English

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

R2 v1 2026-06-28T14:19:46.137Z