6 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…
Finiteness properties of stabilisers of oligomorphic actions
Francesco Fournier-Facio, Peter H. Kropholler, Robert Alonzo Lyman +1
An action of a group on a set is oligomorphic if it has finitely many orbits of -element subsets for all . We prove that for a large class of groups (including all groups of…
On a lemma of Milnor and Schwarz, après Rosendal
Robert Alonzo Lyman
Perhaps the fundamental theorem of geometric group theory, the Milnor--Schwarz lemma gives conditions under which the orbit map relating the geometry of a geodesic metric space and…
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…
Conformal dimension bounds for certain Coxeter group Bowditch boundaries
Elizabeth Field, Radhika Gupta, Robert Alonzo Lyman +1
We give upper and lower bounds on the conformal dimension of the Bowditch boundary of a Coxeter group with defining graph a complete graph and edge labels at least three. The lower…
A hyperbolic free-by-cyclic group determined by its finite quotients
Naomi Andrew, Paige Hillen, Robert Alonzo Lyman +1
We show that the group is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-c…