A classification of the face numbers of Buchsbaum simplicial posets
Combinatorics
2013-10-08 v2
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.
Keywords
Cite
@article{arxiv.1307.1548,
title = {A classification of the face numbers of Buchsbaum simplicial posets},
author = {Jonathan Browder and Steven Klee},
journal= {arXiv preprint arXiv:1307.1548},
year = {2013}
}
Comments
16 pages. Updated; added section 5 (on manifolds)