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What does one point compactification of singly, doubly, triply punctured plane $\mathbb{R}^2$ look like? What would their fundamental groups look like? I'm trying to visualize but can't seem to draw it out.

sas
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chris c
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    The punctured plane is (topologically) a cilinder. Viewing it this way, looks like its one point compactification is $S^2$ with north and south poles identified. About its fundamental group, check http://math.stackexchange.com/questions/20282/fundamental-group-of-s2-with-north-and-south-pole-identified . – Ugo Iaba Jan 14 '15 at 15:32
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    The plane $\Bbb R^2$ is the same as a sphere $S^2$ with one point missing, for example $(1,0,0)$. So an $n$-punctured plane is like a sphere with $(n+1)$ points missing, you could take the $(n+1)$-th roots of unity on the circle $S^1$ which is the equator of $S^2$. For the one point compactification, you fill in these points and then identify all of them. – Stefan Hamcke Jan 14 '15 at 15:44

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