Can we put arrows in RAAGs?
In the realm of Geometric Group Theory, the family of right-angled Artin groups has gained more and more importance through the years. They generalize at the same time both free and free abelian groups, and moreover their combinatorial nature has led to proving important results. On top of that, they also have a rich geometric nature. But what happens if we put some arrows in the defining graph of a RAAG? During this seminar we will discuss the consequences of such decision and we will see the analogies and the differences between classical and oriented RAAGs. We will also briefly talk about the family of hypercubical groups, to which both RAAGs and oriented RAAGs belong. If time permits, we will also see some results related to the pro-2 completion of an oriented RAAG. Most of this is a joint work with S. Blumer, I. Foniqi, C. Quadrelli and T. Weigel.