Convergence and isotopy type for graphs of finite total curvature

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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.
12 pages, 3 figures; final version, to appear in "Discrete Differential Geometry", Oberwolfach Seminars 38, Birkhauser, 2008

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Geometric Topology, 57M25 (Primary); 05C10, 57M15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/140647

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606008
 http://arxiv.org/abs/math/0606008

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arXiv