Abstract: Commutator length is a group theoretical analogue of genus. By taking a limit, stable commutator length, scl, is obtained. This is a group invariant for studying metric properties of bounded group cohomology, and detects the existence of surface subgroups. There are open questions regarding computability of scl and the structure of its unit norm ball. This talk will give some background on scl in low dimensional topology, and will outline work in progress of the speaker towards resolving these questions for closed surface and 3-manifold groups.