论文标题
重新审视同源性操作
Homology operations revisited
论文作者
论文摘要
E-infinity空间的Mod P同源性是传统上用染色器操作来接近代数拓扑的古典主题。在本文中，我们通过对替代性同源操作系列的详细研究提供了相当于但与染色器 - 拉什（Lashof）操作不同的同源性操作系列，从而提供了有关该主题的新观点。除其他事项外，我们将将这些操作与染色器操作（描述它们产生的代数）联系起来，并用它们来描述自由e-Infinity空间的同源性。我们还将研究由e-infinity环空间上的添加剂和乘法E-赋值结构产生的操作之间的关系。在这种情况下，这些操作具有特别好的特性，可以简单而概念化的“混合ADEM关系”，描述了从两个不同的E-赋值结构产生的操作如何相互作用。
The mod p homology of E-infinity spaces is a classical topic in algebraic topology traditionally approached in terms of Dyer--Lashof operations. In this paper, we offer a new perspective on the subject by providing a detailed investigation of an alternative family of homology operations equivalent to, but distinct from, the Dyer--Lashof operations. Among other things, we will relate these operations to the Dyer--Lashof operations, describe the algebra generated by them, and use them to describe the homology of free E-infinity spaces. We will also investigate the relationship between the operations arising from the additive and multiplicative E-infinity structures on an E-infinity ring space. The operations have especially good properties in this context, allowing for a simple and conceptual formulation of "mixed Adem relations" describing how the operations arising from the two different E-infinity structures interact.
