3 papers
math.GT2006
Convergence and isotopy type for graphs of finite total curvature
Elizabeth Denne, John M Sullivan
Generalizing Milnor's result that an FTC (finite total curvature) knot has an isotopic inscribed polygon, we show that any two nearby knotted FTC graphs are isotopic by a small iso…
math.GT2005
Alternating Quadrisecants of Knots
E. Denne
It is known that for every knotted curve in space, there is a line intersecting it in four places, a quadrisecant. Comparing the order of the four points along the line and knot we…
math.GT2004
The Distortion of a Knotted Curve
Elizabeth Denne, John M Sullivan
The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we…