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arxiv: 0802.3021 · v1 · submitted 2008-02-21 · 🧮 math.GT

Complexity of planar and spherical curves

classification 🧮 math.GT
keywords curvescrossingsplanarsphericalalongcomplexitydonefurthermore
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We show that the maximal number of singular moves required to pass between any two regularly homotopic planar or spherical curves with at most n crossings, grows quadratically with respect to n. Furthermore, this can be done with all curves along the way having at most n+2 crossings.

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