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 bundles over 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.
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