Recognition of being fibered for compact 3–manifolds

Jaikin-Zapirain, Andrei¹

¹ Departamento de Matemáticas, University Autónoma de Madrid and Instituto de Ciencias Matemáticas, Madrid, Spain

Geometry & topology, Tome 24 (2020) no. 1, pp. 409-420.

Résumé

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.

Détail

DOI : 10.2140/gt.2020.24.409

Classification : 57M27, 20E18, 20J05, 57M05
Keywords: fibered $3$–manifold, profinite rigidity, cohomological goodness

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