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Quadrisecants of knots and links

1997/12/31 by Greg Kuperberg
Mathematics · #math.GT

paper · pdf

published as J. Knot Theory Ramifications 3 (1994), 41-50 · 7 pages. Figures added, retypeset in REVTeX, spelling corrected

arxiv created 2002/06/25 · arxiv updated 2009/11/30

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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