Abstract: 

From the question whether a given 3-manifold is a surface bundle over the circle, we get a group theoretic analogue which asks if certain subgroups of the fundamental group are finitely generated. It might be surprising that for groups, being finitely generated does usually not pass to subgroups. Sigma theory (also known as BNS invariants) is a classical tool to find the finiteness properties of a given normal subgroup - but only, if the quotient by that subgroup is abelian. In this talk, I will explain about Sigma theory and present a method to get around the restriction of abelian quotients. We will also see some applications where a generalised Sigma theory is useful.