Buchsbaum* complexes
Combinatorics
2011-08-09 v3 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.0909.1931,
title = {Buchsbaum* complexes},
author = {Christos A. Athanasiadis and Volkmar Welker},
journal= {arXiv preprint arXiv:0909.1931},
year = {2011}
}
Comments
Proposition 2.8 corrected, Sections 3-6 permuted and Sections partly reorganized