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arXiv · 2401.09545

Tiling in some nonpositively curved groups

Joseph MacManus·Lawk Mineh
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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.

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Joseph MacManus, Lawk Mineh. 2024-01-17. Tiling in some nonpositively curved groups. https://arxiv.org/abs/2401.09545

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