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math.GR2024★ 1 cited
Graphical models for topological groups: A case study on countable Stone spaces
Beth Branman, George Domat, Hannah Hoganson +1
By analogy with the Cayley graph of a group with respect to a finite generating set or the Cayley--Abels graph of a totally disconnected, locally compact group, we detail countable…
math.GT2024
Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps
Ryan Dickmann, Hannah Hoganson, Sanghoon Kwak
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 sufficien…
math.LO2024
The Complexity of Proper Homotopy Equivalence of Graphs
Hannah Hoganson, Jenna Zomback
We demonstrate that the proper homotopy equivalence relation for locally finite graphs is Borel complete. Furthermore, among the infinite graphs, there is a comeager equivalence cl…