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Let $ X = \mathbb R^3 \setminus A$, where $A$ is a circle. I'd like to calculate $\pi_1(X)$, using van Kampen. I don't know how to approach this at all - I can't see an open/NDR pair $C,D$ such that $X = C \cup D$ and $C \cap D$ is path connected on which to use van Kampen.

Any help would be appreciated. Thanks

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    Try removing an open cylinder passing through the circle.2012-05-22
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    @QiaochuYuan Thanks, but I'm still not seeing it...2012-05-22

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