4 citations · 10 across the 10 of their papers we have counts for
10 papers
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…
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…
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…
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…
Generating Sets and Algebraic Properties of Pure Mapping Class Groups of Infinite Graphs
George Domat, Hannah Hoganson, Sanghoon Kwak
We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pur…
The Automorphism Group of the Infinite-Rank Free Group is Coarsely Bounded
George Domat, Hannah Hoganson, Sanghoon Kwak
We prove that the full automorphism group and the outer automorphism group of the free group of countably infinite rank are coarsely bounded. That is, these groups admit no continu…
Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs
George Domat, Hannah Hoganson, Sanghoon Kwak
We discuss the large-scale geometry of pure mapping class groups of locally finite, infinite graphs, motivated by recent work of Algom-Kfir--Bestvina and the work of Mann--Rafi on…
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…
Groups with Context-Free Co-Word Problem and Embeddings into Thompson's Group
Rose Berns-Zieve, Dana Fry, Johnny Gillings +2
Let be a finitely generated group, and let be a finite subset that generates as a monoid. The \emph{word problem of with respect to } consists of all words in th…