Originally Posted by

**DJDorianGray** Hi all,

So I have read the theory of fundamental groups on a couple of introductory textbooks, but I still don't have the slightest idea of how I would go about finding the fundamental group of a path connected space. For example:

"Find the fundamental group of $\displaystyle \mathbb{R}^3 \backslash l$, where $\displaystyle l$ is a line".

Could anyone help me through this? I guess I should try to show that the space is homotpy equivalent to something whose group is well-known, such as $\displaystyle S^1$ right? The truth is I don't know where to start. Any help is really appreciated. Thanks.