The topological structure of 3-pseudomanifolds

Amos Altshuler, Ulrich Brehm

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)63-73
Number of pages11
JournalIsrael Journal of Mathematics
Volume39
Issue number1-2
DOIs
StatePublished - 1 Mar 1981

ASJC Scopus subject areas

  • Mathematics (all)

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