A combinatorial classification of buchsbaum simplicial posets

Abstract

The family of Buchsbaum simplicial posets over a field K provides an algebraic abstraction of the family of (K-homology) manifold triangulations. In 2008, Novik and Swartz established lower bounds on the face numbers of a Buchsbaum simplicial poset as a function of its dimension and its topological Betti numbers over K. They conjectured that these lower bounds are sufficient to classify face numbers of Buchsbaum simplicial posets with prescribed Betti numbers. We prove this conjecture by using methods from the theory of (pseudo)manifold crystallizations to construct simplicial posets with prescribed face numbers and Betti numbers.