# Algorithmic homeomorphism of 3-manifolds as a corollary of geometrization

@article{Kuperberg2019AlgorithmicHO, title={Algorithmic homeomorphism of 3-manifolds as a corollary of geometrization}, author={Greg Kuperberg}, journal={Pacific Journal of Mathematics}, year={2019} }

In this paper we prove two results, one semi-historical and the other new. The semi-historical result, which goes back to Thurston and Riley, is that the geometrization theorem implies that there is an algorithm for the homeomorphism problem for closed, oriented, triangulated 3-manifolds. We give a self-contained proof, with several variations at each stage, that uses only the statement of the geometrization theorem, basic hyperbolic geometry, and old results from combinatorial topology and…

## 27 Citations

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