14 papers
Finiteness properties and Higman's rope trick
Francesco Fournier-Facio, Matthew C. B. Zaremsky
In 1961 Higman proved that every finitely generated recursively presented group embeds into a finitely presented group. In 2018 Leary proved that every finitely generated group emb…
Action graphs, semiconjugacy, and non-embedding in Thompson's group
James Hyde, Rachel Skipper, Matthew C. B. Zaremsky
We prove a variety of results about subgroups of Thompson's group . First we prove that every action graph of a finitely generated subgroup of acting on an orbit in Cantor s…
Hyperbolic actions of Thompson's group and generalizations
Sahana Balasubramanya, Francesco Fournier-Facio, Matthew C. B. Zaremsky
We study the poset of hyperbolic structures on Thompson's group and its generalizations for . The global structure of this poset is as simple as one would expec…
Abstract twisted Brin--Thompson groups
Francesco Fournier-Facio, Xiaolei Wu, Matthew C. B. Zaremsky
Given a group acting faithfully on a set , one gets a simple group denoted , called a twisted Brin--Thompson group. In this paper we drop the faithfulness assumption,…
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…
Dense and empty BNSR-invariants of the McCool groups
Mikhail Ershov, Matthew C. B. Zaremsky
An automorphism of the free group is called pure symmetric if it sends each generator to a conjugate of itself. The group of all pure symmetric automorphisms…