- #1

- 5

- 0

## Main Question or Discussion Point

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.

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.

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.