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Residues and the fundamental group

  1. Mar 24, 2012 #1
    I've been thinking about complex residues and how they relate to the topology of a function's Riemann's surface. My conclusion is this: it definitely tells us something, but it relates more directly to the Riemann surface of its antiderivative. Specifically:

    A closed contour in the plane is closed when projected to the Riemann surface of f's antiderivative iff the sum of the residues of f interior to it are zero.

    Is this correct?
  2. jcsd
  3. Mar 30, 2012 #2

    What do you mean mathematically by "projected to the Riemann Suerface of f's derivative"? What kind of projection are you thinking about? Can you give some example(s)?

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