Séminaires : Séminaire Géométrie et Topologie

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ

The topology of plane algebraic curves, initiated by the work of Enriques and Zariski.

The fundamental group of their complement is a natural invariant, strong enough to show that the combinatorial description of the curve may not determine its embedding.

The twisted Alexander polynomials provide an accessible invariant of the group, still very sensitive to these phenomena.

Our work lies at the intersection of low-dimensional topology, representation theory, and algebraic geometry.

We study twisted Alexander polynomials, focusing on the reducible non-abelian SL2 (C) representations.

We describe a geometric parametrization of all such metabelian families as projective varieties whose dimensions are governed by characteristic varieties.

Within this framework, we obtain new divisibility relations for the corresponding twisted Alexander polynomials and explain geometrically that they vary across reducible strata.

In the case of plane algebraic curves, we show that these invariants can be computed explicitly and that their variation is controlled by a finite linear stratification of the reducible non-abelian representation variety (up to conjugation), on which the Reidemeister torsion remains locally constant.