extra discs $D_{0}$ and $D_{1}$. The invariant thus constructed will depend on the initial curve and on a choice of a **homotopy class for the swaddling map $\beta$**.

2.  We may look at the linking number of two copies of the knot, when the second copy is “pushed off” to a distance of $\varepsilon$ from the first copy, and calculate what happens as $\varepsilon\rightarrow 0$. But this linking number will depend on **which direction** we decided to push off the second copy of the knot in relation to the first copy at each point, which implicitly specifies a knot framing. As $\epsilon\rightarrow 0$, the limit will not necessarily be an integer, forcing the introduction of a framing dependant correction term which will turn out to be the total holonomy of the curve. The invariant thus constructed will depend on the initial curve, along with a choice of **framing** for it.

It is not at all clear at first what these two constructions should have to do with one another. The aim of this note is to present both approaches in a clear and accessible fashion, and to showing how they relate in basic differential geometric terms. We are not trying 