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Groups acting properly on (products of) hyperbolic graphs

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A group with a geometric action on some hyperbolic space is necessarily word hyperbolic. We might therefore ask what can be said if we relax this to acting properly by isometries but every countable group acts (metrically) properly on a locally finite hyperbolic graph.

We will investigate what happens when we restrict the space being acted on, for instance to (finite products of) quasitrees, combined with finiteness conditions on the group (being finitely generated) and/or the action (having a locally finite orbit).

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

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