Geometry & Topology

Invariants for Lagrangian tori

Ronald Fintushel and Ronald J Stern

Full-text: Open access

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

Permanent link to this document
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

Subjects
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

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

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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