Abstract

In this paper we classify symplectic Lefschetz fibrations (with empty base locus) on a four-manifold which is the product of a three-manifold with a circle. This result provides further evidence in support of the following conjecture regarding symplectic structures on such a four-manifold: if the product of a three-manifold with a circle admits a symplectic structure, then the three-manifold must fiber over a circle, and up to a self-diffeomorphism of the four-manifold, the symplectic structure is deformation equivalent to the canonical symplectic structure determined by the fibration of the three-manifold over the circle.

Keywords
4–manifold, symplectic structure, Lefschetz fibration, Seiberg–Witten invariants
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57R17, 57R57
References
Forward citations
Publication
Received: 12 April 2000
Revised: 8 December 2000
Accepted: 17 December 2000
Published: 21 December 2000
Proposed: Dieter Kotschick
Seconded: Robion Kirby, Yasha Eliashberg
Authors
Weimin Chen
University of Wisconsin at Madison
Madison
Wisconsin 53706
USA
Rostislav Matveyev
SUNY at Stony Brook
Stony Brook
New York 11794
USA