Quadrisecant approximation of hexagonal trefoil knot

Details Quadrisecant approximation of hexagonal trefoil knot Quadrisecant approximation of hexagonal trefoil knot

2010-10-14

arxiv.org/abs/1010.2926v1

Mathematics

Geometric Topology

8 pages

Scientific paper

It is known that every nontrivial knot has at least two quadrisecants. Given a knot, we mark each intersection point of each of its quadrisecants. Replacing each subarc between two nearby marked points with a straight line segment joining them, we obtain a polygonal closed curve which we will call the quadrisecant approximation of the given knot. We show that for any hexagonal trefoil knot, there are only three quadrisecants, and the resulting quadrisecant approximation has the same knot type.

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