Invariants for Lagrangian tori

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)].

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper25.abs.html

References in corpus (3)

• The Seiberg-Witten invariants and 4-manifolds with essential tori
• Torsion, TQFT, and Seiberg-Witten invariants of 3-manifolds
• Non-isotopic Symplectic Tori in the Same Homology Class

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• Homologous Non-isotopic Symplectic Surfaces of Higher Genus
• Symplectic Tori in Homotopy E(1)'s
• An interesting symplectic 4-manifold with small Euler characteristic
• Embedded and Lagrangian Knotted Tori in $\BR^4$ and Hypercube Homology
• Computations of Floer Homology for certain Lagrangian Tori in closed 4-manifolds
• Invariants of Lagrangian surfaces
• Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds