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 Theorem## Cite this as:

Weisstein, Eric W. "Whitney-Graustein Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Whitney-GrausteinTheorem.html