论文标题
半领产品动作的模棱两可的共同体
The equivariant cohomology for semidirect product actions
论文作者
论文摘要
紧凑型谎言组的作用的理性鲍尔硼e骨同学通过限制对最大圆环的作用来确定。我们表明，当有一个封闭的亚组$ k $时，任何紧凑的谎言组$ g $都具有类似的减少，因此分类空间$ bk $的共同体比$ bg $的field系数免费。当$ g $是半导体产品时，我们研究了特定情况，而$ k $是其在特征两个领域中具有系数的最大基本Abelian 2-Subgroup，用于同居。这提供了一种不同的方法来研究具有圆环动作和兼容的空间的模棱两可的共同体的共同顺序，我们将此描述与2多道的作用的结果联系起来。
The rational Borel equivariant cohomology for actions of a compact connected Lie group is determined by restriction of the action to a maximal torus. We show that a similar reduction holds for any compact Lie group $G$ when there is a closed subgroup $K$ such that the cohomology of the classifying space $BK$ is free over the cohomology of $BG$ for field coefficients. We study the particular case when $G$ is a semi-direct product and $K$ is its maximal elementary abelian 2-subgroup for cohomology with coefficients in a field of characteristic two. This provides a different approach to investigate the syzygy order of the equivariant cohomology of a space with a torus action and a compatible involution, and we relate this description with results for 2-torus actions.
