论文标题
结缔组织理论中的操作
Operations in connective K-theory
论文作者
论文摘要
在本文中，我们将连接K理论中的加性操作与各种无扭转系数分类。我们发现整体案例的答案需要了解$ \ hat {\ mathbb {z}} $一个。此外，尽管积分添加剂操作是由Adams操作拓扑生成的，但这些操作并未将其简化为后者的无限线性组合。我们描述了稳定操作的拓扑基础，并将其与分级K理论中稳定操作的基础联系起来。我们对这两个理论进行了乘法操作进行分类，并表明具有$ \ hat {\ mathbb {z}} $的同质添加稳定操作 - 系数是由稳定的乘法操作拓扑生成的。对于整体操作而言，情况并非如此。
In this article we classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the $\hat{\mathbb{Z}}$ one. Moreover, although integral additive operations are topologically generated by Adams operations, these are not reduced to infinite linear combinations of the latter ones. We describe a topological basis for stable operations and relate it to a basis of stable operations in graded K-theory. We classify multiplicative operations in both theories and show that homogeneous additive stable operations with $\hat{\mathbb{Z}}$-coefficients are topologically generated by stable multiplicative operations. This is not true for integral operations.
