Nickel(II) hydrosalicylamide complexes

RIGID DUALIZING COMPLEXES

Let $X$ be a sufficiently nice scheme. We survey some recent progress on dualizing complexes. It turns out that a complex in $kinj X$ is dualizing if and only if tensor product with it induces an equivalence of categories from Murfet's new category $kmpr X$ to the category $kinj X$. In these terms, it becomes interesting to wonder how to glue such equivalences.

Chessboard Complexes and Matching Complexes

Complexes of $C$-projective modules

Inspired by a recent work of Buchweitz and Flenner, we show that, for a semidualizing bimodule $C$, $C$--perfect complexes have the ability to detect when a ring is strongly regular.It is shown that there exists a class of modules which admit minimal resolutions of $C$--projective modules.

Simple Homotopy Types of Hom-complexes, Neighborhood Complexes, Lovász Complexes, and Atom Crosscut Complexes

In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...

Complexes of directed trees and independence complexes

The theory of complexes of directed trees was initiated by Kozlov to answer a question by Stanley, and later on, results from the theory were used by Babson and Kozlov in their proof of the Lovász conjecture. We develop the theory and prove that complexes on directed acyclic graphs are shellable. A related concept is that of independence complexes: construct a simplicial complex on the vertex s...