论文标题
多面体产品的共同体及其应用于环结构的cartan公式
A Cartan formula for the cohomology of polyhedral products and its application to the ring structure
论文作者
论文摘要
我们提供了一种几何方法，用于确定在适当的Freeness条件下或在野外采用系数的情况下，确定多面体产品的共同体组和产物结构。这是通过首先考虑一类CW对来完成的，我们为此得出类似于cartan公式的多面体产品的分解。然后将结果推广到任意CW对的有限类型。这导致了Hilbert-Poincaré系列和其他应用的直接计算。 通过cartan分解标记的添加剂发电机计算了多面体产品的共同体的产物结构。描述足以启用明确的计算。
We give a geometric method for determining the cohomology groups and the product structure of a polyhedral product, under suitable freeness conditions or with coefficients taken in a field. This is done by considering first a special class of CW pairs for which we derive a decomposition of the polyhedral product resembling a Cartan formula. The result is then generalized to arbitrary CW pairs of finite type. This leads to a direct computation of the Hilbert-Poincaré series and to other applications. The product structure on the cohomology of the polyhedral product is computed in terms of the additive generators, labelled via the Cartan decomposition. The description given suffices to enable explicit calculations.
