Buongiorno,

Vi ricordo che il prossimo seminario di Geometria e Topologia sarà tenuto da Elia Fioravanti e si terrà Giovedì 30 Gennaio alle ore 14:30 presso l'aula Riunioni.

Per gli interessati ad andare a pranzo con lo speaker, l'appuntamento è in atrio alle 13:00.

Allego titolo e abstract

Titolo: Growth of automorphisms of special groups

Abstract: Given a (nice) group G, we are interested in how fast the length of a group element can grow when we apply powers of a given outer automorphism of G. If the group G is free or the fundamental group of a closed surface, classical train-track techniques give a complete and precise picture. This can be extended to automorphisms of all negatively curved (a.k.a. Gromov hyperbolic) groups G, using Rips-Sela theory and the canonical JSJ decomposition. Very little seems to be known beyond this setting. We study this problem for a broad class of non-positively curved groups: "virtually special" groups in the Haglund-Wise sense. In this setting, we prove that:

(1) the stretch factor of any automorphism is an algebraic integer;

(2) if the automorphism is untwisted, then it admits only finitely many growth rates, each of these is polynomial-times-exponential, and there is a Nielsen-Thurston decomposition.

A presto,

Carlo e Filippo