On the regions bounded by homotopic curves

A. Marden; I. Richards; B. Rodin

doi:10.2140/pjm.1966.16.337

On the regions bounded by homotopic curves

A. Marden, I. Richards, B. Rodin

Research output: Contribution to journal › Article › peer-review

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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)
Pages (from-to)	337-339
Number of pages	3
Journal	Pacific Journal of Mathematics
Volume	16
Issue number	2
DOIs	https://doi.org/10.2140/pjm.1966.16.337
State	Published - Jan 1966
Externally published	Yes

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10.2140/pjm.1966.16.337

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title = "On the regions bounded by homotopic curves",

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.",

author = "A. Marden and I. Richards and B. Rodin",

year = "1966",

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doi = "10.2140/pjm.1966.16.337",

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AU - Rodin, B.

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AB - 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.

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On the regions bounded by homotopic curves

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