Hi, let ## \alpha, \gamma ## be non-isotopic curves in a compact, oriented surface S. There is a result to the effect that ## S-\alpha## is homeo. to ## S- \gamma ## . This is not true as stated; we can , e.g., remove a disk (trivial class) in a copy of S and then remove a meridian ( a generator of ## H^1 (T^2) ##). Does anyone know the corrected result? This is not true either if we only remove essential curves. It seems like if ##\alpha, \gamma## actually _were_ isotopic , then this would be true. Or maybe if they were homologous?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks.

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# Complements of Curves in Closed Surfaces: Homeomorphic?

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