Recognition of being fibered for compact 3–manifolds

Let $M$ be a compact orientable aspherical $3$ –manifold. We show that if the profinite completion of $π_{1} (M)$ is isomorphic to the profinite completion of a free-by-cyclic group or to the profinite completion of a surface-by-cyclic group, then $M$ fibers over the circle with compact fiber.

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Keywords

fibered $3$–manifold, profinite rigidity, cohomological goodness

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 20E18, 20J05, 57M05

References

Publication

Received: 27 September 2018

Revised: 11 March 2019

Accepted: 13 July 2019

Published: 25 March 2020

Proposed: Ian Agol

Seconded: Martin Bridson, Cameron Gordon

Authors

Andrei Jaikin-Zapirain
Departamento de Matemáticas University Autónoma de Madrid and Instituto de Ciencias Matemáticas Madrid Spain
http://matematicas.uam.es/~andrei.jaikin

Volume 24, issue 1 (2020)

Andrei Jaikin-Zapirain

Abstract