Sheaves over complexes of groups and developability

通过组合层实现 Cohen–Macaulay 复形的对偶

Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves

本文用组合层语言证明 Cohen–Macaulay 单纯复形的对偶定理，推广庞加莱对偶，并为离散群的 Bieri–Eckmann 对偶提供联系。

群的团复形与序层

Clique complexes of groups and order sheaves

介绍有限群的团复形\(X_G\)，其\(1\) - 骨架以\(\Gamma_G\)为商，有限单群由其确定到同构。团复形可赋予序层，通过顶点链同调计算任意单纯复形同调，还计算了某些特殊群的序层系数团复形同调。

Weighted sheaves and homology of Artin groups

In this paper we expand the theory of weighted sheaves over posets, and use it to study the local homology of Artin groups. First, we use such theory to relate the homology of classical braid groups with the homology of certain independence complexes of graphs. Then, in the context of discrete Morse theory on weighted sheaves, we introduce a particular class of acyclic matchings. Explicit formulas for the homology of the corresponding Morse complexes are given, in terms of the ranks of the associated incidence matrices. We use such method to perform explicit computations for the new affine cas…