5 papers · 1 filter
Profinite rigidity in lattices of
Xiaoyu Xu
A finitely generated group is profinitely rigid among a class of finitely generated groups if it can be distinguished among this class by its set of finite quotient groups. This pa…
Profinite rigidity of simple closed curves in surface groups
Zhongzi Wang, Xiaoyu Xu
This paper establishes a new characterization of simple closed curves on a closed orientable surface. Let be the fundamental group of a closed orientable surface. We prove that…
Profinite rigidity for two-bridge links and 3-tangle Montesinos links
Tamunonye Cheetham-West, Xiaoyu Xu
For any two-bridge link or 3-tangle Montesinos link (including knot), this paper proves that is profinitely rigid among the fundamental groups of compac…
Profinite rigidity witnessed by Dehn fillings of cusped hyperbolic 3-manifolds
Xiaoyu Xu
Any profinite isomorphism between two cusped finite-volume hyperbolic 3-manifolds carries profinite isomorphisms between their Dehn fillings. With this observation, we prove that s…
Profinite almost rigidity in 3-manifolds
Xiaoyu Xu
We prove that any compact, orientable 3-manifold with empty or toral boundary is profinitely almost rigid among all compact, orientable 3-manifolds. In other words, the profinite c…