|Mar24-12, 08:23 PM||#1|
Residues and the fundamental group
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?
|Mar30-12, 02:16 PM||#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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