Abelian splittings of pro-p right angled Artin groups
Beauville structures for quotients of infinite Grigorchuk-Gupta-Sidki groups acting on the pn-adic tree
Groups of surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called Beauville structure. Gul and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, that act on the p-adic tree, admit Beauville structures. We extend their result by showing that quotients of infinite periodic GGS-groups, that act on the pn-adic tree, also admit Beauville structures for all primes p and positive integers n. This is joint work with Elena Di Domenico and Şükran Gül.
The goal of this seminar is to give an introduction to Bass-Serre theory, a branch of modern geometric group theory which studies structural properties of groups by exploiting their action on trees. See the programme for more details.
Main references:
Amalgams and fixed points
The tree of SL2 over a local field I
The tree of SL2 over a local field II
Profinite graphs and pro-p trees
Pro-p groups acting on pro-p trees
Totally disconnected locally compact groups
Mixed Topics
Word Growth in Groups
Bass-Serre Theory and Profinite Analogues
p-Adic analytic pro-p groups
Invariant random subgroups
Probabilistic methods in group theory
Buildings