30 citations · 60 across the 16 of their papers we have counts for
18 papers
Generating simple vigorous groups
Collin Bleak, Casey Donoven, Scott Harper +1
The simple vigorous groups form a broad class of groups of homeomorphisms of Cantor space that includes Thompson's group , its various generalisations and many others such as Ne…
Finitely presented simple left-orderable groups in the landscape of Richard Thompson's groups
James Hyde, Yash Lodha
We construct the first examples of finitely presented simple groups of orientation-preserving homeomorphisms of the real line. Our examples are also of type , have infi…
Stabilizers in Higman-Thompson groups
James Belk, James Hyde, Francesco Matucci
We investigate stabilizers of finite sets of rational points in Cantor space for the Higman-Thompson groups . We prove that the pointwise stabilizer is an iterated ascendi…
Subgroups of which do not embed into Thompson's group
James Hyde, Justin Tatch Moore
We will give a general criterion - the existence of an -obstruction - for showing that a subgroup of does not embed into Thompson's group . An immediate con…
Two new families of finitely generated simple groups of homeomorphisms of the real line
James Hyde, Yash Lodha, Cristóbal Rivas
The goal of this article is to exhibit two new families of finitely generated simple groups of homeomorphisms of . These families are strikingly different from existing…
Sufficient conditions for a group of homeomorphisms of the Cantor set to be two-generated
Collin Bleak, Luke Elliott, James Hyde
Let be some Cantor space. We study groups of homeomorphisms of which are vigorous, or, which are flawless, where we introduce both of these terms here…
Embedding into a Finitely Presented Group
James Belk, James Hyde, Francesco Matucci
We observe that the group of all lifts of elements of Thompson's group to the real line is finitely presented and contains the additive group of the rational numbe…
Uniformly perfect finitely generated simple left orderable groups
James Hyde, Yash Lodha, Andrés Navas +1
We show that the finitely generated simple left orderable groups constructed by the first two authors in arXiv:1807.06478 are uniformly perfect - each element in the group ca…
The Group of Boundary Fixing Homeomorphisms of the Disc is Not Left-Orderable
James Hyde
A left-order on a group is a total order on such that for any , and in we have . We construct a finitely generated subgrou…
Finitely generated infinite simple groups of homeomorphisms of the real line
James Hyde, Yash Lodha
We construct examples of finitely generated infinite simple groups of homeomorphisms of the real line. Equivalently, these are examples of finitely generated simple left (or right)…
Sets of universal sequences for the symmetric group and analogous semigroups
James Hyde, Julius Jonušas, James D. Mitchell +1
A universal sequence for a group or semigroup is a sequence of words such that for any sequence , the equations , $n\in \ma…
On the asynchronous rational group
James Belk, Francesco Matucci, James Hyde
We prove that the asynchronous rational group defined by Grigorchuk, Nekrashevych, and Sushchanskii is simple and not finitely generated. Our proofs also apply to certain subgroups…
Enumeration of idempotents in planar diagram monoids
Igor Dolinka, James East, Athanasios Evangelou +5
We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms…
Enumeration of idempotents in diagram semigroups and algebras
Igor Dolinka, James East, Athanasios Evangelou +4
We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving…
Sierpiński rank of the Symmetric inverse semigroup
James T. Hyde, Yann Péresse
We show that every countable set of partial bijections from an infinite set to itself can be obtained as a composition of just two such partial bijections. This strengthens a resul…
Dimension and measure for generic continuous images
Richárd Balka, Ábel Farkas, Jonathan M. Fraser +1
We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, , into . The key question is `what is the gener…
A note on the 1-prevalence of continuous images with full Hausdorff dimension
Jonathan M. Fraser, James T. Hyde
We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and…
The Hausdorff dimension of graphs of prevalent continuous functions
Jonathan M. Fraser, James T. Hyde
We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on…