I have been trying to determine the fundamental group of S^2 union a line connecting the north and south pole by using the Seifert Van Kampen Theorem. But every time I try and pick my two subsets U and V they are either not open or not arcwise connected or their intersection isn't particularly nice.(adsbygoogle = window.adsbygoogle || []).push({});

My guess is that the fundamental group should be $\mathbb{Z}$, but other than my intuition, I can't seem to find a way to show this.

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# S^2 union a line connecting the north and south pole

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