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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 π1(M).

Keywords
3–manifold, Kleinian group, word problem, recognition problem, geometric structure
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 20F10
References
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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