On Positive Braids, Monodromy Groups and Framings

Abstract

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.

46 pages, 57 figures; final version, accepted for publication; improved exposition, added details and figures in the proof of Prop.5.2

References in corpus (4)

• Vanishing cycles, plane curve singularities, and framed mapping class groups
• Checkerboard graph monodromies
• On the genus defect of positive braid knots
• Curves intersecting in a circuit pattern