Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary

TL;DR

This paper studies the deformation space of hyperbolic structures on Haken 3-manifolds with incompressible boundary, focusing on complex cases beyond simple interval bundles, extending previous work with clarifications and additional figures.

Contribution

It advances the understanding of hyperbolic structures on complex Haken 3-manifolds with incompressible boundary, especially in non-acylindrical cases, refining earlier results from 1986.

Findings

Analysis of deformation spaces for complex Haken 3-manifolds

Clarifications and figures added to previous results

No connection to later developments like R-tree actions

Abstract

This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical, but are more complicated than interval bundles over surfaces. This is a slight revision of a 1986 preprint, with a few figures added, and slight clarifications of some of the text, but with no attempt to connect this to later developments such as groups acting on R-trees, etc.