DGA模块和截面类别的连接
Joins of DGA modules and sectional category
摘要：
本文从纤维化p和p '的半树模型出发，构造了两个纤维化p：E -> B和p'：E' -> B的纤维连接的显式半树模型.利用这个模型，我们引入了纤维化p的截面范畴的一个下界，它可以从p的任何Sullivan模型计算出来，并且比由p^* 的核的幂零性给出的经典上同调下界更接近p的截面范畴：H^*（B;Q）--> H^*（E;Q）。在评价纤维化X^I --> X x X的特殊情况下，我们得到了Farber拓扑复杂度TC（X）的一个可计算的下界.我们证明了这个下界和经典上同调下界之间的差别可以是任意大的。
英文摘要：
We construct an explicit semifree model for the fiber join of two fibrations p: E --> B and p': E' --> B from semifree models of p and p'. Using this model, we introduce a lower bound of the sectional category of a fibration p which can be calculated from any Sullivan model of p and which is closer to the sectional category of p than the classical cohomological lower bound given by the nilpotency of the kernel of p^*: H^*(B;Q) --> H^*(E;Q). In the special case of the evaluation fibration X^I --> X x X we obtain a computable lower bound of Farber's topological complexity TC(X). We show that the difference between this lower bound and the classical cohomological lower bound can be arbitrarily large.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
