#### Geometry & Topology, Vol. 6 (2002)
Paper no. 1, pages 1--26.

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

### Jason Manning

**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(M).
**Keywords**.
3-manifold, Kleinian group, word problem, recognition problem, geometric structure

**AMS subject classification**.
Primary: 57M50.
Secondary: 20F10.

**DOI:** 10.2140/gt.2002.6.1

**E-print:** `arXiv:math.GT/0102154`

Submitted to GT on 20 February 2001.
(Revised 26 October 2001.)
Paper accepted 12 January 2002.
Paper published 16 January 2002.

Notes on file formats
Jason Manning

Department of Mathematics, University of California at Santa Barbara

Santa Barbara, CA 93106, USA

Email: manning@math.ucsb.edu

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