Profinite rigidity properties of central extensions of 2-orbifold groups

Piwek, Paweł

doi:10.2140/agt.2026.26.565

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Profinite rigidity properties of central extensions of $2$-orbifold groups

Paweł Piwek

Algebraic & Geometric Topology 26 (2026) 565–597

DOI: 10.2140/agt.2026.26.565

Abstract

We extend Wilkes’ results on the profinite rigidity of Seifert fibre spaces to the setting of central extensions of 2-orbifold groups with higher-rank centre. We prove that both rigid and nonrigid phenomena arise in this setting and that the nonrigid phenomena are transient in the sense that if ${\hat{G}}_{1} ≅ {\hat{G}}_{2}$ , then $G_{1} \times ℤ ≅ G_{2} \times ℤ$ .

Keywords

profinite rigidity, group cohomology, $2$-orbifolds

Mathematical Subject Classification

Primary: 20E26

Secondary: 20E18

References

Publication

Received: 27 March 2024

Revised: 24 November 2024

Accepted: 19 March 2025

Published: 11 February 2026

Authors

Paweł Piwek
Mathematical Institute University of Oxford Oxford United Kingdom

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Volume 26, issue 2 (2026)