Tiling in some nonpositively curved groups
Group Theory
2026-05-14 v2
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.
Keywords
Cite
@article{arxiv.2401.09545,
title = {Tiling in some nonpositively curved groups},
author = {Joseph MacManus and Lawk Mineh},
journal= {arXiv preprint arXiv:2401.09545},
year = {2026}
}
Comments
17 pages. This version: minor corrections. To appear in Trans. Am. Math. Soc