The homeomorphism problem for closed 3–manifolds

Scott, Peter; Short, Hamish

doi:10.2140/agt.2014.14.2431

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The homeomorphism problem for closed $3$–manifolds

Peter Scott and Hamish Short

Algebraic & Geometric Topology 14 (2014) 2431–2444

DOI: 10.2140/agt.2014.14.2431

Abstract

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

Volume 14, issue 4 (2014)