Graph Houghton groups form a genuinely new family of Houghton-type groups with finiteness type F_{r-1} but not FP_r, and with explicit presentations of their pure subgroups.
Finiteness properties of asymptotically rigid handlebody groups
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abstract
We introduce asymptotically rigid mapping class groups of handlebodies and determine their finiteness properties, which vary depending on the space of ends of the underlying handlebody. As it turns out, in some cases, the homology of these groups coincides with the stable homology of handlebody groups, as studied by Hatcher and Wahl.
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Asymptotically rigid mapping class groups of infinite graphs
Graph Houghton groups form a genuinely new family of Houghton-type groups with finiteness type F_{r-1} but not FP_r, and with explicit presentations of their pure subgroups.