A classification of the face numbers of Buchsbaum simplicial posets
arXiv:1307.1548
Abstract
The family of Buchsbaum simplicial posets generalizes the family of simplicial cell manifolds. The -vector of a simplicial complex or simplicial poset encodes the combinatorial and topological data of its face numbers and the reduced Betti numbers of its geometric realization. Novik and Swartz showed that the -vector of a Buchsbaum simplicial poset satisfies certain simple inequalities; in this paper we show that these necessary conditions are in fact sufficient to characterize the -vectors of Buchsbaum simplicial posets with prescribed Betti numbers.
16 pages. Updated; added section 5 (on manifolds)