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Date: 31-5-2021
1429
Date: 10-5-2021
2002
Date: 7-7-2021
1271
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Let a knot be parameterized by a vector function with , and let be a fixed unit vector in . Count the number of local minima of 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 the infimum 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.
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