Volume 5, issue 1 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Geography of symplectic 4–manifolds with Kodaira dimension one

Scott Baldridge and Tian-Jun Li

Algebraic & Geometric Topology 5 (2005) 355–368

arXiv: math.SG/0505030

Abstract

The geography problem is usually stated for simply connected symplectic 4–manifolds. When the first cohomology is nontrivial, however, one can restate the problem taking into account how close the symplectic manifold is to satisfying the conclusion of the Hard Lefschetz Theorem, which is measured by a nonnegative integer called the degeneracy. In this paper we include the degeneracy as an extra parameter in the geography problem and show how to fill out the geography of symplectic 4–manifolds with Kodaira dimension 1 for all admissible triples.

Keywords
symplectic 4–manifolds, symplectic topology
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D05, 57R57, 57M60
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Publication
Received: 22 January 2005
Revised: 30 March 2005
Accepted: 12 April 2005
Published: 21 April 2005
Authors
Scott Baldridge
Department of Mathematics
Louisiana State University
Baton Rouge LA 70803
USA
Tian-Jun Li
School of Mathematics
University of Minnesota
Minneapolis MN 55455
USA