Volume 6, issue 1 (2002)

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

Jason Fox Manning

Geometry & Topology 6 (2002) 1–26
 arXiv: math.GT/0102154
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 ${\pi }_{1}\left(M\right)$.

Keywords
3–manifold, Kleinian group, word problem, recognition problem, geometric structure
Primary: 57M50
Secondary: 20F10
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