Buchsbaum* complexes |
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Authors: | Christos A. Athanasiadis Volkmar Welker |
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Affiliation: | 1. Department of Mathematics, Division of Algebra-Geometry, University of Athens, Panepistimioupolis, Athens, 15784, Greece 2. Fachbereich Mathematik und Informatik, Philipps-Universit?t Marburg, 35032, Marburg, Germany
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Abstract: | 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. |
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