CMSA Freedman Seminar: 4-manifold topology and collision rank of groups

I will introduce collision rank and show that groups of finite collision rank are good in the sense of topological 4-manifold theory. Finitely generated groups of collision rank two are shown to exist outside the class of subexponentially amenable groups. I will describe examples given by commutator subgroups of topological full groups of Sturmian systems, they include continuum many pairwise nonisomorphic infinite simple amenable groups.

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