Algorithmic detection and description of hyperbolic structures on closed 3–manifolds with solvable word problem

Abstract

We outline a rigorous algorithm, first suggested by Casson, for determining whether a closed orientable $3$-manifold $M$ is hyperbolic, and to compute the hyperbolic structure, if one exists. The algorithm requires that a procedure has been given to solve the word problem in ${\pi }_1\left(M\right)$.