Classifying spaces for knots: new bridges between knot theory and algebraic number theory

In this thesis we discuss how, in the context of knot theory, the classifying space of a knot group for the family of meridians arises naturally. We provide an explicit construction of a model for that space, which is particularly nice in the case of a prime knot. We then show that this classifying space controls the behaviour of the finite branched coverings of the knot. We present a 9-term exact sequence for knot groups that strongly resembles the Poitou-Tate exact sequence for algebraic number fields. Finally, we show that the homology of the classifying space behaves towards the former sequence as Shafarevich groups do towards the latter.