%0 Journal Article
%T Convergence and isotopy type for graphs of finite total curvature
%A Elizabeth Denne
%A John M Sullivan
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0606008v2