  We associate to every positive braid a braid monodromy group, generalizing
the geometric monodromy group of an isolated plane curve singularity. If the
closure of the braid is a knot, we identify the corresponding group with a
framed mapping class group. In particular, this gives a well defined knot
invariant. As an application, we obtain that the geometric monodromy group of
an irreducible singularity is determined by the genus and the Arf invariant of
the associated knot.
