Geography of symplectic 4–manifolds with Kodaira dimension one

Baldridge, Scott; Li, Tian-Jun

doi:10.2140/agt.2005.5.355

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Geography of symplectic 4–manifolds with Kodaira dimension one

Scott Baldridge and Tian-Jun Li

Algebraic & Geometric Topology 5 (2005) 355–368

DOI: 10.2140/agt.2005.5.355

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

Volume 5, issue 1 (2005)