Simple locally compact groups from full groups and branch groups (Alejandra Garrido, Universidad Complutense de Madrid)

28.05.2024 10:30

Since the start of the century there has been increased interest in totally disconnected locally compact (tdlc) groups and a structure theory is starting to emerge. A special role is played by the class S of tdlc groups that are compactly generated, topologically simple and not discrete. The theory is in need of more examples with a view to some sort of classification.
Full groups of homeomorphisms of Cantor space are a rich source of simple groups. In joint work with Colin Reid, it is shown that, given the right conditions on the "seed" group, the full group can be given a totally disconnected locally compact topology and it contains a big simple compactly generated subgroup. An example of this is Neretin's group of almost automorphisms of a tree. Further examples include commensurators of profinite regular branch groups and full groups of Burger-Mozes universal groups.
It is also shown that this construction accounts for all groups in one of the five types of groups in S, up to local isomorphism (the totally disconnected analogue of having the same Lie algebra in the connected case).
I will focus more on the examples than on the theory, since we are looking for more examples than those above.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 28.05.24, Séminaire "Groupes et géométrie"

entrée libre