Thick hyperbolic 3-manifolds with bounded rank

Abstract

We construct a geometric decomposition for the convex core of a thick hyperbolic 3-manifold M with bounded rank. Corollaries include upper bounds in terms of rank and injectivity radius on the Heegaard genus of M and on the radius of any embedded ball in the convex core of M.

This is v2, which is 225 pp, as opposed to 170 in the original version. Major changes: 1) a reworking of the theory of simplicial ruled surfaces, 2) extra discussion of the geometry of the convex core boundary in variable negative curvature, and 3) a reworking of Section 10.3, which in the first version relied on an incorrect topological lemma

References in corpus (4)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Tameness of hyperbolic 3-manifolds
• Existence of ruled wrappings in hyperbolic 3-manifolds
• Automorphisms of the compression body graph