English

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.

Keywords

Cite

@article{arxiv.0802.3021,
  title  = {Complexity of planar and spherical curves},
  author = {Tahl Nowik},
  journal= {arXiv preprint arXiv:0802.3021},
  year   = {2008}
}
R2 v1 2026-06-21T10:14:30.637Z