Recognizing the 3-sphere

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A modification of the Rubinstein-Thompson criterion for a 3-manifold to be the 3-sphere is proposed. Special cell decompositions, called Q-triangulations and irreducible Q-triangulations, for closed compact orientable 3-manifolds are introduced. It is shown that if a closed compact orientable 3-manifold M3 is given by a triangulation (or by a Q-triangulation) then one can effectively decompose M3 into a connected sum of finitely many 3-manifolds some of which are given by irreducible Q-triangulations and others are 2-sphere bundles over a circle. Furthermore, it is shown that the problem whether a 3-manifold given by an irreducible Q-triangulation is homeomorphic to the 3-sphere is in NP, and the problem whether a Q-triangulation of a 3-manifold is irreducible is in coNP.

Original languageEnglish (US)
Pages (from-to)1073-1117
Number of pages45
JournalIllinois Journal of Mathematics
Issue number4
StatePublished - 2001

ASJC Scopus subject areas

  • General Mathematics


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