Socles of Buchsbaum modules, complexes and posets
By Isabella Novik, Ed Swartz. 2007
110 citations recorded by the source corpus.
The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative K\"uhnel's conjecture for the maximum value of the Euler characteristic of a $2k$-dimensional simplicial manifold on $n$ vertices as well as Kalai's conjecture providing a lower bound on the number of edges of a simplicial manifold in terms of its dimension, number of vertices, and the first Betti number.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b389f691cbbee5ec6e3c4d7022f66370e6a26255
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Gorenstein rings through face rings of manifolds (2008, background): “he socle of k(∆), its other part, S, remains a mystery. Here we solve this mystery in the special case of a connected orientable k-homology manifold without boundary, thus verifying Conjecture 7.2 of [12]. A connected k-homology manifold ∆ without boundary is called orientable if H˜ d−1(∆) ∼= k. The”