论文标题
置换架的同源
The homology of permutation racks
论文作者
论文摘要
尽管架子上的研究活动及其同源性二十多年的研究活动都在当代数学的中心部分有不同的应用记录，但仍然很少有架子的同源性的架子的例子。在本文中，我们计算所有排列架的整个整体同源性。我们的选择方法涉及同位代数，该代数直到最近才在架子的同源性上。对于我们的主要结果，我们建立了一个频谱序列，该频谱序列将问题降低到了等效同源性中的一个问题，并为此表明它总是退化的。本文给出的蓝图证明了进一步开发这些技术的潜力。
Despite a blossoming of research activity on racks and their homology for over two decades, with a record of diverse applications to central parts of contemporary mathematics, there are still very few examples of racks whose homology has been fully calculated. In this paper, we compute the entire integral homology of all permutation racks. Our method of choice involves homotopical algebra, which was brought to bear on the homology of racks only recently. For our main result, we establish a spectral sequence, which reduces the problem to one in equivariant homology, and for which we show that it always degenerates. The blueprint given in this paper demonstrates the high potential for further exploitation of these techniques.
