Geometry & Topology, Vol. 8 (2004) Paper no. 25, pages 947--968.

Invariants for Lagrangian tori

Ronald Fintushel, Ronald J Stern

Abstract. We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4-manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We further show that for a large class of examples that lambda(T) is actually a C-infinity invariant. In addition, this invariant is used to show that many symplectic 4-manifolds have nontrivial homology classes which are represented by infinitely many pairwise inequivalent Lagrangian tori, a result first proved by S Vidussi for the homotopy K3-surface obtained from knot surgery using the trefoil knot in [Lagrangian surfaces in a fixed homology class: existence of knotted Lagrangian tori, J. Diff. Geom. (to appear)].

Keywords. 4-manifold, Seiberg-Witten invariant, symplectic, Lagrangian

AMS subject classification. Primary: 57R57. Secondary: 57R17.

DOI: 10.2140/gt.2004.8.947

E-print: arXiv:math.SG/0304402

Submitted to GT on 4 September 2003. (Revised 19 April 2004.) Paper accepted 3 June 2004. Paper published 29 June 2004.

Notes on file formats

Ronald Fintushel, Ronald J Stern
Department of Mathematics, Michigan State University
East Lansing, Michigan 48824, USA
Department of Mathematics, University of California
Irvine, California 92697, USA


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