INTERMEDIARIES IN BREDON (CO)HOMOLOGY AND CLASSIFYING SPACES
INTERMEDIARIES IN BREDON (CO)HOMOLOGY AND CLASSIFYING SPACES
复制标题
布雷登（共）同源性和分类空间中的中介体
DOI：
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发表时间：
2011
期刊：
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通讯作者：
O. Talelli
中科院分区：
文献类型：
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作者：
Fotini Dembegioti;N. Petrosyan;O. Talelli
对于某些可收缩的G- cw -配合物和F族G的子群，我们构造了一个收敛于G的F- bredon上同调的谱序列，其e1项由稳定子群的F- bredon上同调给出。作为应用，我们得到了关于分类空间EFG的上同调维和几何维数的若干推论。对于群F的任何子群闭类，我们也引入了一个层次定义的群类，并证明了如果群G在该类中，则G具有有限的F∩G- bredon （co）同调维当且仅当G具有跳F∩G- bredon （co）同调维。
For certain contractible G-CW-complexes and F a family of subgroups of G, we construct a spectral sequence converging to the F-Bredon cohomology of G with E1-terms given by the F-Bredon cohomology of the stabilizer subgroups. As applications, we obtain several corollaries concerning the cohomological and geometric dimensions of the classifying space EFG. We also introduce, for any subgroup closed class of groups F, a hierarchically de ned class of groups and show that if a group G is in this class, then G has finite F ∩ G-Bredon (co)homological dimension if and only if G has jump F ∩ G-Bredon (co)homology.