On commensurability of fibrations on a hyperbolic 3-manifold (Q395030)

This paper is about fibered commensurability of fibered hyperbolic 3-manifolds, a notion introduced by \textit{D. Calegari} et al. [Pac. J. Math. 250, No. 2, 287--317 (2011; Zbl 1236.57022)].NEWLINENEWLINERecall that a fibered face is a face of the unit ball for the Thurston norm whose rational points correspond to fibrations of the 3-manifold \(M\) and a fibered cone is a cone over a fibered face. Two fibrations of \(M\) are symmetric if there exists a self-homeomorphism of \(M\) that maps one to the other.NEWLINENEWLINEOne of the main results is Theorem 1.3: there exist hyperbolic 3-manifolds that admit two fibrations which are commensurable, belong to the same fibered cone, but are not symmetric.NEWLINENEWLINETheorem 1.4 ensures that if \(M\) has no hidden symmetries, then this phenomenon cannot happen.