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.
That result was recently generalized to finite total curvature knots REF .
Convergence and isotopy type for graphs of finite total curvature
In “Discrete Differential Geometry”, Birkhäuser
Mathematics