A new alternative for amenable groups acting on finite-dimensional CAT(0)-spaces

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• Anders Karlsson (Université de Genève)
• Thursday 04 September 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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OGGW02 - Actions on graphs and metric spaces

In this talk I will discuss a new alternative for finitely generated amenable groups acting by isometry on finite-dimensional CAT -spaces, first established together with H. Izeki for Liouville groups and then extended to the amenable case in a forthcoming joint work with H. Izeki, R. Ji and Y. Wu. Given a finitely generated amenable group, either every action on a finite-dimensional complete CAT -space has a fixed point or the group has an action on a Euclidean space without a fixed point. The alternative implies that amenable torsion groups and simple amenable groups (such as important classes of groups constructed by Grigorchuk, Juschenko-Monod, Matte Bon, Nekrashevych, and others) cannot act on any finite-dimensional CAT -space without having a global fixed point.

This talk is part of the Isaac Newton Institute Seminar Series series.

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