Mathematische Annalen

, Volume 326, Issue 1, pp 185–203

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

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

DOI: 10.1007/s00208-003-0418-9

Cite this article as:
Auroux, D., Donaldson, S. & Katzarkov, L. Math. Ann. (2003) 326: 185. doi:10.1007/s00208-003-0418-9

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].

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