## Abstract

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 M^{3} is given by a triangulation (or by a Q-triangulation) then one can effectively decompose M^{3} 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 language | English (US) |
---|---|

Pages (from-to) | 1073-1117 |

Number of pages | 45 |

Journal | Illinois Journal of Mathematics |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - 2001 |

## ASJC Scopus subject areas

- Mathematics(all)