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

Abstract

By the work of Thurston, it is known that if a hyperbolic fibered [Formula: see text]-manifold [Formula: see text] has Betti number greater than 1, then [Formula: see text] admits infinitely many distinct fibrations. For any fibration [Formula: see text] on a hyperbolic [Formula: see text]-manifold [Formula: see text], the number of fibrations on [Formula: see text] that are commensurable in the sense of Calegari–Sun–Wang to [Formula: see text] is known to be finite. In this paper, we prove that the number can be arbitrarily large.