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.
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ReferencesWhitney, H. "On Regular Closed Curves in the Plane." Compos. Math. 4, 276-284, 1937.
Referenced on Wolfram|AlphaWhitney-Graustein Theorem
Cite this as:
Weisstein, Eric W. "Whitney-Graustein Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Whitney-GrausteinTheorem.html