29 citations · 79 across the 13 of their papers we have counts for
22 papers
CAT(0) cube complexes and inner amenability
Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek
We here consider inner amenability from a geometric and group theoretical perspective. We prove that for every non-elementary action of a group on a finite dimensional irreduci…
A new lattice invariant for lattices in totally disconnected locally compact groups
Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek
We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices…
On the Cantor-Bendixson rank of the Grigorchuk group and the Gupta-Sidki group
Rachel Skipper, Phillip Wesolek
We study the Cantor--Bendixson rank of the space of subgroups for members of a general class of finitely generated self-replicating branch groups. In particular, we show for ei…
Geometric stability theory for -structures
Junguk Lee, Michael Cohen, Phillip Wesolek
We introduce a notion of -structures which are certain locally compact group actions and prove some counterparts of results on Polish structures(introduced by Krupinski in \cite…
Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms
Bruno Duchesne, Nicolas Monod, Phillip Wesolek
Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relat…
On elementary amenable bounded automata groups
Kate Juschenko, Benjamin Steinberg, Phillip Wesolek
There are several natural families of groups acting on rooted trees for which every member is known to be amenable. It is, however, unclear what the elementary amenable members of…
Indicability, residual finiteness, and simple subquotients of groups acting on trees
Pierre-Emmanuel Caprace, Phillip Wesolek
We establish three independent results on groups acting on trees. The first implies that a compactly generated locally compact group which acts continuously on a locally finite tre…
Approximating simple locally compact groups by their dense locally compact subgroups
Pierre-Emmanuel Caprace, Colin D. Reid, Phillip Wesolek
The class, denoted by , of totally disconnected locally compact groups which are non-discrete, compactly generated, and topologically simple contains many compelling e…
On the residual and profinite closures of commensurated subgroups
Pierre-Emmanuel Caprace, Peter H. Kropholler, Colin D. Reid +1
The residual closure of a subgroup of a group is the intersection of all virtually normal subgroups of containing . We show that if is generated by finitely many…
Commensurated subgroups in tree almost automorphism groups
Adrien Le Boudec, Phillip Wesolek
We prove that the tree almost automorphism groups admit exactly three commensurability classes of closed commensurated subgroups. Our proof utilizes an independently interesting ch…
Commensurated subgroups in finitely generated branch groups
Phillip Wesolek
A subgroup is commensurated if for all . We show a finitely generated branch group is just infinite if and only if every commensurated…
On strongly just infinite profinite branch groups
François Le Maître, Phillip Wesolek
For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the conditi…
The essentially chief series of a compactly generated locally compact group
Colin D. Reid, Phillip R. Wesolek
We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated…
Chief factors in Polish groups
Colin D. Reid, Phillip R. Wesolek
In finite group theory, chief factors play an important and well-understood role in the structure theory. We here develop a theory of chief factors for Polish groups. In the develo…
Homomorphisms into totally disconnected, locally compact groups with dense image
Colin D. Reid, Phillip R. Wesolek
Let be a group homomorphism such that is a totally disconnected locally compact (t.d.l.c.) group and the image of is dense. We show that all such homom…
Amenable Invariant Random Subgroups
Uri Bader, Bruno Duchesne, Jean Lecureux
We show that an amenable Invariant Random Subgroup of a locally compact second countable group lives in the amenable radical. This answers a question raised in the introduction of…
Chain conditions, elementary amenable groups, and descriptive set theory
Phillip Wesolek, Jay Williams
We first consider three well-known chain conditions in the space of marked groups: the minimal condition on centralizers, the maximal condition on subgroups, and the maximal condit…
A note on relative amenability
Phillip Wesolek
P-E. Caprace and N. Monod isolate the class of locally compact groups for which relatively amenable closed subgroups are amenable. It is unknown if is c…
Totally disconnected locally compact groups locally of finite rank
Phillip Wesolek
We study totally disconnected locally compact second countable (t.d.l.c.s.c.) groups that contain a compact open subgroup with finite rank. We show such groups that additionally ad…
Elementary totally disconnected locally compact groups
Phillip Wesolek
We identify the class of elementary groups: the smallest class of totally disconnected locally compact second countable (t.d.l.c.s.c.) groups that contains the profinite groups and…
Conjugacy class conditions in locally compact second countable groups
Phillip Wesolek
Many non-locally compact second countable groups admit a comeagre conjugacy class. For example, this is the case for the automorphism group of the rational order and the automorphi…
Radical subgroups of totally disconnected locally compact groups
Phillip Wesolek
We observe a correspondence between collections of closed subgroups and normal subgroups in totally disconnected locally compact groups. This correspondence is applied to prove str…