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1 results

  • Lecture 1 - Closed Holomorphic Curves in Symplectic 4-Manifolds

  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book:
    Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
    Published online:
    06 March 2020
    Print publication:
    26 March 2020, pp 11-25

  • Summary

    The first lecture introduces the study of closed symplectic manifolds via closed pseudoholomorphic curves, focusing in particular on McDuff’s famous theorem from 1990 that characterizes symplectic ruled surfaces via symplectically embedded spheres. The theorem is stated in a slightly more modern formulation using Lefschetz fibrations, and a proof modulo of some technical lemmas is sketched. The topic of intersection theory is then introduced by considering the natural question of what kinds of holomorphic curves can be proven to form leaves of smooth foliations by holomorphic curves.