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1 results

  • Lecture 2 - Intersections, Ruled Surfaces, and Contact Boundaries

  • 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 26-43

  • Summary

    This lecture concludes our survey of closed holomorphic curves with a discussion, in the first section, of local intersection numbers, positivity of intersections and the adjunction formula for closed holomorphic curves, and then, in the second section, with an explanation of how these figure into the proof of McDuff’s theorem on symplectic ruled surfaces. The last two sections then begin a shift in focus toward punctured holomorphic curves: this discussion starts with a general introduction to contact manifolds and their symplectic fillings and then continues by defining the moduli space of punctured asymptotically cylindrical holomorphic curves in a completed symplectic cobordism between contact manifolds.