The Thurston norm of a 3-manifold M measures the minimal topological complexity of a surface dual to a character of M . In this talk, we will introduce a real-valued function on the first cohomology of an arbitrary group which generalises the Thurston norm. We will propose a strategy for proving that such a function defines a seminorm using the theory of L2-invariants. Finally, we will implement this strategy for some classes of right-angled Artin groups.