Let S be a closed surface and $\gamma$ be a nonseparating simple closed curve. I was told that $\pi_1(S)$ can be written down as an HNN extension of $\pi_1(S\setminus\gamma)$. Why is that true? What is the precise statement?
2026-04-05 18:50:07.1775415007
Nonseparating curve on a surface and HNN extension
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