Profinite rigidity for Seifert fibre spaces

By Gareth Wilkes. 2015

46 citations recorded by the source corpus.

An interesting question is whether two 3-manifolds can be distinguished by computing and comparing their collections of finite covers; more precisely, by the profinite completions of their fundamental groups. In this paper, we solve this question completely for closed orientable Seifert fibre spaces. In particular, all Seifert fibre spaces are distinguished from each other by their profinite completions apart from some previously-known examples due to Hempel. We also characterize when bounded Seifert fibre space groups have isomorphic profinite completions, given some conditions on the boundary.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/186159b10091eb0cf04bdc2fd75b7bbd2521fa6c

Citations in the corpus

• Absolute profinite rigidity and hyperbolic geometry (2018, unknown): “[8], [11], [13], [14], [26], [28], [50] and [51].”