Geometry and Topology Seminar

The stable commutator length (scl) is a relative version of the Gromov-Thurston norm. It is a group invariant sensitive to geometric and dynamical properties. Scl can be used to understand homomorphism rigidity and to find surface subgroups. The latter problem is related to the rationality of scl, and the former is about lower bounds.

In this talk, we will discuss the computation and rationality of scl in certain groups acting on trees by linear programming. In the special case of Baumslag-Solitar groups, we will see a convergence to scl in free groups resembling the convergence of metrics under hyperbolic Dehn surgeries. If time permits, I will also briefly explain lower bounds of scl in 3-manifold groups and right-angled Artin groups, which is joint work with Nicolaus Heuer.