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

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 $π_{1} (M)$ .

Keywords

3–manifold, Kleinian group, word problem, recognition problem, geometric structure

Mathematical Subject Classification 2000

Primary: 57M50

Secondary: 20F10

References

Forward citations

Publication

Received: 20 February 2001

Revised: 26 October 2001

Accepted: 12 January 2002

Published: 16 January 2002

Proposed: David Gabai

Seconded: Jean-Pierre Otal, Robion Kirby

Authors

Jason Fox Manning
Department of Mathematics University of California at Santa Barbara Santa Barbara California 93106 USA

Volume 6, issue 1 (2002)

Jason Fox Manning