Il seminario dei baby geometri di questa settimana si terrà domani Martedì 23 Aprile alle 14.30 in Aula Riunioni. Manousos Manouras (Université de Pau / Universidad de Zaragoza) parlerà di "Alexander type invariants of line arrangements". Di seguito l'abstract.

There have been various definitions of the Alexander invariants of a knot. Following some

of these definitions one can generalise them so as to have coefficients twisted by a linear

representation. The Alexander type invariants are known to detect non-trivial topological

information(genus, hyperbolic volume of a knot etc). The twisted Alexander polynomial was

introduced by Wada for knots and has been studied thereafter for more general manifolds

as the complement of algebraic curves or line arrangements. We will discuss the relation

of the twisted Alexander polynomial of the exterior manifold of a line arrangement and

the twisted Alexander polynomial of its boundary manifold. We will present how using

twisted Alexander polynomials induced by reducible representations, we can retract nontrivial

topological information.

We will also deal with the characteristic varieties of line arrangements, studied by various

authors such as Zariski, Libgober, Artal. The main problem is to understand if the characteristic

varieties are combinatorially determined in general. This is known to be true for their

”homogeneous part”, which corresponds to the resonance variety, as well as for the translated

components having dimension at least one, as they are determined by orbifold pencils.

This does not work in the same way for the 0-dimensional translated components. Here

we present examples such that the characteristic variety has some translated 0-dimensional

global component.