The monodromy group of a positive braid

Livio Ferretti (University of Geneva)

Monday 20th November, 2023 16:00-17:00 Maths 311B

Abstract

The geometric monodromy group is a classical yet rather poorly understood topological invariant of isolated plane curve singularities. In this talk we will discuss a generalization of it to the setting of positive braids, and see how working in this wider context can help understanding the original invariant of singularity theory. In particular we obtain that, for irreducible singularities not of type A_n, up to finitely many exceptions the geometric monodromy group is determined by two simple knot invariants: the genus and the Arf invariant. Our main technical tools are invariant framings on the surface, and we end discussing some questions concerning the use of such tools for studying more general fibred links.

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