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 -