From the 1 of 6 linked papers with an AI index.
6 papers
Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps
Ryan Dickmann, Hannah Hoganson, Sanghoon Kwak
The paper characterizes which second‑countable orientable surfaces (possibly of infinite type with non‑compact boundary) are properly homotopy equivalent to graphs, and studies the…
Coarse geometry of homeomorphism groups: Classifying countable Stone spaces
George Domat, Hannah Hoganson, Robert Alonzo Lyman
Towards developing the tools of geometric group theory for non-locally compact topological groups, we give one of the first complete classifications of a family of such groups up t…
A new construction of subgroups of big mapping class groups
Carolyn R. Abbott, Hannah Hoganson, Marissa Loving +2
We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solit…
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…
Constructing reducibly geometrically finite subgroups of the mapping class group
Tarik Aougab, Harrison Bray, Spencer Dowdall +3
In this article, we consider qualified notions of geometric finiteness in mapping class groups called parabolically geometrically finite (PGF) and reducibly geometrically finite (R…
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…