Málstofa: Matthias Hamann

Ágrip: The notion of hyperbolicity for metric spaces, graphs and groups is a topic that got a lot of attention since Gromov’s seminal paper. While there have been several attempts to obtain a similar notion for monoids, Gray and Kambites were the first who offered a geometric notion of hyperbolic monoids based on thin geodesic triangles in the Cayley digraphs that took the directions of edges into account. We will pick up this notion of hyperbolic monoids and digraphs and discuss its interaction with quasi-isometries and thereby give a partial answer to a problem of Gray and Kambites. Furthermore, we will define a suitable hyperbolic boundary and discuss some of its properties and we will talk about free submonoids of hyperbolic monoids.