Quadrisecants of knots and links
Greg Kuperberg
Abstract
We show that every non-trivial tame knot or link in R3 has a quadrisecant, i.e. four collinear points. The quadrisecant must be topologically non-trivial in a precise sense. As an application, we show that a nonsingular, algebraic surface in R3 which is a knotted torus must have degree at least eight.
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