Seminario T. Grupos UAM-UCM-UC3M-ICMAT

10/3/20, 11:30, Aula 520, UAM

Alejandra Garrido (UC3M)

Title: Molecular gastronomy à la Neretin: a recipe for simple totally disconnected locally compact groups

Abstact: This talk will be a combination of survey and new results; all necessary notions will be defined.  The general theory of totally disconnected locally compact groups (think automorphism groups of locally finite graphs, or  Lie groups over the field of p-adic numbers) has made great advances in the last decade. One of the bottlenecks for further progress is understanding the structure of totally disconnected locally compact groups that are compactly generated (the analogue in this world of finite generation), topologically simple (no continuous nontrivial quotients) and not discrete (the discrete topology is totally disconnected locally compact).


A prototypical example of such a group is Neretin´s group, the group of almost automorphisms of a regular tree. It is also a typical example of a piecewise full group: each element can be obtained by "stitching together" finitely many automorphisms of the tree. Discrete versions of this, topological full groups, have yielded the first examples of finitely generated simple groups with extra properties (amenability -- Juschenko+Monod -- intermediate growth -- Nekrashevych), obtained via groupoids of germs, equivalently, some special kinds of inverse semigroups.

I will report on ongoing work with C. Reid and D. Robertson where we use the piecewise full "recipe" on topological inverse semigroups to obtain many relatives of Neretin´s group.