Link Conditions for the Haagerup Property

Abstract

We provide a condition on the links of a polygonal complex X that is sufficient to ensure Aut(X) has the Haagerup property, and hence so do any closed subgroups of Aut(X) (in particular, any group acting properly on X). We provide an application of this work by considering the group of automorphisms of simply-connected triangle complexes where the link of every vertex is isomorphic to the graph F090A, as constructed by Świątkowski.

arXiv comment21 pages, V2: typos correctex. arXiv admin note: text overlap with arXiv:2012.09019