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Buchsbaum* complexes

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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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Authors and Affiliations

  1. Department of Mathematics, Division of Algebra-Geometry, University of Athens, Panepistimioupolis, Athens, 15784, Greece

    Christos A. Athanasiadis

  2. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, 35032, Marburg, Germany

    Volkmar Welker

Authors
  1. Christos A. Athanasiadis
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  2. Volkmar Welker
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Correspondence to Christos A. Athanasiadis.

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Athanasiadis, C.A., Welker, V. Buchsbaum* complexes. Math. Z. 272, 131–149 (2012). https://doi.org/10.1007/s00209-011-0926-3

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  • DOI: https://doi.org/10.1007/s00209-011-0926-3

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