Hyperbolization of infinite-type 3-manifolds

Abstract

We study the class ${\mathcal{M}}^B$ of 3-manifolds $M$ that have a compact exhaustion $M={\cup }_{i\in \mathbb{N}}{M}_i$ satisfying: each $M_i$ is hyperbolizable with incompressible boundary and each component of $\partial M_i$ has genus at most $g=g(M)$. For manifolds in ${\mathcal{M}}^B$ we give necessary and sufficient topological conditions that guarantee the existence of a complete hyperbolic metric.

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
• Centralizers in 3-manifold groups