The Second Hull of a Knotted Curve

Details The Second Hull of a Knotted Curve The Second Hull of a Knotted Curve

2002-04-10

arxiv.org/abs/math/0204106v2

Mathematics

Geometric Topology

7 pages, 6 figures; final version (only minor changes) to appear in Amer.J.Math

Scientific paper

The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points which are "multiply surrounded" by the curve. Our main theorem shows that if a curve is knotted then it has a nonempty second hull. This provides a new proof of the Fary/Milnor theorem that every knotted curve has total curvature at least 4pi.

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