Operations in connective K-theory

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-09-09 DOI:10.2140/ant.2023.17.1595

Alexander Merkurjev, Alexander Vishik

引用次数: 0

Abstract

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 $\hat{ℤ}$ case. 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 $\hat{ℤ}$ -coefficients are topologically generated by stable multiplicative operations. This is not true for integral operations.

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连通K理论中的运算

我们对具有不同无扭系数的连通K理论中的加法运算进行了分类。我们发现，积分情况的答案需要理解ℤ^ 案例此外，尽管积分加法运算在拓扑上是由亚当斯运算生成的，但这些运算并没有被简化为后者的无限线性组合。我们描述了稳定运算的拓扑基，并将其与分级K理论中稳定运算的一个基联系起来。我们在这两个理论中对乘法运算进行了分类，并证明了具有ℤ^-系数是由稳定的乘法运算拓扑生成的。对于积分运算，情况并非如此。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

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