English

Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle

Geometric Topology 2024-09-25 v3 Group Theory

Abstract

We show that hyperbolic four-punctured S2S^2-bundles over S1S^1 are distinguished by the finite quotients of their fundamental groups among all 3-manifold groups. To do this, we upgrade a result of Liu to show that the topological type of a fiber is detected by the profinite completion of the fundamental group of a fibered hyperbolic 3-manifold.

Keywords

Cite

@article{arxiv.2308.00266,
  title  = {Profinite rigidity and hyperbolic four-punctured sphere bundles over the circle},
  author = {Tamunonye Cheetham-West},
  journal= {arXiv preprint arXiv:2308.00266},
  year   = {2024}
}

Comments

11 pages, 5 figures. Significant corrections to Version 2 caused by an error in the attempted proof of Theorems 1.1 - 1.3 (Version 2). The critical mistake (in Lemma 5.1 (Version 2)) was not distinguishing between pseudoAnosov elements of mapping class groups and conjugacy classes of pseudoAnosovs

R2 v1 2026-06-28T11:45:09.839Z