On the regions bounded by homotopic curves

A. Marden, I. Richards, B. Rodin

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We give a short proof of the following theorem of H. I. Levine [2]: Let A? and B be nonintersecting simple closed curves on an orientable surface S (compact or not). (i) If A? is homotopic to zero, then A bounds a closed disk in S. (ii) If A and B are freely homotopic but not homotopic to zero then A ∪ B? bounds a closed cylinder in S.

Original languageEnglish (US)
Pages (from-to)337-339
Number of pages3
JournalPacific Journal of Mathematics
Volume16
Issue number2
DOIs
StatePublished - Jan 1966

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