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Seifert-Van Kampen Theorem Application

Mathematics Asked on February 1, 2021

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Given above diagram how can we calculate the fundamental group? I thought we could apply Seifert-Van Kampen. Thus we need to decide open path connected $U$ and $V$. What is a good choice for $U$ and $V$? Here is my attempt.

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I don’t know how to calculate the fundamental group of $V$.

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