4 citations · 14 across the 14 of their papers we have counts for
14 papers
Asymptotically conformal and asymptotically rigid mapping class groups
Javier Aramayona, George Domat, Christopher Leininger
We give conditions ensuring that an asymptotically rigid mapping class group, specifically a surface Houghton group , has finite index in the asymptotically conform…
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…
The infinite dimensional geometry of conjugation invariant generating sets
Sabine Chu, George Domat, Christine Gao +2
We consider a number of examples of groups together with an infinite conjugation invariant generating set, including: the free group with the generating set of all separable elemen…
Classification of Stable Surfaces with respect to Automatic Continuity
Mladen Bestvina, George Domat, Kasra Rafi
We provide a complete classification of when the homeomorphism group of a stable surface, , has the automatic continuity property: Any homomorphism from Homeo to a separabl…
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…
Isomorphisms and commensurability of surface Houghton groups
Javier Aramayona, George Domat, Christopher J. Leininger
We classify surface Houghton groups, as well as their pure subgroups, up to isomorphism, commensurability, and quasi-isometry.
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…
Multitwists in big mapping class groups
George Domat, Federica Fanoni, Sebastian Hensel
We show that the closure of the compactly supported mapping class group of an infinite-type surface is not generated by the collection of multitwists (i.e. products of powers of tw…
Thurston's Theorem: Entropy in Dimension One
Ryan Dickmann, George Domat, Thomas Hill +4
In his paper, Thurston shows that a positive real number is the topological entropy for an ergodic traintrack representative of an outer automorphism of a free group if and onl…
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…
Free products from spinning and rotating families
Mladen Bestvina, Ryan Dickmann, George Domat +3
The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup (or a collec…
Big pure mapping class groups are never perfect
George Domat, Ryan Dickmann
We show that the closure of the compactly supported mapping class group of an infinite type surface is not perfect and that its abelianization contains a direct summand isomorphic…
First cohomology of pure mapping class groups of big genus one and zero surfaces
George Domat, Paul Plummer
We prove that the first integral cohomology of pure mapping class groups of infinite type genus one surfaces is trivial. For genus zero surfaces we prove that not every homomorphis…