## Abstract

A 3-pseudomanifold (briefly 3-pm) is a finite connected simplicial 3-complex in which the link of every vertex is a closed 2-manifold. Such a link is singular if it is not a sphere. It is proved that for a preassigned list Σ of closed 2-manifolds (other than spheres), there is a 3-pm in which the list of singular links is precisely Σ, iff the number of the non-orientable members in Σ with odd genus is even. Close relationship is found between 3-pms and 3-manifolds with boundary. This yields a simple proof for the 2-dimensional case of Pontrjagin-Thom's theorem (i.e., necessary and sufficient condition for a 2-manifold to bound a 3-manifold). The concept of a 3-pm is generalized to higher dimensions.

Original language | English |
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Pages (from-to) | 63-73 |

Number of pages | 11 |

Journal | Israel Journal of Mathematics |

Volume | 39 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Mar 1981 |

## ASJC Scopus subject areas

- General Mathematics