21 citations · 63 across the 21 of their papers we have counts for
24 papers · 1 filter
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…
Kuperberg Dreams
Steven Hurder, Ana Rechtman
The ``Seifert Conjecture'' stated, ``Every non-singular vector field on the 3-sphere has a periodic orbit''. In a celebrated work, Krystyna Kuperberg gave a constru…
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…
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…