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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The homeomorphism problem for closed $3$–manifolds

Peter Scott and Hamish Short

Algebraic & Geometric Topology 14 (2014) 2431–2444
Abstract
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We give a geometric approach to an algorithm for deciding whether two hyperbolic 3–manifolds are homeomorphic. We also give an algebraic approach to the homeomorphism problem for geometric, but nonhyperbolic, 3–manifolds.

Keywords
hyperbolic manifolds, decision problems
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 20F65, 57M99
References
Publication
Received: 30 January 2013
Revised: 6 November 2013
Accepted: 14 January 2014
Published: 28 August 2014
Authors
Peter Scott
Mathematics Department
University of Michigan at Ann Arbor
Ann Arbor, MI 48109
USA
Hamish Short
CMI
Universite d’aix-Marseille
UMR 7353, 39 Rue Joliot Curie
13453 Marseille
France