I am reading A quick trip through knot theory (link to pdf!) by R.H. Fox, in particular the section of branched covering (section 8 pag. 26 into the document). When he describes his algorithm to find the fundamental group of a branched covering, he says he considers a g-frame. What is a g-frame?
I report here the relevant part of the section:
EDIT Reading carefully the section, I have understood that the g is the number of branches of the covering. So my question no is: what is a frame?
What I gathered by trying to follow the proof (and also by studying the second figure on the page), is that a $g$-frame is $g$ intervals with their first endpoints all identified. Or in other words, a cone on $g$ points. The first figure on the page is meant to illustrate this topological space:
Fox's idea was to glue this into $\Sigma-\Lambda$, which only changes the fundamental group by a free product by a free group, to avoid needing to choose representative paths to the points $p_0,\dots,p_{g-1}$ lying over the basepoint in the covering space $\Sigma-\Lambda$.
In other words, if $\pi:\Sigma-\Lambda\to S-L$ is the covering map and $*\in S-L$ is the chosen basepoint, then what Fox does is construct a new space $(\Sigma-\Lambda)\cup C\pi^{-1}(*)$, where $C\pi^{-1}(*)$ denotes the cone of the set $\pi^{-1}(*)$, and the union is meant to identify $\pi^{-1}(*)\subset \Sigma-\Lambda$ with $\pi^{-1}(*)\subset C\pi^{-1}(*)$. He "coned off" a fiber.
For completeness, here is the second figure on the page, showing the covering along with the attached "$g$-frame":