Right-angled Artin groups are perhaps the most ubiquitous manifestations of polyhedral products in geometric group theory and low-dimensional topology. The theory of their subgroups has been of great importance in the last couple of decades. This is especially true with regards to what are known as ‘finiteness properties’ – meaningful criteria for measuring ways in which infinite groups may behave like finite ones – as well as the theory of three-dimensional manifolds. We will visit some celebrated theorems and, if time allows, discuss problems arising from deck transformations of branched covering maps.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Polyhedral Products: a Path Between Homotopy Theory and Geometric Group Theory.
