|Name||Gyo Taek Jin|
|Time||Jan 12 09:10~10:00|
|Title||Quadrisecant approximation of minimal polygonal knots|
It is known that every nontrivial knot has a quadrisecant. 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 heptagonal figure eight knot in general position, there are only six quadrisecants, and the resulting quadrisecant approximation has the same knot type. Furthermore, the resulting quadrisecant approximation has no new quadrisecants other than those of the heptagonal figure eight knot. We also discuss related results on some minimal polygonal torus knots.