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Accessibility of partially acylindrical actions

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A graph of groups is a common way of decomposing a group into subgroups. Suppose we are given a group G. A natural question to ask is if there is some bound on the complexity on a graph of groups decomposition for G. A basic example of a result in this direction is due to Dunwoody, who gives a bound for finitely presented groups on the number of edges given that every edge group is finite. Conversely there is no such bound for a general finitely generated group; again shown by Dunwoody. The purpose of this talk is to show that a similar bound exists for groups which act acylindrically on the corresponding Bass-Serre tree except on a class of subgroups with “bounded height”.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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