## Geometry & Topology

### Invariants for Lagrangian tori

#### 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.

#### Article information

Source
Geom. Topol., Volume 8, Number 2 (2004), 947-968.

Dates
Revised: 19 April 2004
Accepted: 3 June 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883421

Digital Object Identifier
doi:10.2140/gt.2004.8.947

Mathematical Reviews number (MathSciNet)
MR2087074

Zentralblatt MATH identifier
1052.57045

#### Citation

Fintushel, Ronald; Stern, Ronald J. Invariants for Lagrangian tori. Geom. Topol. 8 (2004), no. 2, 947--968. doi:10.2140/gt.2004.8.947. https://projecteuclid.org/euclid.gt/1513883421

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