Profinite almost rigidity in 3-manifolds
Year: 2025
Type: article
Abstract: 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 completion of its fundamental group determines its homeomorphism type to finitely many possibilities. Moreover, the profinite completion of the fundamental group of a mixed 3-manifold together with the peripheral structure uniquely determines the homeomorphism type of its Seifert part, i.e. the maximal graph manifold components in the JSJ-decomposition. On the other hand, without assigning the peripheral structure, the profinite completion of a mixed 3-manifold group may not uniquely determine the fundamental group of its Seifert part. The proof is based on JSJ-decomposition.
Source: Advances in Mathematics
Author: Xiaoyu Xu
Institution: Peking University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,790
OpenAlex ID: W4413910733