Dynamical Alternating Groups

Abstract: Topological full groups form a very important class of groups arising from dynamical systems and, more generally, étale groupoids. Their subgroups, especially the alternating subgroup, have been proven to exhibit various properties, some of which were rarely or never before witnessed. In this talk I will introduce these groups in the dynamical setting and go through some of the most important past results on the topic, focusing on those of operator-algebraic interest. I will then briefly introduce the concept of almost finiteness and present a recent result obtained in joint work with Petr Naryshkin. We prove that if a subgroup of a TFG is amenable and contains the alternating subgroup, then all its free actions on finite-dimensional compact metrizable spaces are almost finite.

functional analysisoperator algebras

Audience: advanced learners

Functional analysis and operator algebras in Athens

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