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Topological full groups of etale groupoids Hiroki Matui

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Topological full groups of etale groupoids Hiroki Matui

Abstract: One can construct etale groupoidsGfrom various topological dynamics on Cantor setsX. The topological full group [[G]] ofGis a subgroup ofHomeo(X) consisting of all homeomorphisms whose graph is ‘contained’ in the groupoid G as a compact open subset. In recent years, it has been found that the group [[G]]

possesses several interesting properties. First, I will explain that whenGarise from minimal Z–actions, [[G]] provide us finitely generated, simple, amenable, infinite groups. Next, for G arising from one-sided SFT, I will show that [[G]] is of type F∞and its commutator subgroup is simple. This is regarded as a generalization of Higman-Thompson groups.

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