Rigorous Computer-Aided Proofs in the Theory of 3-Manifolds
by
G. Robert Meyerhoff
Boston College
Coauthors: Chris Cao, David Gabai, Nathaniel Thurston

Two recent theorems about 3-manifolds have used computers in their proofs. The two theorems are: 1.) Homotopy hyperbolic 3-manifolds are hyperbolic. [Gabai-Meyerhoff-NThurston] 2.) The figure-eight knot complement and its sibling are the unique orientable cusped hyperbolic 3-manifolds of minimum volume. [Cao-Meyerhoff] In this talk we will discuss the use of computers in the proofs of these theorems. The first theorem involves a fundamental use of the computer, while the second involves a minimal use. As such, we will emphasize the first theorem.

Date received: February 13, 1998