  Any manifold with boundary gives rise to a Poincare duality algebra in a
natural way. Given a simplicial poset $S$ whose geometric realization is a
closed orientable homology manifold, and a characteristic function, we
construct a manifold with boundary such that graded components of its Poincare
duality algebra have dimensions $h_k"(S)$. This gives a clear topological
evidence for two well-known facts about simplicial manifolds: the nonnegativity
of $h"$-numbers (Novik--Swartz theorem) and the symmetry $h"_k=h"_{n-k}$
(generalized Dehn--Sommerville relations).
