On Positive Braids, Monodromy Groups and Framings
Geometric Topology
2025-03-12 v3 Algebraic Geometry
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.
Cite
@article{arxiv.2111.08150,
title = {On Positive Braids, Monodromy Groups and Framings},
author = {Livio Ferretti},
journal= {arXiv preprint arXiv:2111.08150},
year = {2025}
}
Comments
46 pages, 57 figures; final version, accepted for publication; improved exposition, added details and figures in the proof of Prop.5.2