A note on finiteness properties of vertex stabilisers

2025/02/20 by Li, Kevin, Saldaña, Luis Jorge Sánchez
#20F65 #20J05 #57M07 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2502.14751

Abstract

We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of G-CW-complexes, given the finiteness properties of the group 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, we deduce the existence of uncountably many quasi-isometry classes of one-ended groups that are of type FP_n and not of type FP_n+1.

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