A theorem that classifies planar regular closed curves up to regular homotopy by their contour winding numbers
(Whitney 1937). In his thesis, S. Smale generalized this result to regular closed
curves on an 
-manifold.
Whitney-Graustein Theorem
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References
Whitney, H. "On Regular Closed Curves in the Plane." Compos. Math. 4, 276-284, 1937.Referenced on Wolfram|Alpha
Whitney-Graustein TheoremCite this as:
Weisstein, Eric W. "Whitney-Graustein Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Whitney-GrausteinTheorem.html