Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Nicolaus Heuer
Affiliation:

University of Oxford
Date:

Fri, 2019-02-01 11:00 - 12:00 Stable commutator length ($\mathrm{scl}$) is a well established invariant of elements $g$ in the

commutator subgroup (write $\mathrm{scl}(g)$) and has both geometric and algebraic meaning.

Many classes of "non-positively curved" groups have a gap in stable commutator length: This is, for every non-trivial element $g$, $scl(g) > C$ for some $C > 0$. This gap may be thought of as an algebraic injectivity radius and can be found in hyperbolic groups, Baumslag-solitair groups, free products and Mapping Class Groups. 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 $1/2$.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/9098