Name  Gyo Taek Jin 

Affiliation  KAIST 
Talk type  Plenary 
Time  Jan 12 09:10~10:00 
Location  E11304 
Title  Quadrisecant approximation of minimal polygonal knots 
Abstract 
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.

Slide  304112/qsapprox8eas.pdf 