Matthew C. b. Zaremsky

activity

20092026

most citedThe braided Thompson's groups are of type

F_{\infty}

24 citations · 118 across the 48 of their papers we have counts for

collaborators

57 papers

math.GR2026

Word length, Morse theory, and Vietoris-Rips complexes

Seth Hulbert, Matthew C. B. Zaremsky

We present a discrete Morse theoretic approach to proving high connectivity or contractibility of a Vietoris-Rips complex using distance to a fixed point as an initial measurement.…

math.GR2026

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…

math.GR2026

Action graphs, semiconjugacy, and non-embedding in Thompson's group $V$

James Hyde, Rachel Skipper, Matthew C. B. Zaremsky

We prove a variety of results about subgroups of Thompson's group $V$ . First we prove that every action graph of a finitely generated subgroup of $V$ acting on an orbit in Cantor s…

math.GR2026

Abstract twisted Brin--Thompson groups

Francesco Fournier-Facio, Xiaolei Wu, Matthew C. B. Zaremsky

Given a group $G$ acting faithfully on a set $S$ , one gets a simple group denoted $S V_{G}$ , called a twisted Brin--Thompson group. In this paper we drop the faithfulness assumption,…

math.GR2025

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 $n$ -element subsets for all $n$ . We prove that for a large class of groups (including all groups of…

math.GR2025

Dense and empty BNSR-invariants of the McCool groups

Mikhail Ershov, Matthew C. B. Zaremsky

An automorphism of the free group $F_{n}$ is called pure symmetric if it sends each generator to a conjugate of itself. The group $PSA_{n}$ of all pure symmetric automorphisms…

math.GR2025

Boone-Higman embeddings of $Aut (F_{n})$ and mapping class groups of punctured surfaces

James Belk, Francesco Fournier-Facio, James Hyde +1

We prove that the groups $Aut (F_{n})$ satisfy the Boone-Higman conjecture for all $n$ , meaning each $Aut (F_{n})$ embeds in a finitely presented simple group. In fact,…

math.AT2024

Configuration spaces of circles in the plane

Justin Curry, Ryan C. Gelnett, Matthew C. B. Zaremsky

We consider the space of all configurations of finitely many (potentially nested) circles in the plane. We prove that this space is aspherical, and compute the fundamental group of…

math.GR2024

Contractible Vietoris-Rips complexes of $Z^{n}$

Matthew C. B. Zaremsky

We give a new, short proof of a result of Virk, that the Vietoris-Rips complex of the group $Z^{n}$ with the standard word metric is contractible at large enough scales. Thi…

math.GR2024

Hyperbolic actions of Thompson's group $F$ and generalizations

Sahana Balasubramanya, Francesco Fournier-Facio, Matthew C. B. Zaremsky

We study the poset of hyperbolic structures on Thompson's group $F$ and its generalizations $F_{n}$ for $n \geq 2$ . The global structure of this poset is as simple as one would expec…

math.GR2024

Finite presentability of twisted Brin-Thompson groups

Matthew C. B. Zaremsky

Given a group $G$ acting faithfully on a set $S$ , we characterize precisely when the twisted Brin-Thompson group $S V_{G}$ is finitely presented. The answer is that $S V_{G}$ is finitely…

math.GR2024

Embedding finitely presented self-similar groups into finitely presented simple groups

Matthew C. B. Zaremsky

We prove that every finitely presented self-similar group embeds in a finitely presented simple group. This establishes that every group embedding in a finitely presented self-simi…

math.GR2023

Hyperbolic groups satisfy the Boone-Higman conjecture

James Belk, Collin Bleak, Francesco Matucci +1

The 1973 Boone-Higman conjecture predicts that every finitely generated group with solvable word problem embeds in a finitely presented simple group. In this paper, we show that hy…

math.GR2023

Progress around the Boone-Higman Conjecture

James Belk, Collin Bleak, Francesco Matucci +1

A conjecture of Boone and Higman from the 1970's asserts that a finitely generated group $G$ has solvable word problem if and only if $G$ can be embedded into a finitely presented…

math.GR2023

Finitely presented simple groups with at least exponential Dehn function

Matthew C. B. Zaremsky

We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our…

math.GR2022★ 1 cited

Finitely presented left orderable monsters

Francesco Fournier-Facio, Yash Lodha, Matthew C. B. Zaremsky

A left orderable monster is a finitely generated left orderable group all of whose fixpoint-free actions on the line are proximal: the action is semiconjugate to a minimal action s…

