Algebraic and Geometric Topology 5 (2005), paper no. 15, pages 355-368.

Geography of symplectic 4-manifolds with Kodaira dimension one

Scott Baldridge, Tian-Jun Li

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

AMS subject classification. Primary: 57R17. Secondary: 53D05, 57R57, 57M60.

DOI: 10.2140/agt.2005.5.355

E-print: arXiv:math.SG/0505030

Submitted: 22 January 2005. (Revised: 30 March 2005.) Accepted: 12 April 2005. Published: 21 April 2005.

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Scott Baldridge, Tian-Jun Li
Department of Mathematics, Louisiana State University
Baton Rouge, LA 70803, USA
and
School of Mathematics, University of Minnesota
Minneapolis, MN 55455, USA
Email: sbaldrid@math.lsu.edu, tjli@math.umn.edu

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