Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Invariants for Lagrangian tori

Ronald Fintushel and Ronald J Stern

Geometry & Topology 8 (2004) 947–968

arXiv: math.SG/0304402

Abstract

We define an simple invariant λ(T) 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 λ(T) is actually a C 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.

Keywords
$4$–manifold, Seiberg–Witten invariant, symplectic, Lagrangian
Mathematical Subject Classification 2000
Primary: 57R57
Secondary: 57R17
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Publication
Received: 4 September 2003
Revised: 19 April 2004
Accepted: 3 June 2004
Published: 29 June 2004
Proposed: Peter Kronheimer
Seconded: Robion Kirby, Yasha Eliashberg
Authors
Ronald Fintushel
Department of Mathematics
Michigan State University
East Lansing
Michigan 48824
USA
Ronald J Stern
Department of Mathematics
University of California
Irvine
California 92697
USA