论文标题
理性的本地系统和连接的有限循环空间
Rational local systems and connected finite loop spaces
论文作者
论文摘要
格林勒斯（Greenlees）猜想，紧凑型谎言组的理性稳定均匀同型类别始终具有代数模型。基于这个想法，我们表明连接有限循环空间上的理性本地系统类别始终具有一个简单的代数模型。当循环空间来自一个连接的紧凑型谎言组时，这将恢复Pol和Williamson的特殊情况，内容涉及理性的Cofree $ g $ spectra。更普遍地，我们表明，如果$ k $是紧凑型谎言组$ g $的封闭子组，以便连接weyl group $ w_gk $，那么某些类别的有理$ g $ -spectra'at $ k $'具有代数模型。例如，当$ k $是微不足道的群体时，这只是理性的cofree $ g $ spectra的类别，这将恢复上述结果。在整个过程中，我们要仔细注意扭转和完整类别的作用。
Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson about rational cofree $G$-spectra. More generally, we show that if $K$ is a closed subgroup of a compact Lie group $G$ such that the Weyl group $W_GK$ is connected, then a certain category of rational $G$-spectra `at $K$' has an algebraic model. For example, when $K$ is the trivial group, this is just the category of rational cofree $G$-spectra, and this recovers the aforementioned result. Throughout, we pay careful attention to the role of torsion and complete categories.
