FREE RESOLUTIONS OF SIMPLICIAL POSETS

A simplicial poset, a poset with a minimal element and whose every int erval is a Boolean algebra, is a generalization of a simplicial comple x. Stanley defined a ring A, associated with a simplicial poset P that generalizes the face-ring of a simplicial complex. If V is the set of vertices of P, then A(p) is a k[V]-module; we find the Betti polynomi als of a free resolution of A(p), and the local cohomology modules of A(p), generalizing Hochster's corresponding results for simplicial com plexes. The proofs involve splitting certain chain or cochain complexe s more finely than in the simplicial complex case. Corollaries are tha t the depth of A(p) is a topological invariant, and that the depth may be computed in terms of the Cohen-Macaulayness of skeleta of P, gener alizing results of Munkres and Hibi. (C) 1997 Academic Press.