映射空间的有理高阶Whitehead积及其定义系统
Rational higher order Whitehead products of mapping spaces and defining systems
AI总结：
本文针对映射空间的有理高阶Whitehead积，以Sullivan代表为基础引入导子复形中的定义系统，证明其对应导子括号的上同调类，实例体现定义系统选取的影响。
AI中文摘要：
本文对映射空间中的有理高阶Whitehead积给出代数刻画。给定基映射的Sullivan代表，我们在对应的导子复形中引入定义系统。主要结果表明，在映射空间的有理同伦群与导子复形上同调的标准对应下，有理高阶Whitehead积恰好由相关导子括号表示的上同调类给出。实例展示了定义系统的选取如何产生非平凡元素与不确定性。
英文摘要：
This paper gives an algebraic description of rational higher order Whitehead products in mapping spaces. Given a Sullivan representative of the base map, we introduce defining systems in the corresponding derivation complex. The main result shows that, under the standard identification between rational homotopy groups of mapping spaces and the cohomology of the derivation complex, rational higher order Whitehead products are given exactly by the cohomology classes represented by the associated derivation brackets. The examples show how choices of defining systems produce non-trivial elements and indeterminacy.
