Jorge Alberto Calvo : abstract

Knots and Sticks
Jorge Alberto Calvo
Department of Mathematics
North Dakota State University
Traditional knot theory is the study of simple closed curves in three-dimensional space and their deformations. The only restriction on a legal deformation of a knot is one that it can be extended to a continuous deformation of the entire space containing the knot. This still allows for very flexibile knots. However, if one desires to use knot theory to model something more rigid, like DNA molecules, then a different strategy is required. One solution is to restrict attention to knotted curves which are piecewise linear, so that any knot looks like a bunch of sticks glued end to end. A valid deformation in this scenario has to preserve the stick structure of the knot. We will explore some of the consequences of this new "geometric" theory of knots for a small number of edges.