Geometry of Arrangements

Recently, Cuntz and Kühne introduced the class of a connected subgraph arrangements. This encompasses such classical families as the Shi arrangements in type A and the braid arrangements. Cuntz and Kühne were able to classify all free, supersolvable, factored and simplicial members among them. We revisit this class and investigate some additional properties. In particular, we study the question of asphericity within this class. This is a report on recent joint work with Giordani, Möller and Mücksch.