Profinite rigidity properties of central extensions of 2-orbifold groups

Abstract

We extend Wilkes' results on the profinite rigidity of SFSs to the setting of central extensions of 2-orbifold groups with higher-rank centre. We prove that both rigid and non-rigid phenomena arise in this setting and that the non-rigid phenomena are transient in the sense that if ${\hat{G}}_1\cong {\hat{G}}_2$, then $G_1\times \mathbb{Z}\cong G_2\times \mathbb{Z}$.

45 pages. Removed the unnecessary assumption of at least 2 cone points. Comments welcome!

References in corpus (2)

• Distinguishing geometries using finite quotients
• Cohomology of Fuchsian Groups and Non-Euclidean Crystallographic Groups