Geometry & Topology

Invariants for Lagrangian tori

Ronald Fintushel and Ronald J Stern

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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

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

Received: 4 September 2003
Revised: 19 April 2004
Accepted: 3 June 2004
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
Secondary: 57R17: Symplectic and contact topology

$4$–manifold Seiberg–Witten invariant symplectic Lagrangian


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

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