2009/09/10 by Christos A. Athanasiadis, Athanasiadis, Christos A., Volkmar Welker +1
Computer Science · Mathematics · #05E40 #13F55 #52B05 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.0909.1931
openalex publication_date 2009/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A class of 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 and local cohomology are given. It is proved that Buchsbaum* complexes are doubly Buchsbaum. Enumerative and graph theoretic properties of Buchsbaum* complexes are investigated. It is shown that various constructions, among them one which generalizes convex ear decompositions, yield Buchsbaum* simplicial complexes.