Translation-like actions yield regular maps

Abstract

For finitely generated groups $H$ and $G$, we observe that $H$ admits a translation-like action on $G$ implies there is a regular map, which was introduced in Benjamini, Schramm and Timár's joint paper, from $H$ to $G$. Combining with several known obstructions to the existence of regular maps, we have various applications. For example, we show that the Baumslag-Solitar groups do not admit translation-like actions on the classical lamplighter group.

6 pages. Comments welcome!

Cited by in corpus (1)

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