Geometry and Rank of Fibered Hyperbolic 3-Manifolds

Abstract

Assume that M is a closed hyperbolic 3-manifold fibering over the circle with fiber a closed orientable surface of genus g. We show that if M has large diameter and its injectivity radius is bounded below, then the rank of the fundamental group of M is 2g+1.

References in corpus (4)

• Tameness of hyperbolic 3-manifolds
• Convex cocompact subgroups of mapping class groups
• A characterization of short curves of a Teichmueller geodesic
• The rank of the fundamental group of certain hyperbolic 3-manifolds fibering over the circle

Cited by in corpus (1)

• A finiteness theorem for hyperbolic 3-manifolds