#### 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

and

Department of Mathematics, University of
California

Irvine, California 92697, USA

Email: ronfint@math.msu.edu, rstern@math.uci.edu

GT home page

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