Complexity of planar and spherical curves

Details Complexity of planar and spherical curves Complexity of planar and spherical curves

2008-02-21

arxiv.org/abs/0802.3021v1

Mathematics

Geometric Topology

Scientific paper

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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