The combinatorics of the bar resolution in group cohomology
The combinatorics of the bar resolution in group cohomology
复制标题
群上同调中条形消解的组合数学
DOI：
10.1016/j.jpaa.2003.12.006
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发表时间：
2004
影响因子：
0.8
通讯作者：
P. Webb
中科院分区：
文献类型：
--
作者：
V. Reiner;P. Webb
我们研究了任意单纯复数的序链上的组合定义的双复结构。它的列与单元复数Kn有关，Kn的面偏序集同构于单词上的子词排序，没有来自大小为n的字母表的重复.作为应用，我们给出了Désarménien和WachsArménien[11]所考虑的乱排数和相关对称函数的表示理论解释.在群的条形分辨的情况下，我们分析了由双复产生的两个谱序列。这个谱序列收敛于群的上同调，并提供了一种根据子群的上同调来计算群上同调的方法。它的行为受到群的有限子集的单纯复形的定向链的复形的影响，我们考察了这种复形的Ext类。
We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex Knwhose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by Désarménien and Wachs [11]. We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.