Titu's homotopies of normal curves

George K. Francis

Research output: Contribution to journalArticlepeer-review


A regular homotopy of a plane immersion of the circle, each of whose stages is a normal curve with the exception of a finite number of stages of the homotopy presenting a nonnegative convex double point self tangency or a transverse triple point, preserves the number of topologically inequivalent extensions of the immersion to an orientation preserving immersion of the disk. Extensions to properly interior mappings of the disk are similarly investigated.

Original languageEnglish (US)
Pages (from-to)511-518
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Nov 1971
Externally publishedYes


  • Branch point
  • General position
  • Intersection sequence
  • Light-open maps
  • Monotone homotopy
  • Normal immersions
  • Properly interior maps
  • Regular homotopy
  • Topological equivalence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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