Convergence and isotopy type for graphs of finite total curvature

Elizabeth Denne; John M Sullivan

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arXiv · math/0606008

Convergence and isotopy type for graphs of finite total curvature

Elizabeth Denne·John M Sullivan

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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.

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BibTeX RIS

Elizabeth Denne, John M Sullivan. 2007-10-24. Convergence and isotopy type for graphs of finite total curvature. https://arxiv.org/abs/math/0606008

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