Invariants for Lagrangian tori

Fintushel, Ronald¹ ; Stern, Ronald J²

¹ Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
² Department of Mathematics, University of California, Irvine, California 92697, USA

Geometry & topology, Tome 8 (2004) no. 2, pp. 947-968.

Résumé

We define an simple invariant $\lambda \left(T\right)$ 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 $\lambda \left(T\right)$ is actually a $C^{\infty }$ 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.

Détail

DOI : 10.2140/gt.2004.8.947

Keywords: $4$–manifold, Seiberg–Witten invariant, symplectic, Lagrangian

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