论文标题
一种描述性的方法
A descriptive approach to higher derived limits
论文作者
论文摘要
我们提出了对较高派生限制的研究的一个新方面。更确切地说，我们为定向限制的元素引入了一个复杂性度量，该元素将$ \ m athbb {n} $从$ \ mathbb {n} $到$ \ mathbb {n} $介绍，并证明了这种复杂性的cocycles是大致相同的复杂性的Cochains的图像。在这项工作的过程中，我们隔离了定向集合的分区原理，并表明每当此原理成立时，相应的限制限制$ \ mathrm {lim}^n $都是加法的；该极限的消失结果是典型的推论。该分区假设的表述综合并阐明了该领域的最新进展。
We present a new aspect of the study of higher derived limits. More precisely, we introduce a complexity measure for the elements of higher derived limits over the directed set $Ω$ of functions from $\mathbb{N}$ to $\mathbb{N}$ and prove that cocycles of this complexity are images of cochains of the roughly the same complexity. In the course of this work, we isolate a partition principle for powers of directed sets and show that whenever this principle holds, the corresponding derived limit $\mathrm{lim}^n$ is additive; vanishing results for this limit are the typical corollary. The formulation of this partition hypothesis synthesizes and clarifies several recent advances in this area.
