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Convergence and isotopy type for graphs of finite total curvature

Research paper by Elizabeth Denne, John M Sullivan

Indexed on: 24 Oct '07Published on: 24 Oct '07Published in: Mathematics - Geometric Topology



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.