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.
Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps
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abstract
Motivated by the recent work of Algom-Kfir and Bestinva introducing the mapping class group of an infinite graph via proper homotopy equivalences, we give a necessary and sufficient condition for a surface to be properly homotopy equivalent to a graph. We consider second-countable orientable surfaces that are possibly infinite-type and have noncompact boundary. For surfaces proper homotopy equivalent to graphs, we explore the basic properties of the induced map between the mapping class groups of the surface and the graph. We view this induced map as the basis of a Dehn-Nielsen-Baer analog in the setting of infinite-type surfaces.
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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.