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Uniformly Cohen–Macaulay simplicial complexes and almost Gorenstein* simplicial complexes.
- Source :
-
Journal of Algebra . Jun2016, Vol. 455, p14-31. 18p. - Publication Year :
- 2016
-
Abstract
- In this paper, we study simplicial complexes whose Stanley–Reisner rings are almost Gorenstein and have a -invariant zero. We call such a simplicial complex an almost Gorenstein* simplicial complex. To study the almost Gorenstein* property, we introduce a new class of simplicial complexes which we call uniformly Cohen–Macaulay simplicial complexes. A d -dimensional simplicial complex Δ is said to be uniformly Cohen–Macaulay if it is Cohen–Macaulay and, for any facet F of Δ, the simplicial complex Δ ∖ { F } is Cohen–Macaulay of dimension d . We investigate fundamental algebraic, combinatorial and topological properties of these simplicial complexes, and show that almost Gorenstein* simplicial complexes must be uniformly Cohen–Macaulay. By using this fact, we show that every almost Gorenstein* simplicial complex can be decomposed into those of having one dimensional top homology. Also, we give a combinatorial criterion of the almost Gorenstein* property for simplicial complexes of dimension ≤2. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 455
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 114092049
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2016.02.005