Complexity of planar and spherical curves
Geometric Topology
2008-02-22 v1
Abstract
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.
Cite
@article{arxiv.0802.3021,
title = {Complexity of planar and spherical curves},
author = {Tahl Nowik},
journal= {arXiv preprint arXiv:0802.3021},
year = {2008}
}