Stable commutator length in 3-manifolds

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.