math.GR2022★ 5 cited

Braided Thompson groups with and without quasimorphisms

Francesco Fournier-Facio, Yash Lodha, Matthew C. B. Zaremsky

We study quasimorphisms and bounded cohomology of a variety of braided versions of Thompson groups. Our first main result is that the Brin--Dehornoy braided Thompson group $bV$ has…

math.GR2022

Non-inner amenability of the Higman-Thompson groups

Eli Bashwinger, Matthew C. B. Zaremsky

We prove that the Higman-Thompson groups $T_{n}$ and $V_{n}$ are non-inner amenable for all $n \geq 2$ . This extends Haagerup and Olesen's result that Thompson's groups $T = T_{2}$ and $V=V_…

math.GR2022

Houghton-like groups from "shift-similar" groups

Brendan Mallery, Matthew C. B. Zaremsky

We introduce and study \emph{shift-similar} groups $G \leq Sym (N)$ , which play an analogous role in the world of Houghton groups that self-similar groups play in the…

math.GR2022

A taste of twisted Brin-Thompson groups

Matthew C. B. Zaremsky

This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple g…

math.GR2021★ 3 cited

Braiding groups of automorphisms and almost-automorphisms of trees

Rachel Skipper, Matthew C. B. Zaremsky

We introduce "braided" versions of self-similar groups and Röver--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the f…

math.GR2021

Random subcomplexes of finite buildings, and fibering of commutator subgroups of right-angled Coxeter groups

Eduard Schesler, Matthew C. B. Zaremsky

The main theme of this paper is higher virtual algebraic fibering properties of right-angled Coxeter groups (RACGs), with a special focus on those whose defining flag complex is a…

math.OA2021★ 1 cited

Von Neumann algebras of Thompson-like groups from cloning systems

Eli Bashwinger, Matthew C. B. Zaremsky

We prove a variety of results about the group von Neumann algebras associated to Thompson-like groups arising from so called $d$ -ary cloning systems. Cloning systems are a framewor…

math.GR2020

The BNSR-invariants of the Stein group $F_{2, 3}$

Robert Spahn, Matthew C. B. Zaremsky

The Stein group $F_{2, 3}$ is the group of orientation-preserving homeomorphisms of the unit interval with slopes of the form $2^{p} 3^{q}$ ( $p, q \in Z$ ) and breakpoints in $\math…

Word length, Morse theory, and Vietoris-Rips complexes

Finiteness properties and Higman's rope trick

Action graphs, semiconjugacy, and non-embedding in Thompson's group V

Abstract twisted Brin--Thompson groups

Finiteness properties of stabilisers of oligomorphic actions

Dense and empty BNSR-invariants of the McCool groups

Boone-Higman embeddings of Aut(Fn​) and mapping class groups of punctured surfaces

Configuration spaces of circles in the plane

Contractible Vietoris-Rips complexes of Zn

Hyperbolic actions of Thompson's group F and generalizations

Finite presentability of twisted Brin-Thompson groups

Embedding finitely presented self-similar groups into finitely presented simple groups

Hyperbolic groups satisfy the Boone-Higman conjecture

Progress around the Boone-Higman Conjecture

Finitely presented simple groups with at least exponential Dehn function

Finitely presented left orderable monsters

Braided Thompson groups with and without quasimorphisms

Non-inner amenability of the Higman-Thompson groups

Houghton-like groups from "shift-similar" groups

A taste of twisted Brin-Thompson groups

Braiding groups of automorphisms and almost-automorphisms of trees

Random subcomplexes of finite buildings, and fibering of commutator subgroups of right-angled Coxeter groups

Von Neumann algebras of Thompson-like groups from cloning systems

The BNSR-invariants of the Stein group F2,3​

Action graphs, semiconjugacy, and non-embedding in Thompson's group $V$

Boone-Higman embeddings of $Aut (F_{n})$ and mapping class groups of punctured surfaces

Contractible Vietoris-Rips complexes of $Z^{n}$

Hyperbolic actions of Thompson's group $F$ and generalizations

The BNSR-invariants of the Stein group $F_{2, 3}$