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math.GR2025
Largest acylindrical actions of free-by-cyclic groups
Monika Kudlinska, Harry Petyt
We show that every finitely generated free-by-cyclic group admits a largest acylindrical action on a hyperbolic space obtained by coning off maximal product subgroups of $G…
math.GT2025
Stable cylinders and fine structures for hyperbolic groups and curve graphs
Harry Petyt, Davide Spriano, Abdul Zalloum
In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve grap…