A note on finiteness properties of vertex stabilisers
Abstract
We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of G G -CW-complexes, given the finiteness properties of the group G G and of the stabilisers of positive dimensional cells. This generalises a result of Haglund–Wise for groups acting on trees to higher dimensions. As an application, for n ≥ 2 n\ge 2 , we deduce the existence of uncountably many quasi-isometry classes of one-ended groups that are of type F P n \mathsf {FP}_n and not of type F P n + 1 \mathsf {FP}_{n+1} .
Fields of Study & Subjects
Commutative Algebra and Its Applications
Rings
Modules
and Algebras
Complexity and Algorithms in Graphs
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 11
- Pages
- 4587–4595
- Publication date
- 15 April 2026
- Language
- EN