On the number of commensurable fibrations on a hyperbolic 3-manifold

Abstract

By a work of Thurston, it is known that if a hyperbolic fibred $3$-manifold $M$ has Betti number greater than 1, then $M$ admits infinitely many distinct fibrations. For any fibration $\omega$ on a hyperbolic $3$-manifold $M$, the number of fibrations on $M$ that are commensurable in the sense of Calegari-Sun-Wang to $\omega$ is known to be finite. In this paper, we prove that the number can be arbitrarily large.