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.
CITATION STYLE
Denne, E., & Sullivan, J. M. (2008). Convergence and Isotopy Type for Graphs of Finite Total Curvature. In Discrete Differential Geometry (pp. 163–174). Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8621-4_8
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