Convergence and Isotopy Type for Graphs of Finite Total Curvature
Elizabeth Denne, John M. Sullivan · Birkhäuser Basel eBooks · 2008
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 isotopy. We also show how to obtain sharper constants when the starting curve is smooth. We apply our main theorem to prove a limiting result for essential subarcs of a knot.