I am a condensed matter physicist, and want to understand the [Hopf link][1] from analytic point of view. My question is as follows.

We have two sets of equations, and each set of equations describes a circle in certain space, for example in $\mathbb{R}^3$. In that case, how can we tell from the equations if the two circles are linked, and whether the link is a Hopf link? I want the conditions from analytic geometry point of view.

Could anybody point out some references for this problem?

[1]: http://en.wikipedia.org/wiki/Hopf_link