RAAGs and Stable Commutator Length

17 January 2018
Nicolaus Heuer

Stable commutator length (scl) is a well established invariant of group elements g  (write scl(g)) and  has both geometric and algebraic meaning.

It is a phenomenon that many classes of non-positively curved groups have a gap in stable commutator length: For every non-trivial element g, scl(g) > C for some C>0. Such gaps may be found in hyperbolic groups, Baumslag-solitair groups, free products, Mapping class groups, etc. 
However, the exact size of this gap usually unknown, which is due to a lack of a good source of “quasimorphisms”.

In this talk I will construct a new source of quasimorphisms which yield optimal gaps and show that for Right-Angled Artin Groups and their subgroups the gap of stable commutator length is exactly 1/2. I will also show this gap for certain amalgamated free products.

  • Junior Topology and Group Theory Seminar