Notation:
$L/K$, finite extension of global fields
$K^\times$, unit group of $K$
$L^\times$, units group of $L$
$\mathbb{A}_L^\times$, ideles of $L$
$N_{L/K}$, the norm map
The knot group of an extension of global fields $L/K$ is defined as the quotient group of 'local norms' by 'global norms': $$\mathfrak{K}(L/K):=\frac{K^\times \cap N_{L/K}(\mathbb{A}_L^\times)}{N_{L/K}(L^\times)}.$$
Question: In what way is this related to knots?
Remarks: 1. The terminology knot group appears to have been introduced by Arnold Scholz, in the papers Totale Normenreste, die keine Normen sind, als Erzeuger nichtabelscher Körpererweiterungen. Part I (1936), Part II (1940). (I have not looked into these papers yet.)
2. I don't think this is related to the usual analogy between knots and number fields (but I could be wrong). For example, the usual knot group of a knot $\mathcal{K}$ in $S^3$ is the fundamental group $\pi_1(S^3\setminus \mathcal{K})$. The analog of this should be something like $\pi_1(\text{Spec}(\mathcal{O}_K)\setminus \mathfrak{p})$, where $\mathcal{O}_K$ is the ring of integers of a global field $K$ and $\mathfrak{p}\subset \mathcal{O}_K$ is a prime ideal.
