21 citations · 78 across the 16 of their papers we have counts for
30 papers
Strong Negative Type of Star-shaped Manifolds
Hang Liu, Ziyan Xu
Metric spaces of negative type (NT) and strong negative type (SNT) are fundamental in wide applications across computer science and statistics. It is well-known that spheres equipp…
Profinite geometric iterated monodromy groups of postcritically finite polynomials in degree 3
Mikhail Hlushchanka, Olga Lukina, Dean Wardell
In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute…
Group actions with almost normal stabilizers
María Isabel Cortez, Maik Gröger, Olga Lukina
In this paper, we consider minimal group actions of countable groups on compact Hausdorff spaces by homeomorphisms. We show that the existence of a point with finite stabilizer imp…
Non-Hausdorff germinal groupoids for actions of countable groups
Olga Lukina
We study conditions under which the germinal groupoid associated to a minimal equicontinuous action of a countable group on a Cantor set has non-Hausdorff topology. We develop a ne…
Prime spectrum and dynamics for nilpotent Cantor actions
Steven Hurder, Olga Lukina
A minimal equicontinuous action by homeomorphisms of a discrete group on a Cantor set is locally quasi-analytic, if each homeomorphism has a unique extension from small ope…
Type invariants for non-abelian odometers
Steven Hurder, Olga Lukina
In this work, we introduce the type and typeset invariants for equicontinuous group actions on Cantor sets; that is, for generalized odometers. These invariants are collections of…
Essential holonomy of Cantor actions
Steven Hurder, Olga Lukina
A group action has essential holonomy if the set of points with non-trivial holonomy has positive measure. If such an action is topologically free, then having essential holonomy i…
Settled elements in profinite groups
María Isabel Cortez, Olga Lukina
Given a polynomial of degree d over a number field, the image of the associated arboreal representation of the absolute Galois group of the field is a profinite group acting on the…
The prime spectrum of solenoidal manifolds
Steven Hurder, Olga Lukina
A solenoidal manifold is the inverse limit space of a tower of proper coverings of a compact manifold. In this work, we introduce new invariants for solenoidal manifolds, their asy…
Wild Cantor actions
Jesús Álvarez López, Ramón Barral Lijó, Olga Lukina +1
The discriminant group of a minimal equicontinuous action of a group on a Cantor set is the subgroup of the closure of the action in the group of homeomorphisms of , con…
Cantor dynamics of renormalizable groups
Steven Hurder, Olga Lukina, Wouter Van Limbeek
A group is said to be finitely non-co-Hopfian, or renormalizable, if there exists a self-embedding whose image is a proper subgroup of finite index. Such a pro…
Measures and stabilizers of group Cantor actions
Maik Gröger, Olga Lukina
We consider a minimal equicontinuous action of a finitely generated group on a Cantor set with invariant probability measure , and stabilizers of points for such an acti…
Nilpotent Cantor actions
Steven Hurder, Olga Lukina
A nilpotent Cantor action is a minimal equicontinuous action on a Cantor set , where contains a finitely-generated nilpotent s…
Limit group invariants for non-free Cantor actions
Steven Hurder, Olga Lukina
A Cantor action is a minimal equicontinuous action of a countably generated group G on a Cantor space X. Such actions are also called generalized odometers in the literature. In th…
Pro-groups and generalizations of a theorem of Bing
Alex Clark, Steven Hurder, Olga Lukina
A matchbox manifold is a generalized lamination, which is a continuum whose path components define the leaves of a foliation of the space. A matchbox manifold is M-like if it has t…
Galois groups and Cantor actions
Olga Lukina
In this paper, we study the actions of profinite groups on Cantor sets which arise from representations of Galois groups of certain fields of rational functions. Such representatio…
Orbit equivalence and classification of weak solenoids
Steven Hurder, Olga Lukina
In this work, we study minimal equicontinuous actions which are locally quasi-analytic. The first main result shows that for minimal equicontinuous actions which are locally quasi-…
Arboreal Cantor actions
Olga Lukina
In this paper, we consider minimal equicontinuous actions of discrete countably generated groups on Cantor sets, obtained from the arboreal representations of absolute Galois group…
Manifold--like matchbox manifolds
Alex Clark, Steven Hurder, Olga Lukina
A matchbox manifold is a generalized lamination, and is a continuum whose arc-components define the leaves of a foliation of the space. The main result of this paper implies that a…
Wild solenoids
Steven Hurder, Olga Lukina
A weak solenoid is a foliated space defined as the inverse limit of finite coverings of a closed compact manifold . The monodromy of a weak solenoid defines an equicontinuous mi…
Molino theory for matchbox manifolds
Jessica Dyer, Steven Hurder, Olga Lukina
A matchbox manifold is a foliated space with totally disconnected transversals, and an equicontinuous matchbox manifold is the generalization of Riemannian foliations for smooth ma…
Growth and homogeneity of matchbox manifolds
Jessica Dyer, Steven Hurder, Olga Lukina
A matchbox manifold with one-dimensional leaves which has equicontinuous holonomy dynamics must be a homogeneous space, and so must be homeomorphic to a classical Vietoris solenoid…
The discriminant invariant of Cantor group actions
Jessica Dyer, Steve Hurder, Olga Lukina
In this work, we investigate the dynamical and geometric properties of weak solenoids, as part of the development of a "calculus of group chains" associated to Cantor minimal actio…
Hausdorff dimension in graph matchbox manifolds
Olga Lukina
We study the Hausdorff and the box dimensions of closed invariant subsets of the space of pointed trees, equipped with a pseudogroup action. This pseudogroup dynamical system can b…