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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

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

Jason Fox Manning

Geometry & Topology 6 (2002) 1–26

DOI: 10.2140/gt.2002.6.1

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

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