Proper actions on finite products of quasi-trees

Abstract

We say that a finitely generated group $G$ has property (QT) if it acts isometrically on a finite product of quasi-trees so that orbit maps are quasi-isometric embeddings. A quasi-tree is a connected graph with path metric quasi-isometric to a tree, and product spaces are equipped with the ${\ell }^1$-metric. As an application of the projection complex techniques, we prove that residually finite hyperbolic groups and mapping class groups have (QT).

Minor changes with a few references added. Accepted by Annales Henri Lebesgue

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