Tiling in some nonpositively curved groups

Abstract

We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every group is monotileable. In particular, one-relator groups and many Artin groups are monotileable.

17 pages. This version: minor corrections. To appear in Trans. Am. Math. Soc