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Quasi-isometric rigidity of generic cyclic HNN extensions of free groups

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Sam Shepherd (Oxford)

Abstract:
Studying quasi-isometries between groups is a major theme in geometric group theory. Of particular interest are the situations where the existence of a quasi-isometry between two groups implies that the groups are equivalent in a stronger algebraic sense, such as being commensurable. I will survey some results of this type, and then talk about recent work with Daniel Woodhouse where we prove quasi-isometric rigidity for certain graphs of virtually free groups, which include "generic" cyclic HNN extensions of free groups.