Ranks of mapping tori via the curve complex

Abstract

We show that if the monodromy of a 3-manifold M that fibers over the circle has large translation distance in the curve complex, then the rank of the fundamental group of M is 2g+1, where g is the genus of the fiber.

21 pages, v2 includes referee suggestions

References in corpus (4)

• Tameness of hyperbolic 3-manifolds
• Kleinian groups and the complex of curves
• Existence of ruled wrappings in hyperbolic 3-manifolds
• The structure of a solvmanifold's Heegaard splittings