I want to find a curve which is not homotopic to constant path but the index of every point not on the curve is zero. Here the domain is an open subset of Complex Plane.I was unable to find any such curve, So if anyone can give an example it would be great. Thanks.
2026-04-22 11:37:50.1776857870
A curve not homotopic to constant path but index of every point is zero.
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One example is the Pochhammer Contour. You can read about it here : https://en.wikipedia.org/wiki/Pochhammer_contour