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1 results

  • Introduction: Motivation

  • 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 1-10

  • Summary

    The introduction motivates the remainder of the book via two specific examples of theorems from the early days of symplectic topology in which intersection theory plays a prominent role. We sketch closely analogous proofs of both theorems, emphasizing the way that intersection theory is used, but point out why the second theorem (on symplectic 4-manifolds that are standard near infinity) requires a nonobvious extension of homological intersection theory to punctured holomorphic curves. We then discuss informally some of the properties this theory will need to have and what kinds of subtle issues may arise.