Geodesic
An algorithm for the~recognition of 3-spheres (according to~Thompson)
Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 695-710

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The question of the existence of an algorithm for determining whether given 3-manifolds are homeomorphic is a key question of low-dimensional topology. An algorithm due to A. Thompson for the recognition of the standard 3-sphere is presented. The use of handle decomposition instead of triangulation greatly simplifies both the formulation and the proof of the algorithm. 
@article{SM_1995_186_5_a3,
     author = {S. V. Matveev},
     title = {An algorithm for the~recognition of 3-spheres (according {to~Thompson)}},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_5_a3/}
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S. V. Matveev. An algorithm for the~recognition of 3-spheres (according to~Thompson). Sbornik. Mathematics, Tome 186 (1995) no. 5, pp. 695-710. http://geodesic.mathdoc.fr/item/SM_1995_186_5_a3/