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

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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].

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Authors and Affiliations

  1. Department of Mathematics, M.I.T., Cambridge MA 02139, USA (e-mail: auroux@math.mit.edu), , , , , , US

    D. Auroux

  2. Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom (e-mail: s.donaldson@ic.ac.uk), , , , , , GB

    S.K. Donaldson

  3. Department of Mathematics, University of California, Irvine, CA 92697, USA (e-mail: lkatzark@math.uci.edu), , , , , , US

    L. Katzarkov

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  1. D. Auroux
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  2. S.K. Donaldson
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  3. L. Katzarkov
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Received: 1 July 2002 / Revised version: 12 August 2002 Published online: 28 March 2003

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Auroux, D., Donaldson, S. & Katzarkov, L. Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves. Math. Ann. 326, 185–203 (2003). https://doi.org/10.1007/s00208-003-0418-9

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  • DOI: https://doi.org/10.1007/s00208-003-0418-9

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