Topological models of finite type for tree almost automorphism groups

We show that tree almost automorphism groups, including Neretin groups, satisfy the analogue of the $F_\infty$-finiteness condition in the world of totally disconnected groups: They possess a cellular action on a contractible cellular complex such that the stabilizers are open and compact and the restriction of the action on each $n$-skeleton is cocompact.

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