### 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 language | English (US) |
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Pages (from-to) | 337-339 |

Number of pages | 3 |

Journal | Pacific Journal of Mathematics |

Volume | 16 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1966 |

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## Cite this

Marden, A., Richards, I., & Rodin, B. (1966). On the regions bounded by homotopic curves.

*Pacific Journal of Mathematics*,*16*(2), 337-339. https://doi.org/10.2140/pjm.1966.16.337