The homeomorphism problem for closed 3-manifolds

TL;DR

This paper presents new geometric and algebraic methods to determine whether two 3-manifolds are homeomorphic, improving decision algorithms for hyperbolic and non-hyperbolic cases.

Contribution

It introduces a geometric approach for hyperbolic 3-manifolds and an algebraic approach for non-hyperbolic geometric 3-manifolds in the homeomorphism problem.

Findings

Enhanced algorithms for hyperbolic 3-manifold homeomorphism detection

Algebraic techniques for non-hyperbolic geometric 3-manifolds

Improved decision procedures for 3-manifold classification

Abstract

We give a more geometric approach to an algorithm for deciding whether two hyperbolic 3-manifolds are homeomorphic. We also give a more algebraic approach to the homeomorphism problem for geometric, but non-hyperbolic, 3-manifolds.