Crookedness

Let a Knot be parameterized by a Vector Function with , and let be a fixed Unit Vector in . Count the number of Relative Minimaof the projection function . Then the Minimum such number over all directions and all of the given type is called the crookedness . Milnor (1950) showed that is theInfimum of the total curvature of . For any Tame Knot in , where is the Bridge Index.

References

Milnor, J. W. ``On the Total Curvature of Knots.'' Ann. Math. 52, 248-257, 1950.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 115, 1976.

• Ordinary Differential Equation--First-Order Exact
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