Volume 24, issue 1 (2020)

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Recognition of being fibered for compact $3$–manifolds

Andrei Jaikin-Zapirain

Geometry & Topology 24 (2020) 409–420
Abstract

Let $M$ be a compact orientable aspherical $3$–manifold. We show that if the profinite completion of ${\pi }_{1}\left(M\right)$ 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.

Keywords
fibered $3$–manifold, profinite rigidity, cohomological goodness
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 20E18, 20J05, 57M05
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