Hyperbolic Structures on 3-Manifolds I: Deformation of Acylindrical Manifolds

This is an eprint approximation to [Thu86], which is the definitive form of this paper. This eprint is provided for convenience only; the theorem numbering of this version is different, and not all corrections are present, so any reference or quotation should refer to the published form. Parts II and III ( [Thua] and [Thub]) of this series, although accepted for publication, for many years have only existed in preprint form; they will also be made available as eprints. This is the first in a series of papers dealing with the conjecture that all compact 3-manifolds admit canonical decompositions into geometric pieces. This conjecture will be discussed in detail in part IV. Here is an easily stated special case, in which no decomposition is necessary: Conjecture 0.1 (Indecomposable Implies Geometric). Let M 3 be a closed, prime, atoroidal 3-manifold.