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Mathematische Annalen

, Volume 326, Issue 1, pp 185–203 | Cite as

Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves

  • D. Auroux
  • S.K. Donaldson
  • L. Katzarkov

Abstract.

 We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide a purely topological interpretation of a non-isotopy result for symplectic plane curves with cusp and node singularities due to Moishezon [9].

Keywords

Plane Curf Node Singularity Lagrangian Torus Dehn Surgery Topological Interpretation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • D. Auroux
    • 1
  • S.K. Donaldson
    • 2
  • L. Katzarkov
    • 3
  1. 1.Department of Mathematics, M.I.T., Cambridge MA 02139, USA (e-mail: auroux@math.mit.edu)US
  2. 2.Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom (e-mail: s.donaldson@ic.ac.uk)GB
  3. 3.Department of Mathematics, University of California, Irvine, CA 92697, USA (e-mail: lkatzark@math.uci.edu)US

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