Complexity of plane and spherical curves

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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

Original languageEnglish
Pages (from-to)107-118
Number of pages12
JournalDuke Mathematical Journal
Issue number1
StatePublished - May 2009


Dive into the research topics of 'Complexity of plane and spherical curves'. Together they form a unique fingerprint.

Cite this