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 |
Externally published | Yes |