TY - JOUR
T1 - Complexity of plane and spherical curves
AU - Nowik, Tahl
PY - 2009/5
Y1 - 2009/5
N2 - We show that the maximal number of singular moves required to pass between any two regularly homotopic plane or spherical curves with at most n crossings grows quadratically with respect to n. Furthermore, for any two regularly homotopic curves with at most n crossings, there exists such a sequence of singular moves, satisfying the quadratic bound, for which all curves along the way have at most n+2 crossings. 2009
AB - We show that the maximal number of singular moves required to pass between any two regularly homotopic plane or spherical curves with at most n crossings grows quadratically with respect to n. Furthermore, for any two regularly homotopic curves with at most n crossings, there exists such a sequence of singular moves, satisfying the quadratic bound, for which all curves along the way have at most n+2 crossings. 2009
UR - http://www.scopus.com/inward/record.url?scp=70449713737&partnerID=8YFLogxK
U2 - 10.1215/00127094-2009-022
DO - 10.1215/00127094-2009-022
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AN - SCOPUS:70449713737
SN - 0012-7094
VL - 148
SP - 107
EP - 118
JO - Duke Mathematical Journal
JF - Duke Mathematical Journal
IS - 1
ER -