Convergence and isotopy type for graphs of finite total curvature
Geometric Topology
2007-10-24 v2
Abstract
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.
Cite
@article{arxiv.math/0606008,
title = {Convergence and isotopy type for graphs of finite total curvature},
author = {Elizabeth Denne and John M Sullivan},
journal= {arXiv preprint arXiv:math/0606008},
year = {2007}
}
Comments
12 pages, 3 figures; final version, to appear in "Discrete Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 2008