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(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Residues and the fundamental group

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