Buchsbaum* Complexes

A class of finite simplicial complexes, which we call Buchsbaum* over a field, is introduced. Buchsbaum* complexes generalize triangulations of orientable homology manifolds as well as doubly Cohen-Macaulay complexes. By definition, the Buchsbaum* property depends only on the geometric realization and the field. Characterizations in terms of simplicial homology are given. It is proved that Buchsbaum* complexes are doubly Buchsbaum. Various constructions, among them one which generalizes convex ear decompositions, are shown to yield Buchsbaum* simplicial complexes. Graph theoretic and enumerative properties of Buchsbaum* complexes are investigated.