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Warped cones, (non-)rigidity, and piecewise properties, with a joint appendix with Dawid Kielak
We prove that if a quasi-isometry of warped cones is induced by a map between the base spaces of the cones, the actions must be conjugate by this map. The converse is false in general, conjugacy of actions is not sufficient for quasi-isometry of the respective warped cones. For a …