Volume 14, issue 4 (2014)

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The homeomorphism problem for closed $3$–manifolds

Peter Scott and Hamish Short

Algebraic & Geometric Topology 14 (2014) 2431–2444
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