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Let $Y$ be a compact Riemann surface of genus $0$, let $B$ be a finite set of points in $Y$, and let $y_0$ be a point in $Y$ that is not in $B$.

Standard generators for the fundamental group $\pi_1(Y - B, y_0)$ are obtained by taking the homotopy classes of loops indexed by $b\in B$ that start at $y_0$ and make a counterclockwise loop about $b$ containing no other elements of $B$. This construction associates a generator to each element of $B$ (there will typically be relations among these generators).

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• Review status: reviewed
• Last edited by Andrew Sutherland on 2018-07-08 22:21:33
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