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

Posted in

- Talk [1]

Speaker:

Jaroslaw Kedra
Affiliation:

U of Aberdeen
Date:

Thu, 31/10/2013 - 16:30 - 17:30 Let G be a normally finitely generated group and let |g| be the conjugation invariant word norm of an element g of G. We are interested in the growth rate of the function n --> |g^n|. A priori this can be anything between bounded and linear. I will show that for many classes of groups there is a dichotomy: |g^n| is either bounded or linear. The groups for which this is true include: braid groups, Coxeter groups, right-angled Artin groups, mapping class groups of closed surfaces, lattices in simply connected solvable Lie groups, Baumslag-Solitar groups, hyperbolic groups, SL(n,Z) and some other lattices. I know no finitely presented group which does not satisfy the above dichotomy (there is a finitely generated example). I don't know if the dichotomy holds for lattices in semisimple Lie groups. This is a recent joint work with M.Brandenbursky, S.Gal and M.Marcinkowski: http://arxiv.org/abs/1310.2921 [4]

**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/3050

[4] http://arxiv.org/abs/1310.2921